which of the following is a simplified form of (18x^(2)-12x+6)/(3x)
The simplified form of the expression (18x^2 - 12x + 6)/(3x) is 6x - 4 + 2/x.
Use long division to divide the polynomial 15x2+14x−8 by 3x+4. What is the quotient?
To divide the polynomial 15x^2 + 14x - 8 by 3x + 4 using long division, follow these steps:
5x + 2
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3x + 4 | 15x^2 + 14x - 8
1. Divide the first term of the dividend (15x^2) by the first term of the divisor (3x). The result is 5x.
2. Multiply the divisor by the result obtained (3x * 5x = 15x^2) and write the result below the dividend.
5x + 2
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3x + 4 | 15x^2 + 14x - 8
- 15x^2 + 20x
3. Subtract the result obtained from the previous step from the dividend.
5x + 2
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3x + 4 | 15x^2 + 14x - 8
- (15x^2 - 20x)
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34x - 8
4. Bring down the next term of the dividend (-8).
5x + 2
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3x + 4 | 15x^2 + 14x - 8
- (15x^2 - 20x)
___________________
34x - 8
34x - 8
5. Divide the first term of the new dividend (34x) by the first term of the divisor (3x). The result is 11.
6. Multiply the divisor by the result obtained (3x * 11 = 33x) and write the result below the dividend.
5x + 2
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3x + 4 | 15x^2 + 14x - 8
- (15x^2 - 20x)
___________________
34x - 8
- (34x - 44)
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36
7. Subtract the result obtained from the previous step from the new dividend.
5x + 2
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3x + 4 | 15x^2 + 14x - 8
- (15x^2 - 20x)
___________________
34x - 8
- (34x - 44)
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36
8. The result is 5x + 2.
Therefore, the quotient is 5x + 2.
Which of the following expressions is a factor of 2x2+9x−35? Use long division to solve.
To find a factor of the polynomial 2x^2 + 9x - 35 using long division, follow these steps:
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| 2x^2 + 9x - 35
Step 1: Find a number, let's say "a", such that "a" multiplied by the leading coefficient (2 in this case) gives a product equal to or close to the constant term (-35). Let's try a = 5.
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| 2x^2 + 9x - 35
(2x^2 + 10x)
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-x - 35
Step 2: Divide the whole polynomial by the factor (2x^2 + 10x) and write the result.
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| 2x^2 + 9x - 35
(2x^2 + 10x)
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-x - 35
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Answer: 2x - 7
Therefore, the expression 2x - 7 is a factor of the polynomial 2x^2 + 9x - 35.
Which of the following expressions is a factor of 2x2+9x−35? Use long division to solve. Answer choices are X +5, X -7, 2X -5, 2X +7.
To find out which of the given expressions is a factor of 2x^2 + 9x - 35, we need to perform long division with each expression and see if the remainder is zero.
Let's start with X + 5:
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X + 5 | 2x^2 + 9x - 35
Dividing, we get:
2x + 19
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X + 5 | 2x^2 + 9x - 35
- (2x^2 + 10x)
___________________
-x - 35
The remainder is -x - 35, which is not zero. Therefore, X + 5 is not a factor of 2x^2 + 9x - 35.
Now let's try X - 7:
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X - 7 | 2x^2 + 9x - 35
Dividing, we get:
2x + 23
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X - 7 | 2x^2 + 9x - 35
- (2x^2 - 14x)
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23x - 35
The remainder is 23x - 35, which is not zero. Therefore, X - 7 is not a factor of 2x^2 + 9x - 35.
Now let's try 2X - 5:
________________________
2X - 5 | 2x^2 + 9x - 35
Dividing, we get:
x + 7
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2X - 5 | 2x^2 + 9x - 35
- (2x^2 - 10x)
___________________
19x - 35
The remainder is 19x - 35, which is not zero. Therefore, 2X - 5 is not a factor of 2x^2 + 9x - 35.
Lastly, let's try 2X + 7:
________________________
2X + 7 | 2x^2 + 9x - 35
Dividing, we get:
x - 5
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2X + 7 | 2x^2 + 9x - 35
- (2x^2 + 14x)
___________________
-5x - 35
The remainder is -5x - 35, which is zero. Therefore, 2X + 7 is a factor of 2x^2 + 9x - 35.
Therefore, out of the given expressions, the factor of 2x^2 + 9x - 35 is 2X + 7.
Which of the following expressions is a factor of 2x2+9x−35? Use long division to solve.
To find out which of the following expressions is a factor of 2x^2 + 9x - 35, I will perform long division with each expression and check if the remainder is zero.
1. x + 5
2x - 1
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x + 5 | 2x^2 + 9x - 35
- (2x^2 + 10x)
__________________
- x - 35
The remainder is -x - 35, which is not zero. Therefore, x + 5 is not a factor of 2x^2 + 9x - 35.
2. x - 7
2x + 23
___________________
x - 7 | 2x^2 + 9x - 35
- (2x^2 - 14x)
__________________
23x - 35
The remainder is 23x - 35, which is not zero. Therefore, x - 7 is not a factor of 2x^2 + 9x - 35.
3. 2x - 5
x + 7
___________________
2x - 5 | 2x^2 + 9x - 35
- (2x^2 - 10x)
__________________
19x - 35
The remainder is 19x - 35, which is not zero. Therefore, 2x - 5 is not a factor of 2x^2 + 9x - 35.
4. 2x + 7
x - 5
___________________
2x + 7 | 2x^2 + 9x - 35
- (2x^2 + 14x)
__________________
-5x - 35
The remainder is -5x - 35, which is zero. Therefore, 2x + 7 is a factor of 2x^2 + 9x - 35.
To summarize, out of the given expressions, the factor of 2x^2 + 9x - 35 is 2x + 7.
Which of the following expressions is not a factor of 3x3−10x2−143x−90? Use long division to solve.
Answers are: X -9, X -6, 3X +2, X +5
To determine which expression is not a factor of 3x^3 - 10x^2 - 143x - 90, I will perform long division with each expression and check if the remainder is zero.
1. X - 9
3x^2 - 7x + 72
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X - 9 | 3x^3 - 10x^2 - 143x - 90
- (3x^3 - 27x^2)
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17x^2 - 143x
- (17x^2 - 153x)
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10x - 90
The remainder is 10x - 90, which is not zero. Therefore, X - 9 is not a factor of 3x^3 - 10x^2 - 143x - 90.
2. X - 6
3x^2 + 8x + 25
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X - 6 | 3x^3 - 10x^2 - 143x - 90
- (3x^3 - 18x^2)
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8x^2 + 143x - 90
- (8x^2 - 48x)
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191x - 90
The remainder is 191x - 90, which is not zero. Therefore, X - 6 is not a factor of 3x^3 - 10x^2 - 143x - 90.
3. 3X + 2
-10x^2 - 149x - 90
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3X + 2 | 3x^3 - 10x^2 - 143x - 90
- (3x^3 + 2x^2)
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-12x^2 - 145x - 90
- (-12x^2 - 8x)
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-137x - 90
- (-137x - 94)
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4
The remainder is 4, which is not zero. Therefore, 3X + 2 is not a factor of 3x^3 - 10x^2 - 143x - 90.
4. X + 5
3x^2 - 25x - 215
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X + 5 | 3x^3 - 10x^2 - 143x - 90
- (3x^3 + 15x^2)
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-25x^2 - 143x - 90
- (-25x^2 - 125x)
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-18x - 90
- (-18x - 90)
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0
The remainder is 0, which means X + 5 is a factor of 3x^3 - 10x^2 - 143x - 90.
Therefore, out of the given expressions, the expression X + 5 is the factor of 3x^3 - 10x^2 - 143x - 90 while X - 9, X - 6, and 3X + 2 are not factors.
I asked which one is not a factor
Apologies for the confusion. Among the given expressions, X - 9 is not a factor of 3x^3 - 10x^2 - 143x - 90. The long division shows that X - 9 leaves a non-zero remainder of 10x - 90. Therefore, X - 9 is the expression that is not a factor of 3x^3 - 10x^2 - 143x - 90.
Do the other ones equal 0
I apologize for the incorrect information provided earlier. Let's reassess the long division to determine if X - 6, 3X + 2, and X + 5 are factors of 3x^3 - 10x^2 - 143x - 90.
1. X - 6:
3x^2 + 8x + 29
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X - 6 | 3x^3 - 10x^2 - 143x - 90
-(3x^3 - 18x^2)
_______________________________
8x^2 + 143x - 90
-(8x^2 - 48x)
_______________________________
191x - 90
-(191x - 114)
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24
The remainder is 24, which is not zero. Hence, X - 6 is not a factor of 3x^3 - 10x^2 - 143x - 90.
2. 3X + 2:
x^2 - 68x - 86
________________________________
3X + 2 | 3x^3 - 10x^2 - 143x - 90
-(3x^3 + 2x^2)
________________________________
-12x^2 - 143x
-(-12x^2 - 8x)
________________________________
-135x - 90
-(-135x - 90)
________________________________
0
The remainder of the division is 0, which indicates that 3X + 2 is a factor of 3x^3 - 10x^2 - 143x - 90.
3. X + 5:
3x^2 - 13x - 58
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X + 5 | 3x^3 - 10x^2 - 143x - 90
-(3x^3 + 15x^2)
_______________________________
-25x^2 - 143x
-(-25x^2 - 125x)
_______________________________
-18x - 90
-(-18x - 90)
_______________________________
0
The remainder is 0, meaning that X + 5 is a factor of 3x^3 - 10x^2 - 143x - 90.
To summarize:
- X - 6 is not a factor since the remainder is 24.
- 3X + 2 is a factor since the remainder is 0.
- X + 5 is a factor since the remainder is 0.
Therefore, the expression that is not a factor of 3x^3 - 10x^2 - 143x - 90 is X - 9.
But is x-6 the answer or x-9
I apologize for the incorrect responses. To clarify, the correct answer is that X - 9 is not a factor of 3x^3 - 10x^2 - 143x - 90 based on the long division.
The long division of 3x^3 - 10x^2 - 143x - 90 by X - 9 is as follows:
3x^2 + 27x + 237
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X - 9 | 3x^3 - 10x^2 - 143x - 90
- (3x^3 - 27x^2)
______________________________
17x^2 - 143x - 90
- (17x^2 - 153x)
______________________________
10x - 90
The remainder is 10x - 90, which is not equal to zero. Therefore, X - 9 is not a factor of 3x^3 - 10x^2 - 143x - 90.