Solve. (-10x^3+30x-20) / (-5x+5)
A) 2x^2-2x+4
B) -2x^2-2x-4
C) -2x^2+2x+4
D) 2x^2+2x-4***
Simplfy x/6x-x^2
A) 1/6-x; where x=0,6 *****
B) 1/6-x ; where x= 6
C) 1/6x ; where x = 0
D) 1/6
Simplfy x-2/x^2+4x-12
A) 1/x+6; where x=-6
B) 1/x+6; where x= -6,2***
C) 1/x+2; where x=-2
D) x+2
Simplfy x^2+3x-4/x+4
A) 1/x-4; where x=4
B) x-4
C) x-1; where x=1
D) x-1; where x= -4***
Multiply x-5/4x+8*(12x^2+32x+16)
A)(3x+2)/4(x-5)
B)(x-5)(3x+2)/4
C)(x-5)(3x+2)*****
D)(x-5)(12x+8)
I have my answers, but it would be nice if someone can break it down step by step.
http://calc101.com/webMathematica/long-divide.jsp#topdoit
many can be done faster by factoring though
eg
Solve. (-10x^3+30x-20) / (-5x+5)
A) 2x^2-2x+4
B) -2x^2-2x-4
C) -2x^2+2x+4
D) 2x^2+2x-4***
===========================================
(2x^3-6x+4)/(x-1)
(2x^2+2x-4) (x-1)/(x-1)
so I agree
By the way, where you type "where" do you not mean "not where"? In other words NOT where the denominator = 0 ?
3 and 4 won't come up on the link
To check answers, it would be necessary to post the questions correctly, i.e. use the correct symbols, e.g. type not= or ≠ (done by & ne; but skip the space between & and ;)
Also, use parentheses appropriately, as in the first question.
x/6x-x^2 means (x/6x) - (x²)
while
x/(6x-x^2) means (x)/(6x-x²) which is probably what you mean.
Sure! I would be happy to break it down step by step for you.
1) Simplify (-10x^3+30x-20) / (-5x+5):
To simplify this expression, we can first factor out a (-5) from both terms in the numerator:
(-5)(2x^3-6x+4) / (-5x+5)
Now we have a common factor of (-5) in the numerator and the denominator, so we can cancel it out and simplify further:
2x^3-6x+4 / (x-1)
Now we can factor the numerator using the grouping method:
2x^2(x-1)-2(x-1) / (x-1)
Now we have a common factor of (x-1) in the numerator, so we can cancel it out and simplify even further:
2x^2-2
So the answer is D) 2x^2+2x-4
2) Simplify x/6x-x^2:
To simplify this expression, we can first rewrite it as x/(6x - x^2). Now we can factor out an x from both terms in the numerator:
x / (x(6 - x))
Next, we can cancel out the common factor of x in the numerator and the denominator:
1 / (6 - x)
So the answer is A) 1/(6-x) where x=0,6
3) Simplify x-2/x^2+4x-12:
To simplify this expression, we can first factor the denominator:
x-2 / (x+6)(x-2)
Now we have a common factor of (x-2) in the numerator and the denominator, so we can cancel it out:
1 / (x+6)
So the answer is D) x+6
4) Multiply (x-5)/(4x+8) * (12x^2+32x+16):
To multiply these two terms, we can first factor out a common factor of 4 from the denominator:
(x-5) / 4(x+2) * (12x^2+32x+16)
Now, let's factor out a common factor of 4 from the numerator as well:
(x-5)(3x+2) / 4(x+2)
So the answer is C) (x-5)(3x+2)
To solve the first problem:
1. Start by factoring the numerator:
(-10x^3 + 30x - 20) can be written as -10(x^3 - 3x + 2)
2. Factor the denominator:
(-5x + 5) can be written as -5(x - 1)
3. Simplify the fraction by canceling out common factors:
(-10(x^3 - 3x + 2)) / (-5(x - 1))
= 2(x^3 - 3x + 2) / (x - 1)
Now, let's expand the numerator before proceeding further.
4. Expand the numerator:
2(x^3 - 3x + 2) = 2x^3 - 6x + 4
5. Now, rewrite the simplified fraction:
(2x^3 - 6x + 4) / (x - 1)
Comparing this with the answer choices, it matches with option D) 2x^2 + 2x - 4.
Moving on to the second problem:
1. Simplify the expression x/6x - x^2:
Dividing x by 6x gives 1/6, so the expression becomes:
1/6 - x^2
Comparing this with the answer choices, it matches with option A) 1/6-x; where x=0,6.
Now, let's simplify the third problem:
1. Simplify the expression x - 2 / x^2 + 4x - 12
Factor the denominator: x^2 + 4x - 12 can be factored as (x + 6)(x - 2)
Now the expression becomes: (x - 2) / (x + 6)(x - 2)
Cancel out the common factor of (x - 2):
= 1 / (x + 6)
Comparing this with the answer choices, it matches with option B) 1/x+6; where x= -6,2.
Finally, let's simplify the fourth problem:
1. Simplify the expression x^2 + 3x - 4 / x + 4
Factor the numerator: x^2 + 3x - 4 can be factored as (x + 4)(x - 1)
Now the expression becomes: (x + 4)(x - 1) / (x + 4)
Cancel out the common factor of (x + 4):
= x - 1
Comparing this with the answer choices, it matches with option D) x-1; where x= -4.
For the multiplication problem, we have:
Multiply (x - 5) / (4x + 8) * (12x^2 + 32x + 16)
To simplify this, we can begin by factoring the second term:
12x^2 + 32x + 16 = 4(3x^2 + 8x + 4)
Then, we can rewrite the expression:
(x - 5) / (4x + 8) * 4(3x^2 + 8x + 4)
Cancel out the common factor of 4:
(x - 5) / (4x + 8) * (3x^2 + 8x + 4)
Now, we can multiply the numerators together and the denominators together:
(x - 5)(3x^2 + 8x + 4) / (4x + 8)
Comparing this with the answer choices, it matches with option C) (x - 5)(3x + 2).