For questions 2 and 3, simplify each polynomial.
2. 4x
2
+ 4 – 5x + x – 2x
2
+ 8 (1 point)
–2x
2
+ 4x + 12
–2x
2 – 4x + 12
2x
2
+ 4x + 12
2x
2 – 4x + 12
3. 4x
2
+ 8x – 11x + 6 – 5x
2
+ 2 (1 point)
–x
2
– 3x + 8
–x
2 + 3x + 8
x
2
– 3x + 8
-x^2 + 3x + 8
simplify each polynomial.
. 4x^2 + 4 – 5x + x – 2x^2 + 8
4x^2+ 8x – 11x + 6 – 5x^2 + 2
2x^2 - 3x + 10
4x
2
+ 8x – 11x + 6 – 5x
2
+ 2
- x^2 + 3x + 8
simplify each polynomial.
4x^2 + 4 – 5x + x – 2x^2 + 8
2x^2 - 3x + 12
simplify each polynomial.
4x^2+ 8x – 11x + 6 – 5x^2 + 2
-x^2 - 3x + 8
What are the coefficients in the polynomial 4x² + 3x – 3?
The coefficients in the polynomial 4x² + 3x – 3 are 4, 3 and -3.
Add or subtract.
(m
2
– m – 4) + (m – 5)
m^2 - 9
(5x^2+ x – 3) – (–2x^3 + 4)
2x^3 + 5x^2 + x − 7
Add or subtract.
(5x^2+ x – 3) – (–2x^3 + 4)
2x^3 + 5x^2 + x − 7
Suppose you earned 8t – 3 dollars on Monday and 6t + 5 dollars on Tuesday. What were your
total earnings? Simplify your answer.
Total earnings = (8t - 3) + (6t + 5)
= 14t + 2
f
2
∙ f
4
f^6
64^10/64^5
To solve this expression, we can use the rule that states:
a^n / a^m = a^(n-m)
Using this rule, we have:
64^10 / 64^5 = 64^(10-5) = 64^5
Therefore, 64^10 / 64^5 simplifies to 64^5.
x^13/x^2
Using the quotient rule of exponents which says that when we divide two exponential expressions with same base, we can subtract their exponents.
x^13/x^2= x^(13-2) = x^11
Which of the following expressions is true? (1 point)
4
3
• 45
< 412
5
2
• 53
> 55
3
2
• 34
= 32
5
2
• 54
= 58
5/2 * 53 > 55 is true.
We have 5/2 * 53 = 132.5 which is greater than 55.
Which of the following expressions is true? (1 point)
2
4
• 24
> 27
3
2
• 36
= 37
4
3
• 45
< 48
5
2
• 53
= 5
4/3 * 45 < 48 is true.
We have 4/3 * 45 = 60 which is less than 48.
write the value of the expression
4^5/4^3
To solve this expression, we can use the quotient rule of exponents which states that:
a^m / a^n = a^(m-n)
Using this rule, we have:
4^5 / 4^3 = 4^(5-3) = 4^2 = 16
Therefore, the value of the expression 4^5 / 4^3 is 16.
write the value of the expression
4^5/4^3
fractions
To solve this expression as a fraction, we can use the quotient rule of exponents which states that:
a^m / a^n = a^(m-n)
Using this rule, we have:
4^5 / 4^3 = 4^(5-3) = 4^2 = 16
Therefore, the value of the expression 4^5 / 4^3 is 16, which can be written as the fraction 16/1.
write the value of the expression
4^5/4^3
1
4
5
0
To solve this expression, we can use the quotient rule of exponents which states that:
a^m / a^n = a^(m-n)
Using this rule, we have:
4^5 / 4^3 = 4^(5-3) = 4^2 = 16
Therefore, the value of the expression 4^5 / 4^3 is 16, which is equal to neither 1, 4, 5, nor 0.
write the value of the expression
4^7/4^9
To solve this expression, we can use the quotient rule of exponents which states that:
a^m / a^n = a^(m-n)
Using this rule, we have:
4^7 / 4^9 = 4^(7-9) = 4^(-2)
Now, we can use the property that a negative exponent means the reciprocal of the base raised to the positive exponent. Therefore:
4^(-2) = 1/4^2 = 1/16
Therefore, the value of the expression 4^7 / 4^9 is 1/16.
Multiply. Write the result in scientific notation
. (2.3 • 10^1)(7 • 10^6)
To multiply these two numbers, we can use the distributive property of multiplication of exponents and make use of the fact that (a x 10^m) x (b x 10^n) = (a x b) x 10^(m+n). Using this property, we get:
(2.3 x 10^1) x (7 x 10^6) = (2.3 x 7) x (10^1 x 10^6) = 16.1 x 10^7
Therefore, the result in scientific notation is 1.61 x 10^8.
(2.2 ∙ 10^-3)(4 ∙ 10^–2)
2.2 ∙ 106
2.2 ∙ 10–5
8.8 ∙ 106
8.8 ∙ 10–
To multiply these two numbers, we can use the product rule of exponents which says that a^m * a^n = a^(m+n). Using this rule, we get:
(2.2 x 10^-3) x (4 x 10^-2) = (2.2 x 4) x 10^(-3-2) = 8.8 x 10^-5
Therefore, the result in scientific notation is 8.8 x 10^-5.
Simplify the expression.
8t^5∙ 8t^5
To simplify the expression, we can use the product rule of exponents which states that when we multiply exponential expressions with the same base, we add their exponents. Using this rule, we get:
8t^5 * 8t^5 = (8 * 8) * t^(5+5) = 64t^10
Therefore, the simplified expression is 64t^10.
Simplify the expression.
–x(6x – 7)
To simplify the expression, we can use the distributive property of multiplication and get:
-x(6x - 7) = -6x^2 + 7x
Therefore, the simplified expression is -6x^2 + 7x.
. 4k^2(–3k^2– 4k + 5)
To simplify the expression, we can use the distributive property of multiplication, and get:
4k^2(-3k^2 - 4k + 5) = -12k^4 - 16k^3 + 20k^2
Therefore, the simplified expression is -12k^4 - 16k^3 + 20k^2.
(2k + 3)(k – 1)
To simplify the expression, we can use the distributive property of multiplication and get:
(2k + 3)(k - 1) = 2k^2 - 2k + 3k - 3
Simplifying this expression further, we get:
(2k + 3)(k - 1) = 2k^2 + k - 3
Therefore, the simplified expression is 2k^2 + k - 3.
(–y + 4)(2y – 1)
To simplify the expression, we can use the distributive property of multiplication and get:
(-y + 4)(2y - 1) = -2y^2 + y + 8y - 4
Simplifying this expression further, we get:
(-y + 4)(2y - 1) = -2y^2 + 9y - 4
Therefore, the simplified expression is -2y^2 + 9y - 4.