Alg2 Dividing Polynomials 24-25

Answer explanation

To simplify \( \frac{24mn^{-9}}{12mn^{-11}} \), divide the coefficients (24/12 = 2) and subtract the exponents of n (\(-9 - (-11) = 2\)). The result is \( 2n^2 \), which matches the correct answer.

Tags

CCSS.MATH.CONTENT.HSA.APR.D.6

Simplify

• 5p² - 16p

• 5p + 4

• 5p - 4

• 5p + 4p

Answer explanation

To simplify, combine like terms: 5p + 4 is the result of adding 5p and 4. The other options do not correctly simplify the expression. Thus, the correct answer is 5p + 4.

Tags

CCSS.MATH.CONTENT.HSA.APR.D.6

Simplify

• 4y⁶

• 4y²²

• 30y⁶

• 30y²²

Answer explanation

To simplify, factor out the common terms. The expression simplifies to 4y^6, which is the correct choice. The other options either have incorrect coefficients or exponents.

Tags

CCSS.MATH.CONTENT.HSA.APR.D.6

Divide the polynomial by the monomial.

• 15x⁹ - 8x³

• 3x⁶ - 8x³

• -5x¹²

• 3x⁶ - 40x³

Answer explanation

To divide the polynomial by the monomial, divide each term separately. For example, dividing -40x^9 by 8x^3 gives 3x^6, and -8x^3 by 8x^3 gives -1. Thus, the result is 3x^6 - 8x^3, which is the correct choice.

Tags

CCSS.MATH.CONTENT.HSA.APR.D.6

Answer explanation

To simplify \( \frac{-9f^{-1}g^8h^{-3}}{6g^2h^9} \), first rewrite as \( \frac{-9g^8}{6g^2h^{12}f} \). Then, simplify coefficients and exponents: \( \frac{-3g^{8-2}}{2fh^{12}} = \frac{-3g^6}{2fh^{12}} \). Thus, the correct answer is \( \frac{-3g^6}{2fh^{12}} \).

Tags

CCSS.MATH.CONTENT.HSA.APR.D.6

Mathematical Equivalence

ON

Tags

CCSS.MATH.CONTENT.HSA.APR.D.6

Identify the polynomial expressions in the division process.

a

b

c

d

Divisor

Quotient

Dividend

Remainder

Answer explanation

Tags

CCSS.MATH.CONTENT.HSA.APR.D.6

If you were dividing x⁶ + 4x³ + 2, how many 0's would you need when setting up the top row of your synthetic division?

• 0

• 2

• 4

• 6

Answer explanation

To perform synthetic division on x^6 + 4x^3 + 2, we need to account for the missing degrees (x^5, x^4, x^2, x^1). Thus, we need 4 zeros in the top row to represent these missing terms, making the correct answer 4.

Tags

CCSS.MATH.CONTENT.HSA.APR.D.6

What should be the order of the polynomial coefficients if
(3x - 4x³ + 6x⁴ + 1) / (x + 3)

• 3   0   -4   6   1

• 6   -4   3   1   0

• 6   -4   0   3   1

• -6   4   0   -3   -1

Answer explanation

To find the order of coefficients after dividing, we identify the leading term of the numerator (6x^4) and the constant term (1). The correct order of coefficients is 6, -4, 0, 3, 1, matching the choice: 6, -4, 0, 3, 1.

Tags

CCSS.MATH.CONTENT.HSA.APR.D.6

For synthetic division, what would be the number in the left hand box?

• 0

• 1

• 2

• 3

Answer explanation

In synthetic division, the left-hand box represents the coefficient of the highest degree term of the polynomial being divided. If the polynomial is of degree 2, the correct number is 2.

Tags

CCSS.MATH.CONTENT.HSA.APR.D.6