Question

kh math 2a 25/26
multiplying polynomials and simplifying expressions
drag each tile to the table to multiply each row heading by
each column heading.
36 -99d 2d³ -4d
-18d² 11d²
2d² 11d -4
d
-9
what is the product of d - 9 and 2d² + 11d - 4?
2d³ - 7d² - 103d + 36
2d³ + 7d² - 95d + 36
2d³ + 7d² - 103d + 36 ×
2d³ - 7d² - 95d + 36

Explanation:

Step1: Apply distributive property (FOIL for polynomials)

Multiply \( d \) by each term in \( 2d^2 + 11d - 4 \):
\( d \times 2d^2 = 2d^3 \), \( d \times 11d = 11d^2 \), \( d \times (-4) = -4d \).

Step2: Multiply \( -9 \) by each term in \( 2d^2 + 11d - 4 \)

\( -9 \times 2d^2 = -18d^2 \), \( -9 \times 11d = -99d \), \( -9 \times (-4) = 36 \).

Step3: Combine like terms

Add the results from Step1 and Step2:
\( 2d^3 + 11d^2 - 4d - 18d^2 - 99d + 36 \).
Combine \( 11d^2 - 18d^2 = -7d^2 \) and \( -4d - 99d = -103d \).

Step4: Simplify the polynomial

\( 2d^3 - 7d^2 - 103d + 36 \).

Answer:

\( 2d^3 - 7d^2 - 103d + 36 \) (corresponding to the first option: \( 2d^3 - 7d^2 - 103d + 36 \))