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.
11d² -4d -18d² -99d
36 2d³
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

Multiply \(d\) with each term in \(2d^{2}+11d - 4\) and \(- 9\) with each term in \(2d^{2}+11d - 4\).

• For \(d\times2d^{2}\): \(d\times2d^{2}=2d^{3}\)
• For \(d\times11d\): \(d\times11d = 11d^{2}\)
• For \(d\times(-4)\): \(d\times(-4)=-4d\)
• For \(-9\times2d^{2}\): \(-9\times2d^{2}=-18d^{2}\)
• For \(-9\times11d\): \(-9\times11d=-99d\)
• For \(-9\times(-4)\): \(-9\times(-4) = 36\)

Step2: Combine like terms

Now, combine the terms:
\(2d^{3}+11d^{2}-4d-18d^{2}-99d + 36\)
Combine the \(d^{2}\) terms: \(11d^{2}-18d^{2}=-7d^{2}\)
Combine the \(d\) terms: \(-4d-99d=-103d\)

So the polynomial becomes \(2d^{3}-7d^{2}-103d + 36\)

Answer:

\(2d^{3}-7d^{2}-103d + 36\) (corresponding to the first option among the given choices)