Question

multiplying a binomial by a trinomial using a table

what is the product of \\(d - 9\\) and \\(2d^2 + 11d - 4\\)?

\\(2d^3 - 7d^2 - 103d + 36\\)
\\(2d^3 - 7d^2 - 95d + 36\\)
\\(2d^3 + 7d^2 - 95d + 36\\)
\\(2d^3 + 7d^2 - 103d + 36\\)

Explanation:

Set up the multiplication terms

$$ (d - 9)(2d^2 + 11d - 4) $$

Distribute each term of the binomial

$$ d(2d^2 + 11d - 4) - 9(2d^2 + 11d - 4) = (2d^3 + 11d^2 - 4d) - (18d^2 + 99d - 36) $$

Combine like terms

$$ 2d^3 + (11 - 18)d^2 + (-4 - 99)d + 36 = 2d^3 - 7d^2 - 103d + 36 $$

Answer:

• (A) \(2d^3 - 7d^2 - 103d + 36\) (Correct answer)
• (B) \(2d^3 - 7d^2 - 95d + 36\)
• (C) \(2d^3 + 7d^2 - 95d + 36\)
• (D) \(2d^3 + 7d^2 - 103d + 36\)