Polynomial Operations — Test

Question 21 • Algebra II

What is the product? open paren 7 x squared close paren times open paren 2 x cubed plus 5 close paren times open paren x squared minus 4 x minus 9 close paren

Answer

14 x to the 7th power minus 56 x to the 6th power minus 126 x to the 5th power plus 35 x to the 4th power minus 140 x cubed minus 315 x squared

14 x to the 5th power minus x to the 4th power minus 46 x cubed minus 58 x squared minus 20 x minus 45

14 x to the 6th power minus 56 x to the 5th power minus 91 x to the 4th power minus 140 x cubed minus 315 x squared

14 x to the 12th power minus 182 x to the 6th power plus 35 x to the 4th power minus 455 x squared

Explanation

First multiply the two expressions in parentheses: (2x³ + 5)(x² − 4x − 9) = 2x⁵ − 8x⁴ − 13x³ − 20x + 5x² − 45. Then multiply every term by 7x², giving 14x⁷ − 56x⁶ − 91x⁵ + 35x⁴ − 140x³ − 315x². This matches choice B.

AI-written and checked against the verified answer.

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