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What is the coefficient of x^2 when -5x^3 - 5x^2 - 7x + 1$ is multiplied by x^2 - 6x + 7 and the like terms are combined?

 May 9, 2022
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We pick one term from each polynomial to try to "make" x^2.

 

\((-5x^3 \color{purple}- 5x^2 \color{blue}- 7x \color{green}+ 1\color{black})(\color{green}x^2 \color{blue}- 6x\color{purple} + 7\color{black})\)

 

If we combine the colored terms with the same color together, we get terms in x^2. We add them up to get the total:

 

Term in x^2 = \(\color{purple}(-5x^2)(+7)\color{black}+\color{blue}(-7x)(-6x)\color{black}+\color{green}(+1)(x^2)\color{black}=8x^2\)

 

Therefore the coefficient of x^2 in the product is 8.

 May 9, 2022

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