The product of the given polynomials is [tex]16x^4 +16x^3 -12x^2-32x-16[/tex]. The correct option is- B. [tex]16x^4 +16x^3 -12x^2-32x-16[/tex]
Product of polynomials
From the question, we are to determine the product of the given polynomials
The given polynomials are
(8x^2-4x-8) (2x^2+3x+2)
Their product can be determined as follows
[tex](8x^2-4x-8) (2x^2+3x+2)[/tex]
[tex](8x^2) (2x^2+3x+2)-4x(2x^2+3x+2)-8 (2x^2+3x+2)[/tex]
Clear the brackets
[tex]16x^4 +24x^3+16x^2 -8x^3-12x^2-8x-16x^2-24x-16[/tex]
Now, collect like terms
[tex]16x^4 +24x^3 -8x^3-12x^2+16x^2-16x^2-8x-24x-16[/tex]
Simplifying
[tex]16x^4 +16x^3 -12x^2-32x-16[/tex]
Hence, the product of the given polynomials is [tex]16x^4 +16x^3 -12x^2-32x-16[/tex]. The correct option is- B. [tex]16x^4 +16x^3 -12x^2-32x-16[/tex]
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