Find the coefficient of x2 in the following polynomials, 3×2+2ẋ-4×2-3x-2 .

# Find the coefficient of ${x}^{2}$ in the following polynomials, $\left(3{x}^{2}+2\stackrel{̇}{x}-4\right)\left({x}^{2}-3x-2\right)$ .

1. A
14
2. B
16
3. C
-16
4. D
-14

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### Solution:

The given polynomial is $\left(3{x}^{2}+2\stackrel{̇}{x}-4\right)\left({x}^{2}-3x-2\right)$.
We know that the coefficient of ${x}^{m}$  in $a{x}^{m}+\mathit{bx}+c$ is $a$.
Therefore, write the expression $\left(3{x}^{2}+2\stackrel{̇}{x}-4\right)\left({x}^{2}-3x-2\right)$ in polynomial form,
$\left(3{x}^{2}+2x-4\right)\left({x}^{2}-3x-2\right)$
$⇒3{x}^{2}\left({x}^{2}-3x-2\right)+2x\left({x}^{2}-3x-2\right)-4\left({x}^{2}-3x-2\right)$
$⇒3{x}^{4}-9{x}^{3}-6{x}^{2}+2{x}^{3}-6{x}^{2}-4x-4{x}^{2}+12x+8\right)$
$⇒3{x}^{4}-7{x}^{3}-16{x}^{2}+8x+8$
Therefore, the coefficient of ${x}^{2}$ in $3{x}^{4}-7{x}^{3}-16{x}^{2}+8x+8$ is -16.
Hence, option 3 is  correct.

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