Question

Find the coefficient of x squared in polynomial p(x) =(5-2x) (7x+5 x square - x 4)

Answer 1

hope it helps................

Answer 2

Answer:

Required coefficient of ${x}^{2}$is 11.

Step-by-step explanation:

Given polynomial is $p(x) = (5 - 2x)(7x + 5 {x}^{2} - {x}^{4})$

Here we want to find coefficient of ${x}^{2}$

So,first we need to multiply $(5 - 2x)$

and $(7x + 5 {x}^{2} - {x}^{4} )$

By Algebraic multiplication rule,

$p(x) = (5 - 2x)(7x + 5 {x}^{2} - {x}^{4} )$

$= 5 \times 7x + 5 + 5 {x}^{2} - 5 \times {x}^{4} - 2x \times 7x - 2x \times 5 {x}^{2} + 2x \times {x}^{4}$

$= 35x + 25 {x}^{2} - 5 {x}^{4} - 14 {x}^{2} - 10 {x}^{3} - 2 {x}^{5}$

$= - 2 {x}^{5} - 5 {x}^{4} - 10 {x}^{3} +11 {x}^{2} + 35x$

Here coefficient of ${x}^{5}$is (-2)

Coefficient of ${x}^{4}$is (-5)

Coefficient of ${x}^{3}$is (-10)

Coefficient of ${x}^{2}$is (+11) and coefficient of x is 35.