Question

check whether that g(x) is a factor of p(x) or not in the following polynomials
1. p(x) =
$4 {x}^{5} + 8x + 8 {x}^{2} + 7$
g(x) =
$2 {x}^{3} - x + 1$
2. p(x) =
${x}^{4} - 5x + 6$
g(x) =
$2 - {x}^{2}$
​

Answer 1

Answer:

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Step-by-step explanation:

Let f(x)=4x3−8x2+8x+1

q(x)=2x−1

r(x)=x+3

f(x)=g(x)×q(x)+r(x)

Degree of g(x) be 2. as degree of f(x) is 3.

∴g(x)=ax2+bx+c

4x3−8x2+8x+1=(ax2+bx+c)(2x−1)+x+3

=2ax3+2bx2+2cx−ax2−bx+c+x+3

=2ax3+(2b−a)x2+(2c−b+1)+(3−c)

Equating coefficient of power of x,

2a=4⇒a=24=2

2b−a=−8⇒