Question

Examine whether x+2 is a factor of the polynomial x^3+3x^2+5x+6​

Answer 1

$\huge\underline\mathbb{POLYNOMIALS}$

First we will find the zero of x+2 that is-

$x + 2 = 0$

$x = 0 - 2$ ( as 2 has been transposed sign will be changed)

$x = - 2$

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Now ATQ,

$p(x) = x {}^{3} +3x {}^{2} + 5x + 6$

$p( - 2) = ( - 2) {}^{3} + 3( - 2)^{2} + 5( - 2) + 6$

$- 8 + 12 - 10 + 6$

$0 \: Ans$

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$\therefore$ x+2 is a factor.

Answer 2

Step-by-step explanation:

as x+2 is factor so,x = -2

substitute x = -2

-8 + 12 - 10 + 6 = 0 》Remainder = 0

I have verified that x+2 is factor of x^3+3x^2+5x+6

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