Question

x+2 is a factor of which of the following polynomial

a x³ + 2x² - 5x + 4
b x³ + 3x² - 5x + 7
c x³ - 2x² - 7x - 2
d x³ + 3x² - 2x - 8​

Answer 1

Answer:

$\huge\underline\mathfrak\blue{Answer}$

by factor theorem-

x+2 is a factor.

x+2= 0

x= -2.

a) given: f(x)= x^3+2x^2-5x+4

f(-2)= (-2)^3+2(-2)^2-5(-2)+4

= -8+8+10+4

0+14

=14

f(-2)= 14

if x+2 was a factor then,f(-2) should have been 0.

so it is not a factor of above polynomial.

b) given: f(x)= x^3+3x^2-5x+7

f(-2)= (-2)^3+3(-2)^2-5(-2)+7

= -8+12+10+7

= -8+29

= 21.

f(-2)= 21.

so x+2 is not a factor of this polynomial too.

c) given: f(x)= x^3-2x^2-7x-2.

f(-2)= (-2)^3-2(-2)^2-7(-2)-2

= -8+8+14-2

= -10+22

= 12.

f(-2)= 12.

so x+2 is not a factor of this one also.

d) given: x^3+3x^2-2x-8

f(-2)= (-2)^3+3(-2)^2-2(-2)-8

= -8+12+4-8

= -16+16= 0.

therefore x+2 is a factor of x^3+3x^2-2x-8 as f(-2)= 0.

(by factor theorem).

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