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Answer with steps question no. 12 & 15​

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Answer:

QUESTION 12:

Let F(x)=x^3-2x^2-5x+6

Factors of 6 are:

+-1,+-2,+-3 and +-6

Now,

TAKE the value of x as 1,

f(1)=(1)^3-2(1)^2-5(1)+6

=1-2-5=+6

=0

Take the value of x as -1,

f(-1)=(-1)^3-2(-1)^2-5(-1)+6

=-1-2+5+6

=-3+11

=8

Take the value of x as 2,

f(2)=(2)^3-2(2)^2-5(2)+6

=8-8-10+6

=-4

Take the value of x as -2,

f(-2)=(-2)^3-2(-2)^2-5(-2)+6

=-8-8+10+6

=0

Take the value of x as 3,

f(3)=(3)^3-2(3)^2-5(3)+6

=27-18-15+6

=0

Therefore ,

The factors of x^3-2x^2-5x+6 are:

(x-1)(x+2)(x-3)


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