Question

Factorise each of the following polynomials using synthetic division:
Exercise 3.8
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Answer 1

1.)Let p(x)=x

3

−3x

2

−10x+24.

Since p(1)



=0 and p(−1)



=0, neither x+1 nor x+1 is a factor of p(x). Therefore, we have to search for different values of x by trial and error method.

When x=2, p(2)=0. Thus, x-2 is a factor of p(x).

To find the other factors, let us use the synthetic division.

∴ The factor is x

2

−x−12.

Now, x

2

−x−12=x

2

−4x+3x−12=(x−4)(x+3)

Hence, x

3

−3x

2

−10x+24=(x−2)(x+3)(x−4)