Question

Using factor theorem,factorize each of the following polynomials
X power 3-6x ki power 2+3x +10

Answer 1

Answer:

Constant term =10

Possible factors of 10=+/-1,+/-2,+/-5,+/-10

P(x)=x^3–6x^2+3x+10

P(-1)=(-1)^3–6(-1)^2+3(-1)+10

=>-1–6–3+10=-10+10=0 gives

(x+1) is a factor of P(x).

=>x^3+x^2–7x^2–7x+10x+10

=>x^2(x+1)-7x(x+1)+10(x+1)

=>(x+1)(x^2–7x+10)

Using split middle term

=>(x+1){(x^2-(5+2)x+10}

=>(x+1){x(x-5)-2(x-5)}

=>(x+1)(x-5)(x-2)------ANSWER