Question

Using factor theorem, factorize each of the following polynomials: (i) x 3– 6x 2 + 3x + 10 (ii) 2y 3– 5y 2 – 19y + 42​

Answer 1

Step-by-step explanation:

let F(y)=2y³-5y²-19y+42

Constand term=42

Factors of 42=+1,+2,+3,+6,+7,+14,+21,+42.

Now,

divide F(y) by (y-2) we get,

y-2÷2y³-5y²-19y+42

2y³-4y²

-y²-19y

-y²+2y

-21y+42

-21y+42

0

F(y)=(y-2)(2y²-y-21)

=(y-2)(2y²-7y+6y-21)

=(y-2)y(2y-7)+3(2g-7)

therefore, F(y)=(y-2)(2y-7)(y+3)