Question

Factorise 2x^3-13x^2+6x+45

Answer 1

we have to factorise ; 2x³ - 13x² + 6x + 45

find prime factors of 45 .

i.e., prime factors of 45 = 3 × 3 × 5

it means, a zero must contain 3 , 3 or 5.

let's put x = 3 in 2x³ - 13x² + 6x + 45

we get, 2(3)³ - 13(3)² + 6(3) + 45

= 54 - 117 + 18 + 45

= 117 - 117 = 0

hence, x = 3 is a zero of given polynomial so, (x - 3) is factor of given polynomial.

now arrange 2x³ - 13x² + 6x + 45

i.e., 2x³ - 6x² - 7x² + 21x - 15x + 45

= 2x²(x - 3) - 7x(x - 3) -15(x - 3)

= (2x² - 7x - 15)(x - 3)

= (x - 3)(2x² - 10x + 3x - 15)

= (x - 3){2x(x - 5) + 3(x - 5)}

= (x - 3)(x - 5)(2x + 3)

hence, answer is (x - 3)(x - 5)(2x + 3)