Question

By using the factor theorem,show that (x-3) is a factor of the polynomial 12x^3-31x^2-18x+9 and then factorise 12x^3-31x^2-18x+9.

Answer 1

Answer:

(x-3)(3x-1)(4x+3)

Step-by-step explanation:

showing that (x-3) is a factor of 12x^3-31x^2-18x+9

x-3=0

×=3

p(x)=12x^3-31x^2-18x+9

p(3)=12(3)^3-31(3)^3-18(3)+9

=324-279-45

=0

hence, the remainder is zero so x-3 is a factor of p(x)

Now to factorise it we will divide x-3 with p(x) by long division.

we have quotient=12x^2+5x-3

By division algorithm,

Dividend = Divisor × quotient +Remainder

p(x)= (x-3)(12x^2+5x-3)+0

=(x-3)(12x^2+5x-3)

=(x-3)((12x^2-4x)(9x-3)) ( by middle term splitting)

=(x-3)(4x (3x-1)+3 (3x-1)

=(x-3)(3x-1)(4x+3)

Answer 2

Answer:

(x-3)(3x-1)(4x+3) this is a answer