# Using the Remainder Theorem, Factorise Each of the Following Completely. 3x3 + 2x2 – 23x – 30 - Mathematics

Using the Remainder Theorem, factorise each of the following completely.

3x3 + 2x2 – 23x – 30

#### Solution

f(x)=3x^3+2x^2-23x-30

for x=-2,

f(x)=f(-2)=3(-2)^3+2(2)^2-23(-2)-30

=-24+8+46-30=-54+54=0

Hence, (x+2)is a factor of  f(x).

∴ 3x^3+2x^2-23x-30=(x+2)(3x^2+4x-15)

=(x+2)(3x^2+5x-9x-15)

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

=  (x-2) (3x+5)(x-3)

Concept: Factor Theorem
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