Question

factorise:f(x)=2x^3-7x^2-3x+18 also solve if f(x)=0​

Answer 1

Let f(x)=2x

3

–7x

2

–3x+18

For x=2, the value of f(x) will be

f(2)=2(2)

3

–7(2)

2

–3(2)+18

=16–28–6+18=0

As f(2)=0,(x–2) is a factor of f(x).

Now, performing long division we have

Thus, f(x)=(x–2)(2x

2

–3x–9)

=(x–2)(2x

2

–6x+3x–9)

=(x–2)[2x(x–3)+3(x–3)]

=(x–2)(x–3)(2x+3)

Now, for f(x)=0

(x–2)(x–3)(2x+3)=0

Hence x=2,3 or −3/2