Question

Factorize 2x^3 - x^2 + 13x - 6

Answer 1

Answer:

Let f(x)=2x

3

+x

2

–13x+6

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

f(2)=2(2)

3

+(2)

2

–13(2)+6=16+4–26+6=0

As f(2)=0, so (x–2) is a factor of f(x)

Answer 2

Answer:

Answer

Let f(x)=2x

3

+x

2

–13x+6

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

f(2)=2(2)

3

+(2)

2

–13(2)+6=16+4–26+6=0

As f(2)=0, so (x–2) is a factor of f(x).

Now, performing long division we have

Thus, f(x)=(x−2)(2x

2

+5x–3)

=(x–2)[2x

2

+6x–x–3]

=(x–2)[2x(x+3)−1(x+3)]

=(x–2)[2x(x+3)−1(x+3)]

=(x–2)(2x–1)(x+3)

Step-by-step explanation:

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