Question

Factorise
$2x {}^{3} - 5 {x}^{2} - 19x + 42$
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Answer 1

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Class 9

>>Maths

>>Polynomials

>>Factorisation of Polynomial

>>Using the factor theorem factorise the f

Question

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Using the factor theorem factorise the following polynomial completely 3x

3

+2x

2

−19x+6.

Medium

Solution

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Let f(x)=3x

3

+2x

2

−19x+6

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

=3(2)

3

+2(2)

2

−19(2)+6

⇒24+8−38+6=0

According to the factor theorem, (x−a) is a factor of f(x) if f(a)=0

∴ (x−2) is a factor of f(x). [∵ f(2)=0]

Now, performing long division as shown in the above image, we have

f(x)=(x−2)(3x

2

+8x–3)

⇒(x−2)(3x

2

+9x−x−3)

⇒(x−2)[3x(x+3)−1(x+3)]

⇒(x−2)(x+3)(3x−1)