Question

x^3+13x^2+32x+30 Factorize
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Answer 1

Answer:

Solution:-

Let p(x)=x

3

+13x

2

+32x+20

P(−1)=(−1)

3

+13(−1)

2

+32(−1)+20=0

∴(x+1) is a factor of p(x).

On dividing p(x) by (x+1), we get

p(x)÷(x+1)=x

2

+12x+20

∴x

3

+13x

2

+32x+20=(x+1)(x

2

+12x+20)

⇒=(x+1)(x

2

+10x+2x+20)

⇒=(x+1)[x(x+10)+2(x+10)]

⇒=(x+1)[(x+10)(x+2)]

⇒=(x+1)(x+2)(x+10)

Hence, x

3

+13x

2

+32x+20=(x+1)(x+2)(x+10)