Question

Factorize

(i)x^3+13x^2+32x+20

(ii)y^3+y^2-y-1​

Answer 1

Step-by-step explanation:

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Answer 2

Required Answer:-

Question:

• Factorise the polynomials.

Solution:

Question 1:

We have,

x³ + 13x² + 32x + 20

= x³ + x² + 12x² + 12x + 20x + 20

= x²(x + 1) + 12x(x + 1) + 20(x + 1)

= (x + 1)(x² + 12x + 20)

= (x +1)[x² + 10x + 2x + 20]

= (x + 1)[x(x + 10) + 2(x + 10)]

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

★ Hence, the factorised form of the polynomial is (x + 1)(x + 2)(x + 30)

Question 2:

We have,

y³ + y² - y - 1

= y²(y + 1) - 1(y + 1)

= (y + 1)(y² - 1)

= (y + 1)[(y)² - (1)²]

= (y + 1)(y + 1)(y - 1) [Using identity x² - y² = (x + y)(x - y)]

= (y - 1)(y + 1)²

★ Hence, the factorised form of the polynomial is (y - 1)(y + 1)²