Factorize
(i)x^3+13x^2+32x+20
(ii)y^3+y^2-y-1
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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
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