Question

Show that x-1 is a factor of the polynomial x3-13x2+32x-20.hence factorise the polynomial

Answer 1

Answer:

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Answer 2

The factorization of $x^3-13x^2+32x-20\text{ is }(x-1)(x-2)(x-10)$.

Explanation:

The given polynomial : $p(x)=x^3-13x^2+32x-20$.

It can be written as :

$p(x)=x^3-(1+12)x^2+(12+20)x-20$

$=x^3-x^2-12x^2+12x+20x-20\\\\=x^2(x-1)-12(x-1)+20(x-1)\\\\=(x-1)(x^2-12x+20)$

Hence, (x-1) is a factor of the given polynomial.

Further, $(x-1)(x^2-12x+20)=(x-1)(x^2-2x-10x+20)$

$(x-1)(x(x-2)-10(x-2))\\\\=(x-1)(x-2)(x-10)$

Hence, the factorization of $x^3-13x^2+32x-20\text{ is }(x-1)(x-2)(x-10)$.

# Learn more :

Find all the zeros of the polynomial x3 + 13x2 +32x +20.

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