Question

factorise x2-6x2+11x-6​

Answer 1

AnSwEr

Therefore, 1, 2, 3 are the factors of f(x)

GiVeN

x2-6x2+11x-6

To FiNd

Factories

SoLuTiOn

The factors are 1, 2, and 3

Step-by-step explanation:

According to Factor theorem, if (x - a) is a polynomial factor f(x), then f(a) = 0

Let f(x) =

$x^{3}-6 x^{2}+11 x-6f(x)=x </h3><h3>3</h3><h3> −6x </h3><h3>2</h3><h3> +11x−6$

Let us check if (x - 1) is the factor of f(x),

Then,

f(1) =

$1^{3}-6(1^{2})+11(1)-6=1-6+11-6=0f(1) \\ =1 </h3><h3>3</h3><h3> −6(1 </h3><h3>2</h3><h3> )+11(1)−6=1−6+11−6 \\ = 0$

Therefore (x-1) is a factor of f(x)

Let us check for the other factors

Hence,

$f(x) \\ =(x-1)(x^{2}-5 x+6)f(x)=(x−1)(x </h3><h3>2</h3><h3> −5x+6)</h3><h3>x^{2}-5 x+6 \\ =x^{2}-2 x-3 x+6x </h3><h3>2</h3><h3> −5x+6 \\ =x </h3><h3>2</h3><h3> −2x−3x+6</h3><h3></h3><h3> \\ =x(x-2)-3(x-2)=x(x−2)−3(x−2)</h3><h3></h3><h3> \\ = (x - 2)(x - 3)=(x−2)(x−3)</h3><h3></h3><h3>f(x) \\ = (x - 1)(x - 2)(x - 3)f(x) \\ =(x−1)(x−2)(x−3)$

Therefore, 1, 2, 3 are the factors of f(x)