Question

factorise x³-2x²-x+2
& x³+13x²+32x+20​

Answer 1

Question:

1) factorise the equation $x^3-2x^2-x+2$

2) factorise the equation $x^3+13x^2+32x+20$

Answer:

1)$(x^2-1)(x-2)$

2)$(x+10)(x+2)(x+1)$

Step-by-step explanation:

1) Let us solve the first question

⇒ $x^3-2x^2-x+2$

We can see that  $x^3,-x$ are common and $-2x^2,2$ are common. So let us

⇒$x(x^2-1)-2(x^2-1)$

⇒$(x^2-1)(x-2)$

Hence the factors are $(x^2-1)(x-2)$.

2)Let us solve the second question

⇒$x^3+13x^2+32x+20$

We can see that we have to use error method.

⇒$p(x)=x^3+13x^2+32x+20$

Let us solve the equation that is

⇒ x+1=0

⇒x=-1

Let us consider -1 as x

⇒$p(-1)=(-1)^3+13(-1)^2+32(-1)+20$

⇒$p(-1)=(-1)+13-32+20$

⇒$p(-1)=-1+13-32+20$

⇒$p(-1)=33-33$

⇒$p(-1)=0$

Hence p(-1) is the one of the factor

We have to divide the equation by  x+1

The division is in the image

Hence after dividing the equation we get  $x^2+12x+20$

One of the factor is (x+1)

Let us factorise the equation

⇒$(x^2+12x+20)(x+1)$

We can see that 10x,2x should be seperated to form to facotrise

⇒$(x^2+10x+2x+20)(x+1)$

⇒$[x(x+10)+2(x+10)](x+1)$

⇒$(x+10)(x+2)(x+1)$

Hence your final answer is (x+10)(x+2)(x+1).