Question

Factorise completely x3-5x2-8x+12​

Answer 1

To factorise the polynomial x^3 - 5x^2 - 8x + 12, we find common factors and use the difference of squares method, resulting in the factored form (x - 5)(x + 2)(x - 2).

Step-by-step explanation:

To factorise the polynomial x3 - 5x2 - 8x + 12, we will look for factors of the constant term, 12, that can be used in combination with the coefficient of x3 to get the middle terms. The polynomial can be factored by grouping or by finding a common factor that simplifies the expression.

Firstly, we can try grouping x2 with -5x2 and -8x with +12. Upon factoring x2 from the first group and -4 from the second, we get:

x2(x - 5) - 4(x - 5)

We now have a common factor of (x - 5), giving us:

(x - 5)(x2 - 4)

Recognize that x2 - 4 is a difference of squares and can be factored further:

(x - 5)(x + 2)(x - 2)

The completely factored form of the polynomial is (x - 5)(x + 2)(x - 2).

Answer 2

Step-by-step explanation:

First, we can try to factor out the greatest common factor, which is 1 in this case. Then, we can try to factor by grouping:

x³ - 5x² - 8x + 12

= x²(x - 5) - 4(x - 3)

= x²(x - 5) - 4(x - 3)

Now we can see that we have a common factor of (x - 3), which we can factor out:

x²(x - 5) - 4(x - 3)

= (x - 3)(x² - 4x + 4)(x - 5)

The expression is now fully factorised, so the complete factorisation of x³ - 5x² - 8x + 12 is:

(x - 3)(x - 2)²(x - 5)