Question

Factorize x^3-10x^2-53x-42

Answer 1

Answer:

(x+1)(x-14)(x+3)

Step-by-step explanation:

The first step in factorising polynomials is to find the smallest factor first. The way to do this is with trial and error. Lets see if x+1 is a factor.

According to the factor theorem, (x-a) is a factor of P(x) if and only when P(a) = 0

In this case we will use f(x) = ((x)^3)-((10x)^2)-53x-42

f(-1) = 0

Therefore (x+1) is a factor of the polynomial.

Now we divide the polynomial with (x+1) via long division to get (x^2)-11x-42.

We now factorise (x^2)-11x-42 using whatever method you would like. I'm going to use the AC method, where we find a number that multiplies to AC and adds to B, In this case AC = -42, and B = -11.

Therefore (x^2)-11x-42 factosied is (x-14)(x+3)

Now merge (x+1) with (x-14)(x+3)

The final answer is (x+1)(x-14)(x+3)

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Answer 2

Answer:

(x+1)(x+3)(x-14)

Step-by-step explanation:

=> x³-10x²-53x-42

We'll break 10x² and -53x into parts

=> x³+x²-11x²-11x-42x-42

Taking common

=> x²(x+1)-11x(x+1)-42(x+1)

Taking x+1 as common will make it

=> (x+1)(x²-11x-42)

Using mid term break formula

=> (x+1)(x²-14x+3x-42)

=> (x+1)[x(x-14)+3(x-14)]

Taking (x-14) as common

=> (x+1)(x+3)(x-14)

This is the required factorized form.

Hope it helps :)