Question 3: Factorize x 2 − 11 x − 42

Factorization of x 2 + px + q type expressions

Question 3: Factorize x 2 − 11 x − 42

Factorization exercises —

Solution:

Let’s see how to evaluate an expression for factorization;

$x^2-11x-42$

Break -11x into two parts such that if these two parts are added they give -11x —- and when these two parts are multiplied, they give $-42x^2$ :

We can think of two terms -14x and +3x as parts of -11 x — such that;

(-14x) + (3x) = -14x+3x = -11x

and

(-14x)(3x) = -42x

So,

$=x^2-14x+3x^2-42$

Taking out common x from first two terms and 3 from last two terms, we get;

$=x(x-14)+3(x-14)$

Can be written as;

$=[x(x-14)+3(x-14)]$

Now (x-14) can be taken out as common;

$=(x-14)[x+3]$

$=(x-14)(x+3)$

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