# Question 3: Factorize 2×2 − 8x − 42

Question 3: Factorize 2×2 − 8x − 42

Factorization exercises , factorization examples

Solution ;

To see as how to evaluate an expression for factorization, we write it;

$2x^2-8x-42$

Taking 2 common from the expression;

$= 2 (x^2-4x-21)$

Now consider expression within brackets – multiply last term i-e  (-21) with first term i-e ​$$x^2$$​ – we gt  ​$$-21x^2$$​. So, we make two parts of mid term i-e ​$$-4x$$​ such that if these two parts if added give ​$$-4x$$​ — and if multiplied , they give ​$$-21x^2$$​.

We can safely think of  ​$$-7x$$​ and  ​$$3x$$​  – becaus;

(​$$(-7x)+(3x)=-7x+3x=-4x$$

and

$$(-7x)(3x)=-21x^2$$

So we write;

$=2[x^2-7x+3x-21]$

In the expression within brackets we take   x common from first two term and take 3 common from last two terms;

$=2[x(x-7)+3(x-7)]$

$=2[(x+3)(x-7)]$

$=2(x+3)(x-7)$

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