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;

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

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

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