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