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Question
Factorize each of the following algebraic expression:
96 − 4x − x2
Solution
\[96 - 4x - x^2 \]
\[ = 100 - 4 - 4x - x^2 \]
\[ = 100 - ( x^2 + 4x + 4)\]
\[ = 100 - ( x^2 + 2 \times x \times 2 + 2^2 )\]
\[ = {10}^2 - (x + 2 )^2 \]
\[ = [10 - (x + 2)][10 + (x + 2)]\]
\[ = (10 - x - 2)(10 + x + 2)\]
\[ = (8 - x)(12 + x)\]
\[ = (x + 12)( - x + 8)\]
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