Factorise the quadratic expression $x^{2} - 7 x + 12$

medium 2 marks Class 7 · Mathematics · Simple Equations

Answer

(x - 3) (x - 4)

The correct answer is $(x - 3) (x - 4)$ — Factor out the common binomial $(x - 3)$ to get $(x - 3) (x - 4)$ .

Step-by-step solution

Find two numbers that multiply to the constant term $12$ and add to $- 7$ ; these are $- 3$ and $- 4$ .
Rewrite the middle term using these numbers: $x^{2} - 3 x - 4 x + 12$ .
Group the terms: $(x^{2} - 3 x) + (- 4 x + 12)$ .
Factor each group: $x (x - 3) - 4 (x - 3)$ .
Factor out the common binomial $(x - 3)$ to get $(x - 3) (x - 4)$ .

Common mistake: Choosing the wrong pair of numbers or forgetting to factor out the common binomial

Concept tested: Factoring quadratic expressions