Fully factorise $x^2 - 12x - 28$
Understand the Problem
The question asks us to factor the quadratic equation $x^2 - 12x - 28$. To fully factorise this quadratic expression, we need to find two numbers that multiply to -28 and add up to -12. Once we find these numbers, we can rewrite the quadratic expression in its factored form.
Answer
$(x + 2)(x - 14)$
Answer for screen readers
$(x + 2)(x - 14)$
Steps to Solve
- Identify the coefficients
The quadratic expression is in the form $ax^2 + bx + c$, where $a = 1$, $b = -12$, and $c = -28$.
- Find two numbers that multiply to $c$ and add up to $b$
We need to find two numbers that multiply to $-28$ and add to $-12$. The factors of $-28$ are:
- $1$ and $-28$
- $-1$ and $28$
- $2$ and $-14$
- $-2$ and $14$
- $4$ and $-7$
- $-4$ and $7$
The pair of factors that add up to $-12$ are $2$ and $-14$.
- Rewrite the quadratic expression in factored form
Using the numbers we found, we can rewrite the quadratic expression in factored form as $(x + 2)(x - 14)$.
$(x + 2)(x - 14)$
More Information
Factoring quadratic equations is a fundamental skill in algebra! It's used to solve equations, simplify expressions, and graph parabolas.
Tips
A common mistake is to get the signs wrong when finding the factors of $c$. For example, confusing $-2$ and $14$ with $2$ and $-14$. Always double-check that your chosen factors multiply to $c$ and add to $b$.
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