Question

7.5 - factoring polynomials - part 1
factor this quadratic expression.
$x^2 - 3x - 28$

Explanation:

Step1: Find pair with sum -3, product -28

We need two numbers that add to $-3$ and multiply to $-28$. These numbers are $4$ and $-7$, since $4 + (-7) = -3$ and $4 \times (-7) = -28$.

Step2: Split middle term and factor

Rewrite the quadratic using the pair, then factor by grouping:
$x^2 + 4x - 7x - 28 = x(x+4) -7(x+4) = (x+4)(x-7)$

Answer:

$(x + 4)(x - 7)$