7(a) Simplify - OCR - GCSE Maths - Question 7 - 2017 - Paper 1

To factorise the expression $5v + 20w$, we look for the greatest common factor (GCF).

The GCF of $5v$ and $20w$ is $5$. Therefore, the factorised form is:

$5(v + 4w)$

To solve the quadratic equation $x² + 10x + 21 = 0$ by factorising, we need to express it in the form of $(x + a)(x + b) = 0$, where $ab = 21$ and $a + b = 10$. The pairs of factors of $21$ are $(1, 21)$ and $(3, 7)$. The correct pair that adds up to $10$ is $(3, 7)$:

$x² + 10x + 21 = (x + 3)(x + 7) = 0$

Setting each factor to zero gives:

$x + 3 = 0 ext{ or } x + 7 = 0$

Thus, the solutions are:

$x = -3 ext{ or } x = -7$