Question

Factorise f²-f-20 step by step​

Answer 1

Answer:

$\fbox{\begin{minipage}{6em}(f +4)(f - 5)\end{minipage}}$

Explanation:

Step 1: Add more suitable components

$A = f^{2} - f - 20$

$A = f^{2} + 4f - 5f - 20$

Step 2: apply associative property

$A = f(f + 4) - 5(f + 4)$

Step 3: combine the common components

$A = (f + 4)(f - 5)$

Note:

To factorize an expression in form of $f^{2} + bf + c$, the coefficient $b$ is often turned into the sum of 2 new components $b_{1}$ and $b_{2}$ that satisfy $b_{1}$ x $b_{2}$ = $c$

In the above problem: $b$ = -1, is then turned into $b_{1} = 4$ and $b_{2} = -5$, that satisfy $b_{1}$ x $b_{2}$ = $(4)$ x $(-5)$ = $-20$ = $c$

Hope this helps!

:)