Question 836899
Factorise the following expressions.
Question A
(i) x2 − x − 42
(ii) 9m2 − 81n2
Question B
In parts (i), (ii) below you should include each step in your
reasoning and check that your solution is correct.
(i) Factorise then solve the equation x2 + 2x−24 = 0.
(ii) Explain how you could use your answer to part (B)(i) to solve the
equation 7x2 + 14x−168 = 0. 

A(i) {{{x^2 - x - 42}}}
We want a pair of numbers such that their product is 42 and 
their sum is -1
-7 and + 6 work for this and {{{x^2 - x - 42}}} factored is
(x - 7)(x + 6)
A(ii) {{{9m^2-81n^2}}}
Binomials of the form {{{x^2-y^2}}} factor as {{{(x+y)(x-y)}}}
so think of {{{9m^2-81n^2}}} as {{{(3m)^2-(9n)^2}}}
which means the factors are
(3m+9n)(3m-9n)
B(i) x2 + 2x−24 = 0.
Here we want a pair of numbers whose product is -24 and their sum is +2
+6 and -4 work for this
(x + 6)(x - 4) = 0
 B(ii)
(ii) Explain how you could use your answer to part (B)(i) to solve the
equation 7x2 + 14x−168 = 0. 
7 is a factor of each term, so 7x2 + 14x−168 = 0 factored is
{{{7(x^2 + 2x - 24) = 0 }}}