Question

alt=" {x}^{2} - 8x + 15" align="absmiddle" class="latex-formula">

Answer 1

To factorise this quadratic, you need to find two numbers that add together to give -8 but also multiply to give 15. These two numbers can be identified as -3 and -5 as -3-5=-8 and -3×-5=15. Therefore, the factorised form is (x-3)(x-5). To find the solutions, write (x-3)(x-5)=0. Deal with each bracket individually:
x-3=0
x=3
x-5=0
x=5
So the two solutions are 3 and 5.