Question

Factors maths question! need help urgently

Answer 1

Factor Theorem

If (x - 4) is a factor then f(4) = 0

`\begin{aligned} f(4) & = 0\\\implies(4)^2+4B-4 & =0\\12+4B & = 0\\4B & = -12\\B & = -3\end{aligned}`

`\begin{aligned} f(4) & = 0\\\implies6(4)^2+4C-12 & =0\\84+4C & = 0\\4C & = -84\\C & = -21\end{aligned}`

Therefore:

`\implies B+C=-3+(-21)=-24`

Part (a)

`3a^2-8ab-3b^2`

`\implies 3a^2+ab-9ab-3b^2`

`\implies a(3a+b)-3b(3a+b)`

`\implies (a-3b)(3a+b)`

Part (b)

Use the factored expression in part (a):

`a=(c+d) \textsf{ and }b=(c-d)`

`\implies 3(c+d)^2-8(c+d)(c-d)-3(c-d)^2`

`=((c+d)-3(c-d))(3(c+d)+(c-d))`

`=(c+d-3c+3d)(3c+3d+c-d)`

`=(4d-2c)(4c+2d)`