ANSWER
4(x + 3)(x + 4)
EXPLANATION
We want to factorise:
4x² + 28x + 48
We simply want to write the expression as a product of its factors.
First, because each of the coefficients in the expression and the constant are divisible by 4, we will factor out 4:
[tex]4(x^2\text{ + 7x + 12)}[/tex]Now, we have to look for two numbers such that adding them will yield 7 and their product will yield 12.
The two numbers we need are:
3 and 4
So, we have that the expression becomes:
[tex]\begin{gathered} 4(x^2\text{ + 3x + 4x + 12)} \\ \Rightarrow\text{ 4\lbrack{}x(x + 3) + 4(x + 3)\rbrack} \\ \Rightarrow\text{ 4(x + 3)(x + 4)} \end{gathered}[/tex]We have factorised it.
