Question

Question 5What are the factors of4x2 + 20x + 25(2x – 5)²0 (20+5)O (2.c + 5)(2x - 5)(2x + 5)2

Answer 1

ANSWER

$(2x+5)^2$

EXPLANATION

We want to find the factors of:

$4x^2\text{ + 20x + 25}$

To do that we simply have to factorise the equation.

That is we need two numbers such that:

their sum = 20

their product = 4 * 25 = 100

The two numbers we need are 10 and 10.

That is:

$\begin{gathered} \Rightarrow4x^2\text{ + 10x + 10x + 25} \\ \text{Factorise by grouping them:} \\ (4x^2\text{ + 10x) + (10x + 25)} \\ =\text{ 2x(2x + 5) + 5}(2x\text{ + 5)} \\ =\text{ (2x + 5)(2x + 5)} \\ =(2x+5)^2 \end{gathered}$

That is the answer.