Question

Find the number to add to x^2 + 8x to make it a perfect square trinomial. Write that trinomial as the square of a binomial.a) add 16; (x + 8)^2b) add 16; (x + 4)^2c) add 64; (x + 8)^2d) add 64; (x + 4)^2

Answer 1

Step 1: Write out out the expression

$x^2+8x$

Step 2: Use completing the square method to find the number

$\begin{gathered} x^2+8x=(x+4)^2-4^2 \\ x^2+8x=(x+4)^2-16 \\ \text{ Adding 16 to both sides we have} \\ x^2+8x+16=(x+4)^2-16+16 \\ x^2+8x+16=(x+4)^2 \end{gathered}$

Hence,

(x² + 8x) + 16 = (x + 4)²

Therefore, the number to add is 16 and the trinomial becomes (x + 4)²

B