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

Answer 1

For perfect square trinomial

`\begin{gathered} c=((b)/(2))^2,\text{ where b = coefficient of x is 8} \\ c=((8)/(2))^2 \\ c=4^2 \\ c=16 \\ \text{Hence,} \\ x^2+8x+c=x^2+8x+16 \end{gathered}`

As the square of a binomial, it is:

`\begin{gathered} x^2+8x+16=(x^2+4x)+(4x+16) \\ \text{factorize,} \\ x(x+4)+4(x+4)=(x+4)(x+4) \\ \therefore x^2+8x+16=(x+4)^2 \end{gathered}`

Therefore, the number added to make x²+8x a perfect square trinomial is 16.

As the square of a binomial, the perfect square trinomial is: (x+4)²