Question

HELP

Sophia’s work factoring a perfect square trinomial is shown below. She has made several mistakes. Explain Sophia’s mistakes and correct her work using complete sentences.

16x^2 – 40x + 25 = (x + 5)^2

Answer 1

Sophia has considered the coefficient of x² as 1 in place of 16 and coefficient of x as 10 in place of - 40 in the original trinomial.

Explanation:

The given trinomial to be factorized into a perfect square is 16x² - 40x + 25.

And Sophia obtained the perfect square as (x + 5)² which gives the trinomial as x² + 10x + 25.

Therefore, Sophia's work is not correct as 16x² - 40x + 25 ≠ x² + 10x + 25.

Therefore, Sophia has considered the coefficient of x² as 1 in place of 16 and coefficient of x as 10 in place of - 40 in the original trinomial and then factorized the wrong trinomial as (x + 5)². (Answer)