Question

Factor the expression. d^2-14d+49

Answer 1

Answer: (d - 7)^2

Procedure to factor:

The expression to factor is a trinomial.

Steps:

1) Probe whether this is a perfect square trinomial, i.e a trinomial that can be factored as (a + b)^2 or (a - b)^2.:

2) Determine if the first and the third terms of the trinomial (once it is ordered, which it is) have exact square roots:

√ (d^2) = d

√49 = 7

3) Since they have exact square roots, test wether the second term of the trinomial equals twice the product of the two square roots determined:

=> 2 * (d) * (7) = 14d which is exactly the second term of the trinomial

4) Now you can write the binomial squared using the sign of the second term. This is:

(d - 7)^2.

You can prove that that is the answer by expanding the binomial squared, which must drive back to the original expression: d^2 - 2(7)(d) + 7^2 = d^2 - 14d + 49.