Question

Is 16x^2-56x+49 a perfect square trinomial? How do you know ? If it is, factor the expression. Please show your work

Answer 1

Answer:

• yes
• (4x -7)^2

Step-by-step explanation:

If it is, the first and last terms are perfect squares, and the middle term is twice the product of the roots of those squares.

  16x^ = (4x)^2 . . . . a perfect square

  49 = 7^2 . . . . . . . a perfect square

  -2(4x)(7) = -56x . . . . . matches the middle term, so the factoring is ...

  16x^2 -56x +49 = (4x -7)^2

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The sign in the binomial factors is the same as the sign of the middle term of the trinomial.