SOLUTION: Factor completely or state that the polynomial is prime. 25x^2 + 30x - 36 Find the value of the integer k so that the trinomial is a perfect square trinomial, and write the f

Algebra ->  Polynomials-and-rational-expressions -> SOLUTION: Factor completely or state that the polynomial is prime. 25x^2 + 30x - 36 Find the value of the integer k so that the trinomial is a perfect square trinomial, and write the f      Log On


   

Question 1165419: Factor completely or state that the polynomial is prime.
25x^2 + 30x - 36
Find the value of the integer k so that the trinomial is a perfect square trinomial, and write the factored form.
49y^2 - 42y + k,
Thank you
Found 3 solutions by Alan3354, MathTherapy, greenestamps:
Answer by Alan3354(69443) About Me  (Show Source):
You can put this solution on YOUR website!
Factor completely or state that the polynomial is prime.
25x^2 + 30x - 36
-------------------
Prime, not factorable with integers.
===============================
Find the value of the integer k so that the trinomial is a perfect square trinomial, and write the factored form.
49y^2 - 42y + k
k = 9
---> (7y - 3)^2

Answer by MathTherapy(10552) About Me  (Show Source):
You can put this solution on YOUR website!

Factor completely or state that the polynomial is prime.
25x^2 + 30x - 36
Find the value of the integer k so that the trinomial is a perfect square trinomial, and write the factored form.
49y^2 - 42y + k,
Thank you
25x2 + 30x - 36 <====== PRIME



49y2 - 42y + k

You can complete the square in order to get the value of k, or use the standard form of a perfect square, them EQUATE terms to find k.

Using either, highlight_green%28matrix%281%2C3%2C+k%2C+%22=%22%2C+9%29%29

Answer by greenestamps(13200) About Me  (Show Source):
You can put this solution on YOUR website!


(1) 25x%5E2%2B30x-36

Spend at most a very little time trying to factor it. Then look at the discriminant, b%5E2-4ac.

The discriminant in this quadratic is 30%5E2-4%2825%29%28-36%29+=+900%2B3600+=+4500

A quadratic is factorable (over the integers) only if the discriminant is a perfect square. 4500 is not a perfect square, so this quadratic is not factorable.

(2) 49y%5E2-42y%2Bk

If this is to be a perfect square trinomial, then it must be of the form %287y-a%29%5E2.

%287y-a%29%5E2+=+49y%5E2-14ay%2Ba%5E2

Since the linear term of the trinomial is -42y, a=3; then a^2 = 3^2 = 9.

ANSWER: k = 9