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

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

(1)

Spend at most a very little time trying to factor it. Then look at the discriminant, .

The discriminant in this quadratic is

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)

If this is to be a perfect square trinomial, then it must be of the form .

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

ANSWER: k = 9

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