Question 1165419
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(1) {{{25x^2+30x-36}}}<br>
Spend at most a very little time trying to factor it.  Then look at the discriminant, {{{b^2-4ac}}}.<br>
The discriminant in this quadratic is {{{30^2-4(25)(-36) = 900+3600 = 4500}}}<br>
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.<br>
(2) {{{49y^2-42y+k}}}<br>
If this is to be a perfect square trinomial, then it must be of the form {{{(7y-a)^2}}}.<br>
{{{(7y-a)^2 = 49y^2-14ay+a^2}}}<br>
Since the linear term of the trinomial is -42y, a=3; then a^2 = 3^2 = 9.<br>
ANSWER: k = 9<br>