91Ó°ÊÓ

Write in factored form by factoring out the greatest common factor. \(25 k^{4}+15 k^{2}\)

Factor completely. If the polynomial cannot be factored, write prime. $$ -32+14 x+x^{2} $$

Factor each trinomial completely. See Examples 1–7. ( Hint: In Exercises 55–58, first write the trinomial in descending powers and then factor.) $$ 15 n^{4}-39 n^{3}+18 n^{2} $$

Factor each trinomial completely. $$ 4 z^{2}-12 z w+9 w^{2} $$

Factor completely. $$ t^{2}-t z-6 z^{2} $$

Factor completely. $$ v^{2}-11 v w+30 w^{2} $$

Factor by grouping. \(4 x^{3}+3 x^{2} y+4 x y^{2}+3 y^{3}\)

Galileo 's formula describing the motion of freely falling objects is $$ d=16 t^{2} $$ The distance d in feet an object falls depends on the time \(t\) elapsed, in seconds. (This is an example of an important mathematical concept, the function.) When you substituted 256 for \(d\) and solved the formula for \(t\) in Exercise \(79,\) you should have found two solutions: 4 and \(-4 .\) Why doesn't \(-4\) make sense as an answer?

Factor by grouping. \(6-3 x-2 y+x y\)

If a trinomial has a negative coefficient for the squared term, as in \(-2 x^{2}+11 x-12,\) it is usually easier to factor by first factoring out the common factor \(-1 .\) $$ \begin{aligned} -2 x^{2}+11 x-12 \\ =&-1\left(2 x^{2}-11 x+12\right) \\ =&-1(2 x-3)(x-4) \end{aligned} $$ Use this method to factor each trinomial. See Example 7(b). $$ $$ -2 a^{2}-5 a b-2 b^{2} $$