91Ó°ÊÓ

Use factoring to solve each quadratic equation. Check by substitution or by using a graphing utility and identifying \(x\) -intercepts. $$x^{2}+7 x=18$$

Factor completely, or state that the polynomial is prime. $$2 x^{3}-72 x$$

Factor completely, or state that the polynomial is prime. $$3 x^{3}+27 x$$

Factor each trinomial, or state that the trinomial is prime. Check each factorization using FOIL multiplication. \(x^{2}-9 x y+14 y^{2}\)

Factor completely. $$y^{4}+2 y^{3}-80 y^{2}$$

Now let's move on to factorizations that may require two or more techniques. Factor completely, or state that the polynomial is prime. Check factorizations using multiplication or a graphing utility. $$10 x^{4}+20 x^{3}+15 x^{2}$$

Factor completely. $$20 x^{2} y-100 x y+120 y$$

Now let's move on to factorizations that may require two or more techniques. Factor completely, or state that the polynomial is prime. Check factorizations using multiplication or a graphing utility. $$9 y^{2}-64$$

Determine whether each statement is true or false. If the statement is false, make the necessary change(s) to produce a true statement. A trinomial can never have two identical factors.

Why is it a good idea to factor out the GCF first and then use other methods of factoring? Use \(3 x^{2}-18 x+15\) as an example. Discuss what happens if one first uses trial and error to factor as two binomials rather than first factoring out the GCF.