Chapter 6

Factor each difference of two squares. $$1-49 x^{2}$$

Before getting to multiple-step factorizations, let's be sure that you are comfortable with exercises requiring only one of the factoring techniques. Factor each polynomial. $$14 x^{2}-9 x+1$$

Find the greatest common factor of each list of monomials. $$x y, x y^{2}, \text { and } x y^{3}$$

Use the method of your choice to factor each trinomial, or state that the trinomial is prime. Check each factorization using FOIL multiplication. $$3 y^{2}+y-4$$

Factor each trinomial, or state that the trinomial is prime. Check each factorization using FOIL multiplication. $$x^{2}-8 x+16$$

Use factoring to solve each quadratic equation. Check by substitution or by using a graphing utility and identifying \(x\) -intercepts. $$x^{2}+5 x+6=0$$

Factor each difference of two squares. $$1-64 x^{2}$$

Before getting to multiple-step factorizations, let's be sure that you are comfortable with exercises requiring only one of the factoring techniques. Factor each polynomial. $$3 x^{2}+2 x-5$$

Find the greatest common factor of each list of monomials. $$x^{2} y, 3 x^{3} y, \text { and } 6 x^{2}$$

Use the method of your choice to factor each trinomial, or state that the trinomial is prime. Check each factorization using FOIL multiplication. $$3 y^{2}-y-4$$

Factor each trinomial, or state that the trinomial is prime. Check each factorization using FOIL multiplication. $$y^{2}-8 y+15$$

Use factoring to solve each quadratic equation. Check by substitution or by using a graphing utility and identifying \(x\) -intercepts. $$x^{2}-2 x-15=0$$

Factor each difference of two squares. $$9-25 y^{2}$$

Before getting to multiple-step factorizations, let's be sure that you are comfortable with exercises requiring only one of the factoring techniques. Factor each polynomial. $$x^{2}-2 x+1$$

Find the greatest common factor of each list of monomials. $$16 x^{5} y^{4}, 8 x^{6} y^{3}, \text { and } 20 x^{4} y^{5}$$

Use the method of your choice to factor each trinomial, or state that the trinomial is prime. Check each factorization using FOIL multiplication. $$3 x^{2}+13 x-10$$

Factor each trinomial, or state that the trinomial is prime. Check each factorization using FOIL multiplication. $$y^{2}-8 y+7$$

Use factoring to solve each quadratic equation. Check by substitution or by using a graphing utility and identifying \(x\) -intercepts. $$x^{2}+x-42=0$$

Factor each difference of two squares. $$16-49 y^{2}$$

Before getting to multiple-step factorizations, let's be sure that you are comfortable with exercises requiring only one of the factoring techniques. Factor each polynomial. $$x^{2}-4 x+4$$

Find the greatest common factor of each list of monomials. $$18 x^{5} y^{4}, 6 x^{6} y^{3}, \text { and } 12 x^{4} y^{5}$$

Use the method of your choice to factor each trinomial, or state that the trinomial is prime. Check each factorization using FOIL multiplication. $$3 x^{2}+14 x-5$$

Factor each trinomial, or state that the trinomial is prime. Check each factorization using FOIL multiplication. $$x^{2}+3 x-10$$

Use factoring to solve each quadratic equation. Check by substitution or by using a graphing utility and identifying \(x\) -intercepts. $$x^{2}-4 x=21$$

Factor each difference of two squares. $$x^{4}-9$$

Before getting to multiple-step factorizations, let's be sure that you are comfortable with exercises requiring only one of the factoring techniques. Factor each polynomial. $$27 x^{3} y^{3}+8$$

Factor each polynomial using the greatest common factor. If there is no common factor other than 1 and the polynomial cannot be factored, so state. $$8 x+8$$

Use the method of your choice to factor each trinomial, or state that the trinomial is prime. Check each factorization using FOIL multiplication. $$3 x^{2}-22 x+7$$

Factor each trinomial, or state that the trinomial is prime. Check each factorization using FOIL multiplication. $$x^{2}+3 x-28$$

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 each difference of two squares. $$x^{4}-25$$

Before getting to multiple-step factorizations, let's be sure that you are comfortable with exercises requiring only one of the factoring techniques. Factor each polynomial. $$216 x^{3} y^{3}+125$$

Factor each polynomial using the greatest common factor. If there is no common factor other than 1 and the polynomial cannot be factored, so state. $$9 x+9$$

Use the method of your choice to factor each trinomial, or state that the trinomial is prime. Check each factorization using FOIL multiplication. $$3 x^{2}-10 x+7$$

Factor each trinomial, or state that the trinomial is prime. Check each factorization using FOIL multiplication. $$y^{2}+10 y-39$$

Use factoring to solve each quadratic equation. Check by substitution or by using a graphing utility and identifying \(x\) -intercepts. $$x^{2}+9 x=-8$$

Factor each difference of two squares. $$49 y^{4}-16$$

Before getting to multiple-step factorizations, let's be sure that you are comfortable with exercises requiring only one of the factoring techniques. Factor each polynomial. $$6 x^{2}+x-15$$

Factor each polynomial using the greatest common factor. If there is no common factor other than 1 and the polynomial cannot be factored, so state. $$4 y-4$$

Use the method of your choice to factor each trinomial, or state that the trinomial is prime. Check each factorization using FOIL multiplication. $$5 y^{2}-16 y+3$$

Factor each trinomial, or state that the trinomial is prime. Check each factorization using FOIL multiplication. $$y^{2}+5 y-24$$

Use factoring to solve each quadratic equation. Check by substitution or by using a graphing utility and identifying \(x\) -intercepts. $$x^{2}-11 x=-10$$

Factor each difference of two squares. $$49 y^{4}-25$$

Before getting to multiple-step factorizations, let's be sure that you are comfortable with exercises requiring only one of the factoring techniques. Factor each polynomial. $$4 x^{2}-x-5$$

Factor each polynomial using the greatest common factor. If there is no common factor other than 1 and the polynomial cannot be factored, so state. $$5 y-5$$

Use the method of your choice to factor each trinomial, or state that the trinomial is prime. Check each factorization using FOIL multiplication. $$5 y^{2}-8 y+3$$

Factor each trinomial, or state that the trinomial is prime. Check each factorization using FOIL multiplication. $$x^{2}-2 x-15$$

Use factoring to solve each quadratic equation. Check by substitution or by using a graphing utility and identifying \(x\) -intercepts. $$x^{2}+4 x=0$$

Factor each difference of two squares. $$x^{10}-9$$

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. $$5 x^{3}-20 x$$