Chapter 6

Introductory Algebra for College Students · 696 exercises

Problem 17

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. $$5 x+30$$

3 step solution

Problem 17

Use the method of your choice to factor each trinomial, or state that the trinomial is prime. Check each factorization using FOIL multiplication. $$3 x^{2}-17 x+10$$

3 step solution

Problem 18

Factor each trinomial, or state that the trinomial is prime. Check each factorization using FOIL multiplication. $$x^{2}-4 x-5$$

3 step solution

Problem 18

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

4 step solution

Problem 18

Factor each difference of two squares. $$x^{10}-1$$

3 step solution

Problem 18

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. $$4 x^{3}-100 x$$

4 step solution

Problem 18

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. $$10 x+30$$

3 step solution

Problem 18

Use the method of your choice to factor each trinomial, or state that the trinomial is prime. Check each factorization using FOIL multiplication. $$3 x^{2}-25 x-28$$

2 step solution

Problem 19

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

2 step solution

Problem 19

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

4 step solution

Problem 19

Factor each difference of two squares. $$25 x^{2}-16 y^{2}$$

2 step solution

Problem 19

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. $$7 x^{3}+7 x$$

3 step solution

Problem 19

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. $$30 x-12$$

3 step solution

Problem 19

Use the method of your choice to factor each trinomial, or state that the trinomial is prime. Check each factorization using FOIL multiplication. $$6 w^{2}-11 w+4$$

4 step solution

Problem 20

Factor each trinomial, or state that the trinomial is prime. Check each factorization using FOIL multiplication. $$x^{2}-5 x-6$$

2 step solution

Problem 20

Use factoring to solve each quadratic equation. Check by substitution or by using a graphing utility and identifying \(x\) -intercepts. $$x^{2}+3 x=0$$

4 step solution

Problem 20

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

3 step solution

Problem 20

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. $$6 x^{3}+24 x$$

3 step solution

Problem 20

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. $$32 x-24$$

3 step solution

Problem 20

Use the method of your choice to factor each trinomial, or state that the trinomial is prime. Check each factorization using FOIL multiplication. $$6 w^{2}-17 w+12$$

6 step solution

Problem 21

Factor each trinomial, or state that the trinomial is prime. Check each factorization using FOIL multiplication. $$x^{2}+4 x+12$$

3 step solution

Problem 21

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

4 step solution

Problem 21

Factor each difference of two squares. $$x^{4}-y^{10}$$

3 step solution

Problem 21

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. $$5 x^{2}-5 x-30$$

3 step solution

Problem 21

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. $$x^{2}+5 x$$

2 step solution

Problem 21

Use the method of your choice to factor each trinomial, or state that the trinomial is prime. Check each factorization using FOIL multiplication. $$8 x^{2}+33 x+4$$

2 step solution

Problem 22

Factor each trinomial, or state that the trinomial is prime. Check each factorization using FOIL multiplication. $$x^{2}+4 x+5$$

4 step solution

Problem 22

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

4 step solution

Problem 22

Factor each difference of two squares. $$x^{14}-y^{4}$$

3 step solution

Problem 22

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. $$5 x^{2}-15 x-50$$

5 step solution

Problem 22

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. $$x^{2}+6 x$$

3 step solution

Problem 22

Use the method of your choice to factor each trinomial, or state that the trinomial is prime. Check each factorization using FOIL multiplication. $$7 x^{2}+43 x+6$$

4 step solution

Problem 23

Factor each trinomial, or state that the trinomial is prime. Check each factorization using FOIL multiplication. $$y^{2}-16 y+48$$

3 step solution

Problem 23

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

4 step solution

Problem 23

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

3 step solution

Problem 23

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. $$2 x^{4}-162$$

3 step solution

Problem 23

Use the method of your choice to factor each trinomial, or state that the trinomial is prime. Check each factorization using FOIL multiplication. $$5 x^{2}+33 x-14$$

5 step solution

Problem 24

Factor each trinomial, or state that the trinomial is prime. Check each factorization using FOIL multiplication. $$y^{2}-10 y+21$$

3 step solution

Problem 24

Use factoring to solve each quadratic equation. Check by substitution or by using a graphing utility and identifying \(x\) -intercepts. $$3 x^{2}=5 x$$

4 step solution

Problem 24

Factor each difference of two squares. $$x^{4}-1$$

3 step solution

Problem 24

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. $$7 x^{4}-7$$

4 step solution

Problem 24

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. $$20 y^{2}+15$$

3 step solution

Problem 24

Use the method of your choice to factor each trinomial, or state that the trinomial is prime. Check each factorization using FOIL multiplication. $$3 x^{2}+22 x-16$$

4 step solution

Problem 25

Factor each trinomial, or state that the trinomial is prime. Check each factorization using FOIL multiplication. $$x^{2}-3 x+6$$

4 step solution

Problem 25

Use factoring to solve each quadratic equation. Check by substitution or by using a graphing utility and identifying \(x\) -intercepts. $$3 x^{2}=-5 x$$

4 step solution

Problem 25

Factor each difference of two squares. $$16 x^{4}-81$$

3 step solution

Problem 25

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. $$x^{3}+2 x^{2}-9 x-18$$

3 step solution

Problem 25

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. $$14 x^{3}+21 x^{2}$$

4 step solution

Problem 25

Use the method of your choice to factor each trinomial, or state that the trinomial is prime. Check each factorization using FOIL multiplication. $$14 y^{2}+15 y-9$$

3 step solution

Problem 26

Factor each trinomial, or state that the trinomial is prime. Check each factorization using FOIL multiplication. $$x^{2}+4 x-10$$

3 step solution

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