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