Chapter 6

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. $$2 y^{3}+3 y^{2}-50 y-75$$

Use the negative of the greatest common factor to factor completely. $$-5 x^{2}+50 x-45$$

Factor by grouping. $$x^{2}+2 x+4 x+8$$

Factor completely. $$9 x^{3}+6 x^{2}+x$$

Factor completely. $$2 x^{3}-3 x^{2}-5 x$$

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. $$12 y^{3}+16 y^{2}-3 y-4$$

Use the negative of the greatest common factor to factor completely. $$-3 x^{2}+36 x-33$$

An explosion causes debris to rise vertically with an initial speed of 72 feet per second. The formula $$h=-16 t^{2}+72 t$$ describes the height of the debris above the ground, \(h\), in feet, t seconds after the explosion. Use this information to solve Exercises \(70-71\) How long will it take for the debris to hit the ground?

Factor by grouping. $$x^{2}+3 x+5 x+15$$

Factor completely. $$25 x^{3}-10 x^{2}+x$$

Factor completely. $$6 x^{3}+4 x^{2}-10 x$$

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. $$2 r^{3}+30 r^{2}-68 r$$

Use the negative of the greatest common factor to factor completely. $$-x^{2}-3 x+40$$

Factor by grouping. $$x^{2}+3 x-5 x-15$$

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

Factor completely. $$9 y^{3}-39 y^{2}+12 y$$

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. $$3 r^{3}-27 r^{2}-210 r$$

Use the negative of the greatest common factor to factor completely. $$-x^{2}-4 x+45$$

Factor by grouping. $$x^{2}+7 x-4 x-28$$

Factor completely. $$2 y^{2}-40 y+200$$

Factor completely. $$10 y^{3}+12 y^{2}+2 y$$

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. $$8 x^{5}-2 x^{3}$$

Use the negative of the greatest common factor to factor completely. $$-2 x^{3}-6 x^{2}+8 x$$

Factor by grouping. $$x^{3}-2 x^{2}+5 x-10$$

Factor completely. $$2 y^{3}+28 y^{2}+98 y$$

Factor completely. $$60 z^{3}+40 z^{2}+5 z$$

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. $$y^{9}-y^{5}$$

Factor by grouping. $$x^{3}-3 x^{2}+4 x-12$$

Factor completely. $$50 y^{3}+20 y^{2}+2 y$$

Factor completely. $$80 z^{3}+80 z^{2}-60 z$$

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. $$3 x^{2}+243$$

Factor completely. $$2 x^{2} y^{2}-32 x^{2} y z+30 x^{2} z^{2}$$

Factor completely. $$-6 x^{2}+24 x-24$$

Factor by grouping. $$x^{3}-x^{2}+2 x-2$$

Factor completely. $$15 x^{4}-39 x^{3}+18 x^{2}$$

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. $$27 x^{2}+75$$

Factor completely. $$2 x^{2} y^{2}-30 x^{2} y z+28 x^{2} z^{2}$$

The alligator, at one time an endangered species, is the subject of a protection program. The formula $$P=-10 x^{2}+475 x+3500$$ models the alligator population, \(P,\) after \(x\) years of the protection program, where \(0 \leq x \leq 12 .\) Use the formula to solve Exercises \(76-77\) After how long is the population up to \(5990 ?\)

Factor completely. $$-5 x^{2}+30 x-45$$

Factor by grouping. $$x^{3}+6 x^{2}-2 x-12$$

Factor completely. $$24 x^{4}+10 x^{3}-4 x^{2}$$

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. $$x^{4}+8 x$$

Factor completely. $$(a+b) x^{2}+(a+b) x-20(a+b)$$

The alligator, at one time an endangered species, is the subject of a protection program. The formula $$P=-10 x^{2}+475 x+3500$$ models the alligator population, \(P,\) after \(x\) years of the protection program, where \(0 \leq x \leq 12 .\) Use the formula to solve Exercises \(76-77\) After how long is the population up to \(7250 ?\)

Factor completely. $$-16 y^{3}-16 y^{2}-4 y$$

Factor by grouping. $$x y+5 x+9 y+45$$

Factor completely. $$10 x^{5}-17 x^{4}+3 x^{3}$$

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. $$x^{4}+27 x$$

Factor completely. $$(a+b) x^{2}-13(a+b) x+36(a+b)$$

Factor completely. $$-45 y^{3}-30 y^{2}-5 y$$