Section 1
Introduction to Factoring
Give the prime factorization of each number and determine the GCF.$$\text { 18, } 24$$
Give the prime factorization of each number and determine the GCF.$$45,75$$
Give the prime factorization of each number and determine the GCF.$$72,60$$
Give the prime factorization of each number and determine the GCF.$$168,175$$
Give the prime factorization of each number and determine the GCF.$$144,245$$
Give the prime factorization of each number and determine the GCF.$$15,50,60$$
Give the prime factorization of each number and determine the GCF.$$14,63,70$$
Give the prime factorization of each number and determine the GCF.$$12,48,125$$
Give the prime factorization of each number and determine the GCF.$$60,72,900$$
Give the prime factorization of each number and determine the GCF.$$252,336,360$$
Determine the GCF of all the terms.$$15 x, 30$$
Determine the GCF of all the terms.$$14 x, 21$$
Determine the GCF of all the terms.$$45 x 4,8 x 3$$
Determine the GCF of all the terms.$$36 \times 5,35 y 2$$
Determine the GCF of all the terms.$$6 x, 27 x, 36 x$$
Determine the GCF of all the terms.$$12 x 3,4 x 2,6 x$$
Determine the GCF of all the terms.$$12 x 2 y, 60 x y 3$$
Determine the GCF of all the terms.$$7 a b 2,2 a 2 b, 3 a 3 b 3$$
Determine the GCF of all the terms.$$6 a 2 b 2,18 a 3 b 2,9 a b 2$$
Determine the GCF of all the terms.$$15 x(x+2), 9(x+2)$$
Determine the GCF of all the terms.$$20 x(2 x-1), 16(2 x-1)$$
Determine the GCF of all the terms.$$20 x 3(x+y) 5,10 x 5(x+y) 2$$
Given the GCF, determine the missing factor.$$25 x 2+10 x=5 x(?)$$
Given the GCF, determine the missing factor.$$12 y 5+7 y 2=y 2(?)$$
Given the GCF, determine the missing factor.$$22 x 4-121 x 2+11 x=11 x(\quad ? \quad)$$
Given the GCF, determine the missing factor.$$30 y 3-45 y 2-3 y=3 y(\quad ? \quad)$$
Given the GCF, determine the missing factor.$$36 a 5 b 7-60 a 6 b 5=12 a 5 b 5(?)$$
Given the GCF, determine the missing factor.$$24 x 2 y+48 x y 2-12 x y=12 x y(\quad ? \quad)$$
Factor out the GCF.$$4 x-8$$
Factor out the GCF.$$27 x-9$$
Factor out the GCF.$$3 x-18$$
Factor out the GCF.$$5 x-10$$
Factor out the GCF.$$25 x-16$$
Factor out the GCF.$$72 x-35$$
Factor out the GCF.$$15 x 2+30 x$$
Factor out the GCF.$$14 a_{2}-7 a$$
Factor out the GCF.$$30 a 5-10 a 2$$
Factor out the GCF.$$8 x 4-16 x 2$$
Factor out the GCF.$$5 x 6+x 3$$
Factor out the GCF.$$3 x 7-9 x 5$$
Factor out the GCF.$$18 a_{2}+30 a-6$$
Factor out the GCF.$$24 a_{2}-36 a-12$$
Factor out the GCF.$$27 x 3-6 x 2+3 x$$
Factor out the GCF.$$8 x 3-12 x 2+2 x$$
Factor out the GCF.$$9 x 4+18 x 3-3 x 2$$
Factor out the GCF.$$12 y 4-16 y 3+20 y 2$$
Factor out the GCF.$$7 x 5-21 x 3-14 x_{2}+28 x$$
Factor out the GCF.$$36 y 10+12 y 8-18 y-6 y 3$$
Factor out the GCF.$$12 x 5 y 2-8 x 3 y$$
Factor out the GCF.$$125 a 8 b 4 c 3-25 a 2 b 3 c 3$$
Factor out the GCF.$$6 x 4 y 3-4 x 3 y_{2}+8 x 2 y$$
Factor out the GCF.$$15 x 4 y 2-30 x 3 y 3+15 x 2 y 4$$
Factor out the GCF.$$81 x 7 y 6 z 2-18 x 2 y 8 z 4+9 x 2 y 5 z 2$$
Factor out the GCF.$$4 x 5 y 4 z 9+26 x 5 y 3 z 4-14 x 6 y 8 z 5$$
Factor out the GCF.$$2 x(x-3)+5(x-3)$$
Factor out the GCF.$$3 x(2 x+1)-4(2 x+1)$$
Factor out the GCF.$$5 x(5 x+2)-(5 x+2)$$
Factor out the GCF.$$2 x(3 x+4)+(3 x+4)$$
Factor out the GCF.$$x 2(4 x-7)-5(4 x-7)$$
Factor out the GCF.$$(x+6)-3 x 2(x+6)$$
Factor out the GCF.$$(a+b) 2-3 a(a+b) 2$$
Factor out the GCF.$$(a b+2) 3+3 a b(a b+2) 3$$
Factor out the GCF.$$7 x(x+7) 5+14 x 2(x+7) 5$$
Factor out the GCF.$$36 x 5(3 x+2) 4-12 x 3(3 x+2) 4$$
Are the following factored correctly? Check by multiplying.$$4 x 2-16 x=4 x(x-4)$$
Are the following factored correctly? Check by multiplying.$$3 a 3-3 a=3 a(a 2)$$
Are the following factored correctly? Check by multiplying.$$3 x 3-5 x 6=x 3(3-x 2)$$
Are the following factored correctly? Check by multiplying.$$5 x 3-10 x 4+15 x 5=5 x 3(1-2 x+3 x 2)$$
Are the following factored correctly? Check by multiplying.$$x 3-x 2+x=x(x 2-x)$$
Are the following factored correctly? Check by multiplying.$$12 x 4 y 3-16 x 5 y 2+8 x 6 y 7=4 x 4 y 2(3 y-4 x+2 x 2 y 5)$$
Use polynomial long division to show that the given factor divides the polynomial evenly.Show that $(x-1)$ is a factor of $(2 x 3-5 x 2+4 x-1)$.
Use polynomial long division to show that the given factor divides the polynomial evenly.Show that $(x+3)$ is a factor of $(3 x 3+7 x 2-4 x+6) .$
Use polynomial long division to show that the given factor divides the polynomial evenly.Show that $(3 x-2)$ is a factor of $(3 x 3+4 x 2-7 x+2)$
Use polynomial long division to show that the given factor divides the polynomial evenly.Show that $(2 x+1)$ is a factor of $(2 x 3-5 x 2+x+2)$.
The height in feet of an object tossed into the air is given by the function $h(t)=-16 t 2+32 t$, where $t$ is the time in seconds after it is tossed. Write the function in factored form.
The height in feet of an object dropped from a 16 -foot ladder is given by the function $h(t)=-16 t 2+16,$ where $t$ is the time in seconds after it is tossed. Write the function in factored form.
The surface area of a cylinder is given by the formula $S A=2 \pi r 2+2 \pi r h,$ where $r$ represents the radius of the base and $h$ is the height of the cylinder. Express this formula in factored form.
The surface area of a cone is given by the formula $S A=\pi r 2+\pi r s,$ where $r$ represents the radius of the base and $s$ represents the slant height. Express this formula in factored form.
Factor by grouping.$$x 2-10 x+2 x-20$$
Factor by grouping.$$x 2-6 x-3 x+18$$
Factor by grouping.$$x 3+2 x 2+2 x+4$$
Factor by grouping.$$x 3-3 x 2+5 x-15$$
Factor by grouping.$$x 3+7 x 2-2 x-14$$
Factor by grouping.$$2 x 3+2 x 2-x-1$$
Factor by grouping.$$x 3-5 x 2+4 x-20$$
Factor by grouping.$$6 x 3-3 x 2+2 x-1$$
Factor by grouping.$$9 x 3-6 x 2-3 x+2$$
Factor by grouping.$$2 x 4-x 3-6 x+3$$
Factor by grouping.$$x 5+x 3+2 x 2+2$$
Factor by grouping.$$6 x 5-4 x 3-9 x 2+6$$
Factor by grouping.$$3 a 3 b+3 a b 2+2 a 2+2 b$$
Factor by grouping.$$2 a 3+2 a b 3-3 a 2 b-3 b 4$$
Factor by grouping.$$2 a 3-a 2 b 2-2 a b+b 3$$
Factor by grouping.$$a 4-3 a 3 b 2+a b 2-3 b 4$$
Factor by grouping.$$3 a 2 b 4-6 b 3-a 2 b+2$$
Factor by grouping.$$3 x 3+2 y 3+x 3 y 3+6$$
Factor by grouping.$$-3 x 3-5 y 3+x 3 y 3+15$$
Factor by grouping.$$2 x 3 y 3+2-y 3-4 x 3$$
Factor by grouping.$$3 x 2-y 3+x y 2-3 x y$$
Factor by grouping.$$2 x 2+y 3-2 x y-x y 2$$
Factor out the GCF first and then factor by grouping.$$5 x 2-35 x-15 x+105$$
Factor out the GCF first and then factor by grouping.$$12 x 2-30 x-12 x+30$$
Factor out the GCF first and then factor by grouping.$$2 x 3+6 x 2-10 x-30$$
Factor out the GCF first and then factor by grouping.$$6 x 3-3 x 2-42 x+21$$
Factor out the GCF first and then factor by grouping.$$4 x 4+4 x 3-12 x 2-12 x$$
Factor out the GCF first and then factor by grouping.$$-9 x 4+6 x 3-45 x 2+30 x$$
Factor out the GCF first and then factor by grouping.$$-12 x 5+4 x 4+6 x 3-2 x 2$$
Factor out the GCF first and then factor by grouping.$$24 x 5-36 x 4+8 x 3-12 x 2$$
Factor out the GCF first and then factor by grouping.$$24 a 3 b 2-60 a 3 b+40 a b 2-100 a b$$
Factor out the GCF first and then factor by grouping.$$a 4 b 2-2 a 3 b 3+a 2 b 3-2 a b 4$$
Research the Euclidean algorithm for finding the GCF of two natural numbers. Give an example that illustrates the steps.
Research and discuss the contributions of Euclid of Alexandria.
Explain what factoring is and give an example.
Is $5 x(x+2)-3(x+2)$ fully factored? Explain.
Make up a factoring problem of your own and provide the answer. Post the problem and the solution on the discussion board.