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Practice Questions for Factoring (3.2-3.7) Group Members: Vinoth, Enoch Chan, Kevin Peng, Ramith, Racle, and Sahan.


 * 3.2 Multiplying Binomials**

Find the product. 1. (a+6)(a+7) = (a^2)+(7a)+(6a)+(42) = a^2+13a+42

2.(d+7)(d-6) = (d^2)-(6d)+(7d)-(42) = d^2+d+42

Expand. 3. 3(x+5)(x-5) = (3x+15)(x-5) = (3x^2)-(15x)+(15x)-(75) = 3x^2-75

4. 6-4(x+2)(x+8)-(x+7)(x+8) = (6x+12-4x-8)(x+8)-(x+7)(x+8) = (2x+4)(x-8)-(x^2+8x+7x+56) = (2x+4)(x-8)-(x^2+15x+56) = (2x^2-16x+4x-36)-(x^2+15x+56) = x^2-27x-92

5. A square with a side length of x cm is extended by 5 cm on one side and 10 cm on the other. Show the area of the new shape as a product of two binomials. **(x+5)(x+10)**


 * 3.3 Special Products**

Expand 1. (x+6)^2 = x^2+12x+36

2. (m-6)(m+6) = m^2-36

3. (4a+2)(4a-2) = 4a^2-4

4. Use x=y+3 to write x^2-3x+6 in terms of y. Then, expand and simplfy. **(y+3)^2-3(y+3)+6 = (y^2+6y+9)-(3y+9)+6 = y^2+3y+6**

5. No, it is not possible to have five terms as the product of two binomials because there are only four terms when there are two binomials (two each). 6. An length of an edge of a cube is represent by the expression 2y+4. Write, expand, and simplify an expression for the volume of the cube.
 * (2y+4)^3 =** **[(2y+4)^2](2y+4) = [(4y^2+16y+16)](2y+4) = (8y^3+16y^2+32y^2+64y+32y+64) = 8y^3+48y^2+96y+64**


 * 3.4 Common Factors**

Factor, if possible. 1. 5x+15 = 5(x+3)

2. 4x(a+b)-2(a+b) = (4x-2)(a+b)

3. 12y-15xy-56 is not possible to factor.

4. 24xy-12x+36 = 12(2xy-x+3)


 * 3.5 Factoring Trinomials**

Factor, if possible. 1. m^2+24m+8 a=1 b=sum=24 c=8 product=ac=8 There are no factors of 8 that add to 24, thus, this expression is not possible to factor.

2. 2x^2+6x+4 a=2 b=sum=6 c=4 product=ac=8 The factors of 8 that add up to 6 are 4 and 2. 2x^2+2x+4x+4 = 2x(x+1)+4(x+1) = (2x+4)(x+1)

3. y^2+17y+52 a=1 b=sum=17 c=52 product=ac=52 The factors of 52 that add up to 17 are 13 and 4. y^2+17y+52 = y^2+4y+13y+52 = y(y+4)+13(y+4) = (y+13)(y+4)

4. x^2-27x+72 a=1 b=sum=-27 c=72 product=ac=72 The factors of 72 that add up to -27 are -24 and -3. x^2-24x-3x+72 = x(x-24)-3(x-24) = (x-3)(x-24)

5. The area of a rectangle can be represented by the expression x^2+14x-32. a) Factor the expression. a=1 b=sum=14 c=-32 product=ac=-32 The factors of -32 that add up to 14 are 16 and -2. x^2-2x+16x-32 = x(x-2)+16(x-2) = (x+16)(x-2)

b) A smaller rectangle is 2 unit shorter on each side than the first rectangle. Write a factored expression for the area of the new rectangle.
 * (x+14)(x-4)**


 * 3.6 Factoring Complex Trinomials**

Factor, if possible. 1.2y^2-y-6 a=2 b=sum=-1 c=-6 product=ac=-12 The factors of -12 that add up to -1 are -4 and 3. 2y^2-4y+3y-6 = 2y(y-2)+3(y-2) = (2y+3)(y-2)

2. 10a^2-17a+3 a=10 b=sum=-17 c=3 product=ac=30 The factors of 30 that add up to -17 are -15 and -2. 10a^2-2a-15a+3 = 2a(5a-1)-3(5a-1) = (2a-3)(5a-1)


 * 3.7 Factoring Special Quadratics**

Factor, if possible. 1. 4^2-81y^2 a^2-b^2=(a+b)(a-b) 4^2-81y^2=(4+81y)(4-81y)

2. 9a^2-26a+16 a=9 b=sum=-26 c=16 product=ac=144 The factors of 144 that add up to -26 are -18 and -8. 9a^2-18a-8a+16 = 9a(a-2)-8(a-2) = (9a-8)(a-2)

3. (y+2)^2-9 a^2-b^2=(a+b)(a-b) (y+2)^2-9=(y+2+9)(y+2-9)=(y+11)(y-7)