Part 1: Distribution and FOILing Name __________________

Multiply the following monomial by the polynomial:

1. 4x(2 2x - x + 7)

2. 1

22s t(4 2t - 10 st + 6 2s )

First, Outer, Inner, Last

2x2 + 8x + -3x + -12 =

2x2 + 5x - 12

Multiply the following binomials:

3. (w – 3)(w + 5)

4. (4x + 7)(x + 2)

5. (4y – 3)(3y + 1)

6. (2f + 8 2)

7. (7m - 3 2)

8. (h + 2

3)(h -

2

3)

Multiply the binomial by the polynomial:

9. (x – 4)( 2x + 2x – 10)

10. (-3y + 3)(- 2y + 5y – 3)

Part 2: Factoring

Factoring is the opposite of multiplication (distribution) and FOILing. You should always start by

factoring out the Greatest Common Factor (GCF). It is the biggest number/letter that is a multiple of all

the terms.

Example: Factor by the GCF

Factor the following questions using the GCF:

Example: Factoring a trinomial with an x2 leading.

Factor the following completely; if the polynomial is prime (not factorable), say so

Example: Factoring a trinomial with a 3x2 leading.

Example: Difference of squares.

Factor the following completely; if the polynomial is prime (not factorable), say so.

Factor the following completely; if the polynomial is prime, say so. (Hint: Start with the GCF)

Part 3: Systems of Equations

Solving a system of equations means find all points of intersection. If there are only two equations, then

there is one point of intersection. There are three methods used for finding the point of intersection of

a system of two equations: graphing, elimination, and substitution.

Graphing Method: Graph each equation and locate the point of intersection.

Example: 4x + 2y = 6

x – y = 3

Step 1: Each equation must be written in y = mx + b form. Solve for y.

4x + 2y = 6 x – y = 3

-4x - 4x -x -x

2y = -4x + 6 -y = -x + 3

2 2 -1 -1

y = -2x + 3 y = x - 3

m =

m =

b = 3 b = -3

Step 2: Graph equation.

y = -2x + 3 y = x - 3

m =

m =

b = 3 b = -3

Start by plotting the y-intercept (b) on the y-axis.

Then from that point count for the slope:

m =

means down 2, right 1

m =

means down 1, right 1

Step 3: Locate the point of intersection.

Solve the system of equations by the graphing method.

51. 3x + y = 4

x – 2y = 6

52. y – x = 4

y = 3x + 2

53. x + y = 1

5x + y = -7

Elimination Method: Add the two equations together so that one variable cancels out and

solve for the remaining variable. Then substitute the first answer back in and solve for the other

variable.

Example 1: 5x + 3y = 8

8x – 3y = 18

Step 1: Notice that the y-terms are exact opposites. This means that they are set up to cancel

out. Add the two equations together.

Step 2: Substitute the x back into one of the equations and solve for y.

Step 3: State the coordinates of the point of intersection.

Example 2: 2x – 5y = 1

3x – 4y = -2

Step 1: Notice that no terms are opposites. Choose either the x or y terms to eliminate and

cancel. For this example, the x terms are chosen. Multiply each equation by a number that will

change the x terms to be exact opposites. (This should be the least common multiple.) Once of

them should be positive and one should be negative.

Step 2: Now add the two equations together and solve for y. (The x terms should cancel out.)

Step 3: Substitute y = -1 back into one of the equations and solve for x.

Step 4: State the coordinates of the point of intersection.

Substitution Method: Solve one equation for either x or y and substitute it into the other equation.

This should result in an equation in terms of only one variable. Solve this equation and then substitute

the answer back into one of the equations to solve for the second variable.

Example 1: x + 2y = 8

2x + 3y = 23

Step 1: Solve one of the equations for either x or y. Look for a variable that has a coefficient of

1 in front. If there is no variable with a coefficient of 1, then look for one that has a

smaller/easier number in front to make any resulting fractions easier.

Step 2: Substitute this equation into the other equation.

Step 3: Solve for y.

Step 4: Substitute y = -7 back into one of the equations and solve for x.

Step 5: Write the coordinates of the point of intersection.

Example 2: 9x + 2y = 2

21x + 6y = 4

Step 1: Solve one equation for either x or y. For this problem, y is chosen in the first equation.

Step 2: Substitute this new equation into the second equation and solve for x. Be sure that you

are not substituting back into the same equation that you started with!

Step 3: Substitute x = into one of the equations and solve for y.

Step 4: State the coordinates of the point of intersection.

Solve the equation by the elimination method.

54. 4x + 15y = 10

3x + 10y = 5

Solve the equation by the substitution method.

55. 5x – y = 1

3x + y = 1

Solve the equation by the method of your choice.

56. 3x + 5y = 14

2x – y = -1

57. 4x + 3y = 1

6x – 2y = 21

58. 3x – 2y = 1

4y = 7 + 3x

59. 3x + 4y = -25

2x – 3y = 6

60.