Group 1 Taivonya Pittman Tysheika Lewis Sh'miyah Bandy 5/25/12

Taivonya Pittman Adding and subtracting polynomials

The prefix “poly” means “many”. So a polynomial is an expression made up of many terms. Remember that a term can be a variable, a number(called a constant), or a variable with a coefficient (a number attached to the front of the variable). For example,x,13,5y are all terms. With either a “+” or a “-” sign you create different types of polynomials.

Adding and subtracting polynomials To add polynomials you simply add any like terms together To subtract Polynomials, first reverse the sign of each term you are subtracting (in other words turn "+" into "-", and "-" into "+"), then add as usual.

Add: -4x 3 +6x 2 -8x-10 and 7x 3 -4x 2 +9x+3 Solution: This time let's see what happens when we put the polynomials inside parentheses. (-4x 3 +6x 2 -8x-10) + (7x 3 -4x 2 +9x+3) To remove the parentheses we must use the distributive property. There is nothing in front of the first parentheses so we can just drop (remove) them. In front of the second parentheses is a "+" sign. When we distribute the sign through the parentheses we multiply each of the signs inside t he parentheses by the "+" sign that is outside and the result is: (-4x 3 +6x 2 -8x-10) + (7x 3 -4x 2 +9x+3) -4x 3 +6x 2 -8x-10+7x 3 -4x 2 +9x+3= 3x 3 +2x 2 +x-7 classification of this polynomial is: cubic trinomial

Subtract: 8a+5b-6c from 10a+8b+7c Solution: We must use parentheses for subtraction! Remember the polynomial after the word "from" is placed first in the subtraction problem. (10a+8b+7c) - (8a+5b-6c) Clear the parentheses by distributing the signs... 10a+8b+7c-8a-5b+6c Then combine the like terms... 10a+8b+7c-8a-5b+6c 2a+3b+13c The classification on this polynomial would be: Linear trinomial

(x 2 +4x+5) + (6x+3)

2(x 4 +5x) -6(x 4 +8x-3) 2x 4 +10x-6x 4 -48x+18 -4x 4 -38x+18

(-8x 2 +13)-(9-2x 2 ) 1(-8x 2 +13)-1(9-2x 2 ) -8x x 2 -6x 2 +4

(3x+5)-(12x-8)+(5x+2) 1(3x+5)-1(12x-8)+1(5x+2) 3x+5-12x+8+5x+2 -4x+15

Tysheika Lewis GCF and factoring by grouping

What is a GCF??  The greatest common factor of 2 or more whole #’s is the Largest Whole Number that divides evenly into each of the numbers. There are Two Ways to find the GCF.  The GCF is the common variable with the smallest exponent.

Factoring by Grouping  Factoring by grouping means that you will group terms with common factors before factoring.

Example 1 (1y 2 + 5y) + (5y + 25) 1y(1y+5) + 5(1y+5) Answer:(y+5)(y+5)

Example 2 (x 2 + 5x) + (3x + 15) 1x(x+15) + 3(1x+5) Answer:(x+5)(x+3)

Example 3 8x 2 – 6x – 12x + 9 (8x 2 – 6x) + (-12x +9) 2x(4x -3) -3(4x -3) Answer:(4x-3)(2x-3)

Example 4 (3a + 1ax) + (3b + 1bx) 1a(3 + x) + 1b(3 + x) Answer:(3 + x)(1a+1b)

Example 5 6a 2 y 2 _ 20b 2 x abxy – 12abxy Answer:(3a 2 y 2 – 10b 2 x 2 + 5abxy – 6abxy)

Example 6 24 – 8a 2 – 30a + 10a 3 24 – 8a + -30a + 10a 3 2(12-4a 2 ) + (-15a + 5a 3 ) 4(3-a 2 ) – 5a(3+a 2 ) Answer:2(3-a)(4-5a)

Remember This Tip Remember The Exponent Rule If You Are Multiplying The Same Base, You Keep The Base And Add The Exponents.

Sh'miyah Bandy Linear Equations

FORMULA FOR FINDING SLOPE The formula is used when you know two points of a line.

Find the slope of the line between the two points (-4, 8) and (10, -4) If it helps label the points. Then use the formula

Correction Y 2 -Y 1 ● ● X 2 -X 1

SLOPE Slope is the ratio of the vertical rise to the horizontal run between any two points on a line. Usually referred to as the rise over run.

SLOPE-INTERCEPT FORM OF A LINE The slope intercept form of a line is y = mx + b, where “ m ” represents the slope of the line and “ b ” represents the y- intercept. When an equation is in slope-intercept form the “y” is always on one side by itself. It can not be more than one y either. If a line is not in slope-intercept form, then we must solve for “y” to get it there.

Quiz 1. 5(2t 2 -5)-4(2t 2 -5)+3(2t 2 -5) a. 8t b. 8t c. 2t d. 8t 2 -60

Quiz 2. 3x-2y=-16 ● A)Y=3/2x+8 ● B)Y=1/2x+4 ● C)Y=2/3x+2 ● D)Y=-2/6x+3 ● 3.Through: (1,2) slope =7 ● A)x+2=2 ● B)7x-y=5 ● C)4X+Y=-3 ● D)5x-3y=0

Quiz 4.25b A.5b(5-7) B.5b(5b-7) C.5(5b 2 -7) D.5(5-7b 2 )