Algebra 1 Honors Parcc Pack #1

ALGEBRA 1 HONORS PARCC PACK #1

THE JOY OF FACTORING POLYNOMIALS

HOW THIS PACKET WORKS

On the pages that follow, you will be given a series of instructions on how to factor and break down polynomials. You will be graded based on your ability to perform these instructions as accurately as possible.

Here is how this pack will be graded:

NOTES: All the information in BOLD TYPE along with ALL of the examples that are on the front page of each section must LATER ON be copied into your notebook for standard notebook points. WORRY ABOUT THIS AFTER EVERYTHING IS DONE.

PRACTICE QUESTIONS – You will be given a series of Practice Questions after each example that you will complete on that page. You MAY come up to ask for help on these questions if you are not sure what to do. When you are finished with these questions, you MUST show them to me for correction. You will earn HOMEWORK POINTS for completing all the practice questions in a group.

OPEN-ENDED MISSIONS – Yes, there is an open-ended mission involved in this topic. Complete it according to the instructions supplied to receive the points for it.

TEST QUESTIONS – Once your Practice Questions have been checked in, you will then receive a final set of Test Questions based on the entire packet. You MAY NOT ask for help on these questions, now it’s all up to you. You will earn TEST POINTS based on your accuracies.

DUE DATE OF THE ENTIRE PACKET AND THE TEST: FRIDAY APRIL 21

DON’T WASTE TIME!

SECTION 8.3A: FACTORING OUT A SINGLE GREATEST COMMON FACTOR

To be able to do anything in this packet, you have to first know how to find a GREATEST COMMON FACTOR.

The goals of doing this are as follows:

Factor each COMPOSITE NUMBER into a series of PRIME NUMBERS.

• (Prime means it can only be divided by itself and 1, you can’t break it up any further.)
• DON’T IGNORE VARIABLES when factoring.
• GCF’s CAN be negative if the first term of the polynomial is negative.

Identify the GREATEST COMMON FACTOR by finding any factors that belong to EVERY term in the polynomial and MULTIPLY them back together.

• Remember: Use each common factor ONLY ONCE.

DIVIDE each term by that GCF to determine the leftover terms that will remain in the polynomial.

EXAMPLES:

A)GCF = ,

FINAL:

B)GCF = ,

FINAL:

C)GCF =

, ,

FINAL:

ALGEBRA 1 ASSIGNMENT 8.3A (100 POINTS)

Factor each polynomial by extracting the Greatest Common Factor.

1)2)

3)4)

5)

6)

7)

8)

9)

10)

SECTION 8.3B – FACTORING BY GROUPING

OK, this section is the tricky one, but only if you let it. Follow me closely here.

SETUP: You will see FOUR terms in each polynomial.A)

As a group, they do NOT have a GCF.

There ARE, however, GCF’s that we can get for PARTS of the polynomial. So... here’s what we’re going to do.

Split the polynomial into 2 halves, each with 2 terms.

Factor the GCF out of each half.

• IMPORTANT: The leftovers for each pair will ALWAYS MATCH.

(Both leftovers say x + 4, they match)

Regroup the final factors to make TWO sets of parentheses.



1st ( ) = The 2 GCF’s 2nd ( ) = The matching leftovers

B)

FINAL:

C)

FINAL:

D)

FINAL:

ALGEBRA 1 ASSIGNMENT 8.3B (160 POINTS)

Factor each polynomial by grouping the four terms into two pairs with separate GCF’s.

11)12)

13)14)

15)16)

17)18)

SECTION 8.3C – SOLVING FACTORED EQUATIONS

OK, now that you’ve factored, it’s time to bring equations into the mix and actually solve for something.

SETUP: A polynomial based on one variable that is set = 0.A)

Factor the polynomial using a GCF.

Set each monomial & binomial = 0.

• WHY? Because for the entire polynomial to = 0, at least ONE of its factored pieces has to = 0.

Solve each factor for the value of the variable.

x + 6 = 0

- 6 - 6

x = -6

FINAL SOLUTIONS:x = 0 or -6

B)2x = 05x + 6 = 0

2 2 - 6 - 6

x = 05x = -6

5 5

C)x + 3 = 0x + 2 = 0

- 3 - 3 - 2 - 2

x = -3x = -2

If needed, cancel ALL terms to one side so that you can SEE an = 0.

D)3x = 0x – 5 = 0

-15x -15x3 3 + 5 + 5

x = 0x = 5

ALGEBRA 1 ASSIGNMENT 8.3C (100 POINTS)

Factor (if needed) each binomial using the GCF, then solve each factor for the value of the variable. Be sure the equation is set equal to 0 before you factor.

19)20)

21)22)

23)24)

25)26)

27)28)

OPEN-ENDED QUESTION – This is the open-ended question that will appear on the next test. Complete it here for 3 rubric points to maintain your Open-Ended grade.

You are making fruit baskets to sell to friends, family, etc. Your mix consists of apples and pears from the trees you have in your backyard. (Your own fresh fruit, wish we all had that.)

This year, your trees gave you 126 apples to pick, and 72 pears. Using these, each basket will contain the same number of apples, and the same number of pears.

Find the GCF to tell you how many fruit baskets you can make from this batch of fruit. Then, use the remaining factors of each to tell you how many apples and pears will be in each basket.

(EX: If you had 60 apples & 75 pears, you could make 15 baskets, each with 4 apples & 5 pears.)

According to the supermarkets that you visit, apples cost $0.25 each, and pears cost $0.35 each. In addition, you also have to spend $1.50 for each basket, the fake straw, etc, that you’re using to package the fruit.

Calculate the total cost of making ONE fruit basket based on these numbers and the number of each fruit you got from the last question.

Now that you know how much each basket costs, you have to sell it at a profit. For this situation, you want to make 30% profit.

Multiply the cost from the last question by 30%, and add it to the cost to find your selling price. Round your answer UP to the next dime. (So if you got $5.43, round it up to $5.50.)