Adding and Subtracting Polynomials



Adding and Subtracting Polynomials Name

Two basic ideas in this section:

1) Change subtraction problems to addition ones by adding the opposite.

2) Don’t change exponents when combining like terms. You will want to, but try to stop yourself!

Find each sum or difference.

1. (4a - 5) + (3a + 6) 2. (3p2 - 2p + 3) - (p2 - 7p + 7)

3. (7x2 - 8) + (3x2 + 1) 4. (x2 + y2) - (-x2 + y2)

5. 5a2 + 3a2x - 7a3 6. 5x2 - x - 4

(+) 2a2 - 8a2x + 4 (-) 3x2 + 8x - 7

7. 2x + 6y - 3z + 5 8. 11m2n2 + 2mn - 11

4x - 8y + 6z - 1 (-) 5m2n2 - 6mn + 17

(+) x - 3y + 6

9. (5x2 - x - 7) + (2x2 + 3x + 4) 10. (5a + 9b) - (4b + 2a)

11. (5x + 3z) + 9z 12. 6p - (8q + 5p)

13. (5a2x + 3ax2 - 5x) + (2a2x - 5ax2 + 7x)

14. (x3 - 3x2y + 4xy2 + y3) - (7x3 -9x2y + xy2 + y3) 15. (d2 - d + 5) - (-d2 + d + 5)

Find the measure of the third side of each triangle. P is the measure of the perimeter.

16. P = 3x + 3y 17. P = 7x + 2y

Which way to Multiply? Name:______________________

There is really only one way to multiply polynomials and that is by distribution. There are different ways to help with this process. Some of you may like to use arrows, or a box, or FOIL in certain cases, but it is all about the distribution method.

Two very important issues you will face:

1) When multiplying you must add exponents

2) Combining like terms at the end means that the exponents stay the same

Examples:

Monomial(Polynomial) --> Fancy words for “one term” times “many terms”

-2x4 (3x5 + 7x3 – 11x – 4) My recommendation: Use arrows

(Binomial)(Binomial) --> “two term” times “two term” **Lots of choices here folks!**

(-5x + 3)(2x – 9)

arrows: box:

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This is the only type of problem you can do with the FOIL method. It will look very similar to the arrows. FOIL stands for First Outer Inner Last.

F L F L

(-5x + 3)(2x – 9)

O I I O

A special problem for a binomial x binomial is one that will look like this:

(9x – 4)2

Don’t freak out because just as 52 = (5)(5) we have the same thing here:

(9x – 4)2 = (9x – 4)(9x – 4) Just solve how you would like!

Personally, I like the box method. It works out nicely for a problem like this…

(Trinomial)(Polynomial) --> “three terms” times “many terms (4 or more)”

(-x2 + 2x – 4)(6x4 – x3 + 7x2 – 8x + 5)

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Scientific Notation Worksheet Name:________________________

Use 3 numbers for all problems when you represent a number in scientific notation.

Ex: 345,734,122 would be 3.46 x 108

Use the internet to help find these answers: (These answers should be in SN)

1) What is the US national debt?

2) What is the US population?

3) If the national debt were split evenly with everyone what would each person owe?

4) How far is a light year in (a) miles and (b) kilometers?

(a)

(b)

5) How far is the planet Uranus from Earth? (Answer in kilometers)

6) How long would it take to get there in light year?

7) What is (a) a nanometer and (b) a nanosecond?

(a)

(b)

8) Where do these numbers exist? (Real world application)

9) How do you convert numbers into scientific notation? How do you convert from scientific notation to regular (or standard) numbers?

Review Name:_____________________

Solve or simplify the following problems

1) [pic] 2) T = 5x + 2y Solve for y

3) [pic] 4) -2(x + 5) = 3x + 10 – 5x

5) 6m + 14 + 3(3m + 7) 6) 3(7x + 2) + 8x

7) (3x – 4) + (2x2 – x + 7) 8) (9x2 + 3x – 2) – (x2 – 11)

9) (9x + 8) (-7x2 – 3x – 2) 10) (x3y)5 (x-3y4z-6)-4

11) (3.4 x 106)(1.3 x 10-15) 12) 9.1 x 103

4 x 108

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2x + y

3x – 5y

x + y

x + y

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