Polynomial Operations - Algebra one

Question

Im have a million assignments to do so I was wondering if you could help me with these, its just a few,, I'll do the other 5 myself. Also please don't use log, we have not learned that yet.

Simplify each expression using addition, subtraction, or multiplication. Be sure to show all work.

1. (4x^2 + 3x + 9) + (6x^2 - 2x + 17)
2. (9x^2 + 6x - 10) - (5x^2 + 2x - 14)
3. (3x + 9) (-2x - 5)
4. (14x + 6) (3x + 1)
5. (-2x - 5) (-3x + 4)

Answer 1

Hi Jules,

Problems 1 & 2 are really an exercise of COMBINING LIKE TERMS....

4x² + 3x + 9 + 6x² - 2x + 17 = (4x² + 6x²) + (3x - 2x) + (9 + 17) = 10x² + x + 26 Ans.

9x² + 6x - 10 - (5x² + 2x - 14)...before combining the like terms, clean up the 2nd term by using the distributive property of multiplication to distribute that (-1) into all the terms of the 2nd group

9x² + 6x - 10 - 5x² - 2x + 14 = (9x² - 5x² ) + (6x - 2x) + (-10 + 14) = 4x² + 4x + 4 Ans.

Problems 3 - 4 require the use of the Distributive Property of Multiplication to simplify. The Distributive Property uses the concept of FOIL in which you apply multiplication to FIRST terms, then the OUTER terms, followed by the INSIDE terms and finally the LAST terms. Remember that accounting of the SIGNS is important and remember the rules of adding, subtracting, and multiplying numbers with the SAME and DIFFERENT signs AND ensure you COMBINE LIKE TERMS.

(3x + 9)(-2x - 5) = (3x)(-2x) + (3x)(-5) + (9)(-2x) + (9)(-5) = -6x² - 15x - 18x - 45 =

Ans. -6x² - 33x - 45

(14x + 6)(3x + 1) = (14x)(3x) + (14x)(1) + (6)(3x) + (6)(1) = 42x² + 14x + 18x + 6 =

Ans. 42x² + 32x + 6

(-2x - 5)(-3x + 4) = (-2x)(-3x) + (-2x)(4) + (-5)(-3x) + (-5)(4) = 6x² -8x + 15x - 20 =

Ans. 6x² + 15x - 20

Hope this helps. Don't be nervous to reach out to a tutor to help you solidify all these math concepts so you can tackle them on your own. Good luck with the rest of your assignment.

Answer 2

combine like terms

4x^2+6x^2 =10x^2

3x-2x = x

9+17= 26

put them altogether

10x^2+x+26