Answer:
12. 26x² + 22x + 25
13. -15x² - 21x - 11
14. x² + 32x + 18
15. [tex]9x^6+6x^5-15x^4+14[/tex]
Step-by-step explanation:
12. To add the polynomials we must combine like terms ( like terms are terms that have the same variable ( represented by a letter ) and the same exponent )
( 19x² + 12x + 12 ) + ( 7x² + 10x + 13 )
19x² and 7x² both have x as a variable and an exponent of 2 which means that they are like terms
Therefore we combine them
19x² + 7x² = 26x²
12x and 10x both have x as a variable and no exponent therefore the are like terms
So we combine them
12 + 10x = 22x
13 and 12 have no variable nor do they have a exponent therefore they are like terms so we combine them
13 + 12 = 25
We would then have 36x² + 22x + 25
None of the terms in the polynomial have the same variable and exponent therefore this is the answer.
We do the same process with 13 -15
13. (4x² - 6x + 7 ) + ( -19x² - 15x - 18 )
4x² - 19x² = -15x²
-6x - 15x = -21x
7 - 18 = -11
-15x² - 21x - 11
14. (20x² + 15x + 13 ) + ( -19x² + 17x + 5 )
20x² -19x² = x²
15x + 17x = 32x
13 + 5 = 18
x² + 32x + 18
15. [tex](9x^6-4x^5)(10x^5-15x^4+14)[/tex]
-4x^4 and 10x^4 are the only like terms so those are the only two numbers we combine
[tex]-4x^5+10x^5=6x^5[/tex]
[tex]9x^6+6x^5-15x^4+14[/tex]
