Adding Polynomials
Simplify:
2(x+3)+(3x-5)
Answer:
5x-1
Simplify:
5(x-4)-(2x+3)
Answer:
3x-23
Solve the following expression:
3x(3x^2+2x+3)
Answer:
9x^3+6x^2+9x
Factor the following expression:
x^2 + 6x
Answer:
x(x + 6)
Simplify:
-4(3x^2-6x+2)+(x+5)
Answer:
-12x^2+25x-3
Simplify:
-5(1+2k)-9(3k-7)
Answer:
-28k+58
Solve the following:
(2x + 5)(x - 3)
Answer:
2x^2 - x - 15
The expression x^2+7x+10 can be written in factored form as (x+5)(x+k). What is the value of k?
Answer:
k=2
Simplify:
(7m^3-2m+8)+(-3m^3+5m-10)
Answer:
4m^3+3m-2
Simplify:
(8p^2-5p+4)-(3p^2+7p-6)
Answer:
5p^2-12p+10
Solve the following:
(-10x+6)(5x+2)
Answer:
-50x^2+10x+12
The expression 2x^2-5x-12 can be written in factored form as (2x+3)(x+k). What is the value of k?
Answer:
k=-4
Simplify:
(5y^4-3y^2+6)+(2y^4-7y^2-11)
Answer:
7y^4-10y^2-5
Samantha is making two rectangular gardens. The area of Garden A is
5x^2+8x+6
and the area of Garden B is
4x^2+3x+2
Find a polynomial representing how much larger Garden A is than Garden B.
Answer:
(5x^2+8x+6)-(4x^2+3x+2)=x^2+5x+4
Marilyn wants to build a pool in her backyard. She measured the length and it was (x - 7) and the width was (3x + 5). What is the area of the pool.
Answer: Area= Length * width
3x^2-16x-35
Factor the following:
3x^2 - 13x - 10
Answer:
(3x + 2)(x - 5)
Alex is buying items for a concert.
The cost of the concert tickets is represented by the polynomial
3x² − 5x − 7.
The cost of drinks at the concert is represented by the polynomial
−7x + 50.
What polynomial represents the total cost of the tickets and drinks?
Answer:
3x^2−12x+43
The height (in meters) of two rockets over time is modeled by polynomials.
Rocket A:
4x^2+7x+9Rocket B:
2x^2−3x+4Find a polynomial that represents how much higher Rocket A is than Rocket B.
Answer:
(4x^2+7x+9)−(2x^2−3x+4) = 2x^2+10x+5
Simplify the following expression.
(2x + 5)(x^2 - 6x + 7)
Answer:
2x^3 - 7x^2 - 16x + 35
Factor the following:
6x^2+11x−10
Answer: (3x−2)(2x+5)