Operations on Polynomial Functions
Read this topicExplanations 4
- Polynomials are the functions we can write in terms of addition and multiplication (of real numbers and variables). For now, we'll stick to polynomials with only one variable. B…
By Misha Lavrov, Expii Team, Moor Xu, Victor Wang, Anusha Rahman
- Adding and subtracting polynomials It turns out that polynomials are like numbers, and we can do arithmetic with them! Let's start with addition of polynomials. If you have two …
By Moor Xu
- (Video) Adding, Subtracting, Multiplying, and Simplifying Polynomials - Part 2 by PatrickJMT Patrick JMT has a good video explaining how to subtract polynomials (complete with a…
By Ben Ferrara, Naomi Burgess, Alex Federspiel, Anusha Rahman
- Function Operations Just like we can add, subtract, and multiply polynomials, we can do the same with polynomial functions. A function is a rule that takes an input, does someth…
By Anusha Rahman
Problems 28
- (7x3−6)(5x2+6x)=?(7x^3 - 6)(5x^2 + 6x) = ?(7x3−6)(5x2+6x)=?
- Suppose f(x)=x2+5x+12f(x)= x^2+5x+12f(x)=x2+5x+12 and g(x)=12x2+10x+4g(x)=12x^2+10x+4g(x)=12x2+10x+4. Which of the answer choices is (f−g)(x)(f-g)(x)(f−g)(x)?
- The sum of x2+x+1x^2 + x + 1x2+x+1 and 3x2−2x+43x^2 - 2x + 43x2−2x+4 is a polynomial. What is the value of this polynomial when x=1x=1x=1?
- Find the sum of the following three polynomials: 2+x32 + x^32+x3 x2−xx^2 - xx2−x x3+x2+1x^3 + x^2 + 1x3+x2+1
- Let f(x)=x2−2xf(x) = x^2 - 2xf(x)=x2−2x and let g(x)=2x2−3xg(x) = 2x^2 - 3xg(x)=2x2−3x. Find f(x)−g(x)f(x) - g(x)f(x)−g(x).
- Let f(x)=x2+2x+3f(x) = x^2 + 2x + 3f(x)=x2+2x+3 and let g(x)=2x+x2−5g(x) = 2x + x^2 - 5g(x)=2x+x2−5. What is f(x)−g(x)f(x) - g(x)f(x)−g(x)?
- Simplify the following expression. (5+x2)−(3−x3)= ?(5 + x^2) - (3 - x^3) = \,?(5+x2)−(3−x3)=?
- If f(x)=x3+2x2+1f(x) = x^3 + 2x^2 + 1f(x)=x3+2x2+1 and g(x)=xg(x) = xg(x)=x, find f(x)g(x)f(x) g(x)f(x)g(x).
- Suppose that f(a,b,c)=a2bcf(a,b,c) = a^2bcf(a,b,c)=a2bc and g(a,b,c)=a3+b2+cg(a,b,c) = a^3 + b^2 + cg(a,b,c)=a3+b2+c. Find f(a,b,c)g(a,b,c)f(a,b,c) g(a,b,c)f(a,b,c)g(a,b,c).
- Find the sum of the following three polynomials: 3+x3+x3 + x^3 + x3+x3+x 2x2−x2x^2 - x2x2−x 2x3+x2+32x^3 + x^2 + 32x3+x2+3
- Simplify the following expression: (6+x2)−(10−x3)(6+ x^2) - (10 - x^3)(6+x2)−(10−x3)
- If f(x)=x4+2x2+1f(x) = x^4 + 2x^2 + 1f(x)=x4+2x2+1 and g(x)=x2g(x) = x^2g(x)=x2, find f(x)g(x)f(x) g(x)f(x)g(x).
- Expand PQPQPQ, where P=x2−3xP = x^2 - 3xP=x2−3x and Q=−2x2+4xQ = -2x^2 + 4xQ=−2x2+4x.
- Expand the product PQPQPQ, where P=x+1P = x+1P=x+1 and Q=x2+10x−1Q = x^2 + 10x - 1Q=x2+10x−1.
- Compute 1352135^21352.
- (2n+2)(6n+1)=?(2n + 2)(6n + 1) = ?(2n+2)(6n+1)=?
- (x−3)(6x−2)=?(x - 3)(6x - 2) = ?(x−3)(6x−2)=?
- (6p+8)(5p−8)=?(6p + 8)(5p - 8) = ?(6p+8)(5p−8)=?
- (4a+2)(6a2−a)=?(4a + 2)(6a^2 - a) = ?(4a+2)(6a2−a)=?
- (7k−3)(k2+7)=?(7k - 3)(k^2 + 7) = ?(7k−3)(k2+7)=?
- (6n2−6n)(7n2−5)=?(6n^2 - 6n)(7n^2 - 5) = ?(6n2−6n)(7n2−5)=?
- (m2−6)(7m2−3)=?(m^2 - 6)(7m^2 - 3) = ?(m2−6)(7m2−3)=?
- (8p3−2)(6p+2)=?(8p^3 - 2)(6p + 2) = ?(8p3−2)(6p+2)=?
- If f(x)=4x3−3x2+2f(x) = 4x^3 - 3x^2 + 2f(x)=4x3−3x2+2 and g(x)=6x7−x3+xg(x) = 6x^7 - x^3 + xg(x)=6x7−x3+x, what is f(x)−g(x)f(x) - g(x)f(x)−g(x)?
- Evaluate 1152.115^2.1152. Write your answer without commas or spaces.
- Let f(x)=2xf(x) = 2xf(x)=2x and g(x)=3−2xg(x) = 3 - 2xg(x)=3−2x. If h(x)=f(x)×g(x)h(x) = f(x)\times g(x)h(x)=f(x)×g(x), what is h(x)h(x)h(x) when x=1x=1x=1?
- If f(x)=3x+2f(x) = 3x + 2f(x)=3x+2, and g(x)=7x−1g(x) = 7x - 1g(x)=7x−1, what is (f∗g)(2)(f*g)(2)(f∗g)(2)?
- If f(x,y)=x2−y,g(x,y)=3y+2xf(x, y) = x^2 - y, g(x, y) = 3y + 2xf(x,y)=x2−y,g(x,y)=3y+2x, and h(x,y)=f(x,y)∗g(x,y)h(x, y) = f(x, y)*g(x, y)h(x,y)=f(x,y)∗g(x,y), what is h(1,2)h(1…