Subtracting Polynomials - Process & Examples
Read this topicExplanations 3
- While solving equations, it often comes in handy to be able to subtract polynomials. Let us begin with an example: 8x3+54x2−23x+4=4x3−6x2+19x−178x^3+54x^2-23x+4=4x^3-6x^2+19x-17…
By Antoine Ego, Moor Xu, Naomi Burgess, Amy Feraco, Anusha Rahman
- (Video) Adding and Subtracting Polynomials by PatrickJMT This video by PatrickJMT shows how you subtract and add polynomials. Summary\large{\text{Summary}}Summary First, we need…
By Stefan Cuevas, Naomi Burgess, Alex Federspiel, Amy Feraco, Jonathan Heller, Caroline K, Anusha Rahman
- Subtracting Polynomials First, let's subtract the coefficients of terms with the same exponents. Be careful when distributing the "-" sign through each polynomial in the equatio…
By Hannah Bonville, Naomi Burgess, Po-Shen Loh, Alex Federspiel, Jonathan Heller, Anusha Rahman
Problems 30
- Simplify (8x3+3x2+x+3)−(5x3+3x−2)(8x^3 + 3x^2 + x +3)-(5x^3 + 3x -2)(8x3+3x2+x+3)−(5x3+3x−2).
- Simplify the following expression: (9x2−3y+z3)−(17y+12z3−2x2)(9x^2-3y+z^3) - (17y+12z^3-2x^2)(9x2−3y+z3)−(17y+12z3−2x2)
- 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)=?
- Simplify the following expression: (6+x2)−(10−x3)(6+ x^2) - (10 - x^3)(6+x2)−(10−x3)
- Let f(x)=x3−3xf(x) = x^3 - 3xf(x)=x3−3x and let g(x)=10x2−8xg(x) = 10x^2 - 8xg(x)=10x2−8x. Find f(x)−g(x)f(x) - g(x)f(x)−g(x).
- Simplify −3(−5x2−4x+6)−10(2x2+x+4).-3(-5x^2-4x+6)-10(2x^2+x+4).−3(−5x2−4x+6)−10(2x2+x+4).
- Simplify (x−2)−(8x2+9x−2).(x-2)-(8x^2+9x-2).(x−2)−(8x2+9x−2).
- Simplify 0.8(5x2+9x−4)−0.9(0.4x2+3x−8)0.8(5x^2+9x-4)-0.9(0.4x^2+3x-8)0.8(5x2+9x−4)−0.9(0.4x2+3x−8)
- (x+2)3−(x3+2)(x+2)^3 - (x^3 + 2)(x+2)3−(x3+2) is a nonzero polynomial. What is its degree?
- (x+2)3−(x3+2)(x+2)^3 - (x^3 + 2)(x+2)3−(x3+2) is a nonzero polynomial. What is its leading coefficient?
- Simplify: (x2x−1+2x2−4x−1)−[−(3x2+4x−2)]\left(x^{2x-1}+2x^2-4x-1\right)-\left[-\left(3x^2+4x-2\right)\right](x2x−1+2x2−4x−1)−[−(3x2+4x−2)]
- Subtract the polynomials. (4x2−2x+3)−(x3+x2−1)(4x^2 - 2x + 3) - (x^3 + x^2 - 1)(4x2−2x+3)−(x3+x2−1)
- Simplify (a2−2ab+b2)−(3a2+ab+2b2)(a^2 - 2ab + b^2) - (3a^2 + ab + 2b^2)(a2−2ab+b2)−(3a2+ab+2b2).
- When simplified, how many terms will the following expression have? (x3+x2−3x+1)−(x2+2x+5)(x^3 + x^2 - 3x + 1) - (x^2 + 2x + 5)(x3+x2−3x+1)−(x2+2x+5)
- Which of the following describes this expression, after simplification? (x3−2x2+x−1)−(x3+2x2−3)(x^3 - 2x^2 + x - 1) - (x^3 + 2x^2 - 3)(x3−2x2+x−1)−(x3+2x2−3)
- Which of the following is equal to (x4−1)−(2x3+4x−2)(x^4 - 1) - (2x^3 + 4x - 2)(x4−1)−(2x3+4x−2)?
- What's another way we can think of subtracting polynomials?
- Lauren and Skyler find 2x2+3x+42x^2 + 3x + 42x2+3x+4 sea shells at the beach. If Lauren found x2−3x^2 - 3x2−3 of them, how many did Skyler find?
- What is (4x3+3x4−2x2)−(−x2+3x+7x3)(4x^3 + 3x^4 - 2x^2) - (-x^2 + 3x + 7x^3)(4x3+3x4−2x2)−(−x2+3x+7x3) in standard form?
- Which of the following equations is equivalent to the following? x4−3x2+2=2x2−1x^4 - 3x^2 + 2 = 2x^2 - 1x4−3x2+2=2x2−1
- A triangle has a perimeter of 4x+74x + 74x+7 inches. If side A has length 2x+42x + 42x+4 in, and side B has length x+1x + 1x+1 in, what is the length of side C?
- Simplify (3x2+x−1)−(2x−3)−(2x2+2)(3x^2 + x - 1) - (2x - 3) - (2x^2 + 2)(3x2+x−1)−(2x−3)−(2x2+2).
- After simplification, how many terms are in the following expression? (32+2x−1)−4\left(3^2+2x-1\right)-\sqrt{4}(32+2x−1)−4
- What is (3x+8y)−(3x−2y)(3x + 8y) - (3x - 2y)(3x+8y)−(3x−2y)?
- Subtract the following polynomials: 4x3+2x2+1x+9−2x3+2x2+2x−9\begin{align}\\ 4x^{3}+2x^{2}+1x&+9\\ -2x^{3}+2x^{2}+2x&-9\\ \end{align}4x3+2x2+1x−2x3+2x2+2x+9−9
- A Sea Life Rehabilitation Center has 8x+148x+148x+14 dolphins in captivity. After 6 months of rehabilitation, 3x−43x-43x−4 dolphins are released back into the wild. How many dol…
- Subtract the following binomials: (6x−4)−(−2x−8)(6x-4)-(-2x-8)(6x−4)−(−2x−8)
- Subtract the two binomials: (5x−9)−(−1x+7)(5x-9)-(-1x+7)(5x−9)−(−1x+7)