Multiplying Polynomials by Monomials - Examples & Practice
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- (Video) Multiplying a Polynomial by a Monomial by thenewboston This video by thenewboston covers distribution of a monomial over a polynomial. Summary\large{\text{Summary}}Summa…
By Stefan Cuevas, Naomi Burgess, Alex Federspiel, Amy Feraco, Jonathan Heller, Anusha Rahman
- Multiplying polynomials by monomials requires that we exploit the distributive property. Recall that, with the distributive property, we drag the term on the outside of the pare…
By Hannah Bonville, Naomi Burgess, Hadley Killen, Alex Federspiel, Joshua Siktar, Jonathan Heller, Anusha Rahman
- Quick Recap Before we begin there's a couple things we need to recap. First, is multiplying monomials. When we multiply two monomials together, we multiply their coefficients, a…
By Alex Federspiel, Anusha Rahman
Problems 25
- Which of the following expressions equals x3(x2−3x)x^3 ( x^2 - 3x)x3(x2−3x)?
- 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).
- Find the product of x7x^7x7 and x8−5x+2x^8 - 5x + 2x8−5x+2.
- Which of the following expressions are equal to x2yz3+x2y3x^2yz^3 + x^2y^3x2yz3+x2y3?
- Which of the following expressions are equal to x2yz3z4+x2y3x^2yz^3z^4 + x^2y^3x2yz3z4+x2y3?
- Which of the following expressions equals x10(x1/3−3x)x^{10} ( x^{1/3}- 3x)x10(x1/3−3x)?
- Write the expression x10(x3−3)x^{10} ( x^3- 3)x10(x3−3) as a polynomial in standard form.
- 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).
- How do you multiply two terms that contain the same variable?
- Which property allows us to multiply two expressions, so that 2x(3x+6)=6x2+12x2x(3x + 6) = 6x^2 + 12x2x(3x+6)=6x2+12x
- What kind of polynomial results from multiplying a monomial and a trinomial?
- 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?
- Which of the following is not equal to 3x(x−2x2+3x3)3x(x - 2x^2 + 3x^3)3x(x−2x2+3x3)?
- Which of the following products do not equal 3x2+6x43x^2 + 6x^43x2+6x4?
- If a rectangle has a length of 2a2a2a and a width of 3a+43a + 43a+4, what is the area of the rectangle?
- What is the degree of this expression when simplified? 3x3(2x4−3)3x^3(2x^4 - 3)3x3(2x4−3)
- Simplify x(x−1)+2x2(3x+1)x(x - 1) + 2x^2(3x + 1)x(x−1)+2x2(3x+1).
- Expand and simplify the following: (x+2)2×(3x2)(x+2)^2\times (3x^2)(x+2)2×(3x2)
- Expand and simplify: (x2+5)(x3)(x^2+5)(x^3)(x2+5)(x3)
- Solve for xxx. x(x+2)<x(x−5)+10x(x+2)<x(x-5) +10x(x+2)<x(x−5)+10
- Evaluate the following: 6x×(3x+2)6x\times(3x+2)6x×(3x+2)
- Use the Distributive Property to simplify the following expression. x×(3x+4)\sqrt{x}\times(3\sqrt{x}+4)x×(3x+4)
- Simplify the following expression: 1x×(3x2+x)\frac{1}{x}\times(3x^{2}+x)x1×(3x2+x)
- If a backyard has length, l=3x+2l=3x+2l=3x+2 and width, w=9xw=9xw=9x, what is the area of the backyard in terms of xxx?
- Simplify the following expression: (6x)×(4x2+3)(6x) \times (4x^{2}+3)(6x)×(4x2+3)