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Algebra

Polynomial Arithmetic

Concept Quizzes

Polynomial Arithmetic Warmup
Multiplying and Dividing Monomials
Multiplying Polynomials
Combining Like Terms
Solving Identity Equations
Simplifying Expressions Warmup
Applying the Difference of Two Squares Identity
Applying the Perfect Square Identity
Applying the Perfect Cube Identity

Challenge Quizzes

Polynomial Arithmetic: Level 2 Challenges
Polynomial Arithmetic: Level 3 Challenges
Polynomial Arithmetic: Level 4 Challenges

Multiplying Polynomials

Which of the following is the correct expansion of $(x+4)(x^2+3) ?$

x^3 + 3 x^2 + 4x + 4

x^3 + 3 x^2 + 4x + 12

x^3 + 4 x^2 + 3x + 12

x^3 + 4 x^2 + 3x + 4

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by Brilliant Staff

What is the sum of all the coefficients in the expansion of the expression $(x-2y)(9x-6y-8)?$

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by Brilliant Staff

If the expansion of $\left(x+\frac{1}{14}y\right)\left(x-\frac{1}{15}y\right)$ gives $x^2+axy+by^2,$ where $a$ and $b$ are constants, what is $\frac{a}{b}?$

-1 0 1 -2

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by Brilliant Staff

The following polynomial in $x$ has a coefficient of $2$ for the quartic (degree four) term: $(3x^4+x^3-19x^2+5x-2k)(x^4+2x^3+3x+k),$ where $k$ is a constant. What is the constant term of the polynomial?

-200 -162 -128 -242

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by Brilliant Staff

If the expansion of $(x+2y)(Ax+9y)$ gives $3x^2+Bxy+18y^2,$ where $A$ and $B$ are constants, what is $A+B?$

12 9 18 15

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by Brilliant Staff

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