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- Common Core MathK - 8High School

721 questions36 skills

285 questions16 skills

Understand that polynomials form a system analogous to the integers, namely, they are closed under the operations of addition, subtraction, and multiplication; add, subtract, and multiply polynomials.

Multiply binomials by polynomials

Multiply monomials by polynomials

Add & subtract polynomials: find the error

Multiply monomials (advanced)

Add & subtract polynomials: two variables

Polynomial special products: perfect square

Multiply binomials

Multiply binomials intro

Multiply monomials

Add polynomials (intro)

Multiply difference of squares

Multiply monomials by polynomials: area model

Add & subtract polynomials: two variables (intro)

Add & subtract polynomials

Multiply monomials by polynomials challenge

Subtract polynomials (intro)

15 questions1 skill

Know and apply the Remainder Theorem: For a polynomial *p*(*x*) and a number *a*, the remainder on division by *x – a* is *p*(*a*), so *p*(*a*) = 0 if and only if (*x – a*) is a factor of *p*(*x*).

43 questions3 skills

Identify zeros of polynomials when suitable factorizations are available, and use the zeros to construct a rough graph of the function defined by the polynomial.

20 questions1 skill

Prove polynomial identities and use them to describe numerical relationships.

16 questions1 skill

Know and apply the Binomial Theorem for the expansion of (*x* + *y*)^{n} in powers of *x* and *y* for a positive integer *n*, where *x* and *y* are any numbers, with coefficients determined for example by Pascal’s Triangle.

142 questions6 skills

Rewrite simple rational expressions in different forms; write ^{a(x)}/_{b(x)} in the form *q*(*x*) + ^{r(x)}/_{b(x)}, where *a*(*x*), *b*(*x*), *q*(*x*), and *r*(*x*) are polynomials with the degree of *r*(*x*) less than the degree of *b*(*x*), using inspection, long division, or, for the more complicated examples, a computer algebra system.

200 questions8 skills

Understand that rational expressions form a system analogous to the rational numbers, closed under addition, subtraction, multiplication, and division by a nonzero rational expression; add, subtract, multiply, and divide rational expressions.

Add & subtract rational expressions: factored denominators

Multiply & divide rational expressions (basic)

Multiply & divide rational expressions (advanced)

Add & subtract rational expressions: like denominators

Nested fractions

Multiply & divide rational expressions

Add & subtract rational expressions: unlike denominators

Add & subtract rational expressions