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- Common Core MathK - 8High School

722 questions44 skills

345 questions21 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 difference of squares

Add polynomials (intro)

Multiply binomials by polynomials

Multiply binomials intro

Multiply binomials by polynomials: area model

Polynomial special products: perfect square

Add & subtract polynomials: two variables

Multiply monomials by polynomials

Multiply monomials (advanced)

Polynomial special products: difference of squares

Multiply monomials by polynomials challenge

Multiply monomials

Add & subtract polynomials

Multiply binomials: area model

Add & subtract polynomials: two variables (intro)

Multiply monomials by polynomials (basic): area model

Multiply perfect squares of binomials

Multiply monomials by polynomials: area model

Add & subtract polynomials: find the error

Subtract polynomials (intro)

Multiply binomials

27 questions2 skills

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*).

40 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.

116 questions8 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.

Divide quadratics by linear expressions (no remainders)

Divide quadratics by linear expressions (with remainders)

Divide polynomials by x (no remainders)

Divide polynomials by monomials (with remainders)

Divide polynomials with remainders

Divide polynomials by linear expressions

Factor using polynomial division

Divide polynomials by x (with remainders)

158 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.

Multiply & divide rational expressions (advanced)

Add & subtract rational expressions

Multiply & divide rational expressions

Nested fractions

Add & subtract rational expressions (basic)

Multiply & divide rational expressions: Error analysis

Add & subtract rational expressions: factored denominators

Add & subtract rational expressions: like denominators