Adding and subtracting polynomialsHSA.APR.A.1Add and subtract polynomials by combining like terms, distributing the minus sign when subtracting.Multiplying polynomialsHSA.APR.A.1Multiply a monomial by a binomial and two binomials together, then combine like terms.The remainder and factor theoremsHSA.APR.B.2Find the remainder of p(x) ÷ (x − a) by evaluating p(a), and decide whether x − a is a factor.Finding zeros of polynomialsHSA.APR.B.3Find the zeros of a cubic polynomial in factored form, from one known zero, and by factoring by grouping.The binomial theoremHSA.APR.C.5Expand powers of binomials with Pascal's triangle and the binomial theorem, and find the coefficient of one term without expanding.Dividing polynomials by monomialsHSA.APR.D.6Divide every term of a polynomial by a monomial, dividing the coefficients and subtracting the exponents.Dividing polynomials (long and synthetic division)HSA.APR.D.6Divide quadratic and cubic polynomials by x − r with synthetic division, giving the quotient and any remainder.Simplifying rational expressionsHSA.APR.D.6Simplify rational expressions by factoring the top and bottom and cancelling common factors, and state the excluded values.Multiplying and dividing rational expressionsHSA.APR.D.7Multiply and divide rational expressions by factoring, flipping the divisor, and cancelling common factors.Adding and subtracting rational expressionsHSA.APR.D.7Add and subtract rational expressions with like denominators, unlike linear denominators, and denominators that share a factor.