Students find solutions to polynomial equations where the polynomial expression is not factored into linear factors.
Students construct a polynomial function that has a specified set of zeros with stated multiplicity.
Students develop the distributive property for application to polynomial multiplication. Students connect multiplication of polynomials with multiplication of multi-digit integers.
Students connect long division of polynomials with the long division algorithm of arithmetic and use this algorithm to rewrite rational expressions that divide without a remainder.
Students perform arithmetic operations on polynomials and write them in standard form.
Students understand the structure of polynomial expressions by quickly determining the first and last terms if the polynomial were to be written in standard form.
Students understand that the sum of two square roots (or two cube roots) is not equal to the square root (or cube root) of their sum.
Students convert expressions to simplest radical form.
Students understand that the product of conjugate radicals can be viewed as the difference of two squares.
Students will use the factored forms of polynomials to find zeros of a function.
Students will use the factored forms of polynomials to sketch the components of graphs between zeros.