Algebra 1 – Unit 7 – Polynomials

Unit 7 – Polynomials

In Algebra 1, understanding polynomials is fundamental as they form the basis for more complex mathematical concepts. A polynomial is an expression consisting of variables and coefficients, structured in terms of powers and summed together. The types of polynomials are classified based on the number of terms they possess: monomials (one term), binomials (two terms), trinomials (three terms). Adding and subtracting polynomials involves combining like terms, which are terms with the same variable raised to the same power. This process requires careful alignment of terms and straightforward arithmetic operations. Multiplying polynomials often employs the distributive property, where each term in the first polynomial is multiplied by each term in the second. This operation is crucial in expanding expressions and simplifying equations. Factoring polynomials is the reverse of multiplication, breaking down a polynomial into simpler, multiplied factors. Common techniques include factoring out the greatest common factor and recognizing special products like differences of squares and perfect square trinomials. Mastery of these skills enhances problem-solving capabilities in Algebra 1 and beyond.