Exercises each polynomial function. Estimate the at which the relative maxima and relative minima x-coordinates occur. 1. = 3 2. = 2 + 3x 3. = 2 3x + 2 f(x) – f(x) – f(x) – 4. = 7x 3 5. = 2 + 2 6. = + 2 3 f(x) f(x) f(x) – – – – 5-5 Study Guide - Solving Polynomial Equations Factor Polynomials For any number of terms, check for: greatest common factor For two check for: Difference of two squares = (a + b)(a b) – – Sum of two cubes + = (a + b)( ab + ) – Difference of two cubes = (a b)( + ab + ) Techniques for Factoring – – Polynomials For three terms, check for: Perfect square trinomials + 2ab + = 2ab + = – General trinomials + (ad + bc)x + bd = (ax + b)(cx + d) For four or more terms, check for: Grouping ax + bx + ay + by = x(a + b) + y(a + b) = (a + b)(x + y) Example: Factor 42x 45. – –
Exercises each polynomial function. Estimate the x-coordinates at which the relative maxima and relative minima occur. 1. f(x) = – 3 2. f(x) = 2 + – 3x 3. f(x) = 2 – 3x + 2 4. f(x) = – 7x – 3 5. f(x) = – 2 + 2 6. f(x) = + 2 – 3 5-5 Study Guide - Solving Polynomial Equations Factor Polynomials Techniques for Factoring Polynomials For any number of terms, check for: greatest common factor For two check for: Difference of two squares – = (a + b)(a – b) Sum of two cubes + = (a + b)( – ab + ) Difference of two cubes – = (a – b)( + ab + ) For three terms, check for: Perfect square trinomials + 2ab + = – 2ab + = General trinomials + (ad + bc)x + bd = (ax + b)(cx + d) For four or more terms, check for: Grouping ax + bx + ay + by = x(a + b) + y(a + b) = (a + b)(x + y) Example: Factor – 42x – 45.