University:
High School
Course:
High School Algebra
Academic year:

2019
Views:

21

Pages:

2
Author:

jazzily607hm

Chapter 4 Study Guide Algebra II 4.1 Graphing Polynomial Functions Decide whether the function is a polynomial function. If so, write it in standard form and state the degree, type, and leading coefficient. 1 f(x) = x⁵ - 8x¹¹ - 6x + √9 Not a polynomial g(x) = x⁴ + 4x + 12x⁻³ Not a polynomial Graph the polynomial function. f(x) = x⁴ - 7x² + 5x + 3 [Graph of the function f(x) is shown, with points plotted and a curve drawn.] 4.2 Adding, Subtracting, & Multiplying Polynomials Simplify (5x⁵ - 7x² + 2) + (-2x³ + 5x² + 6x) = 5x⁵ - 2x³ + 6x + 2 (x³ - 2x² + 5) - (4x³ - 5x² + x) = x³ - 2x² + 5 - 4x³ + 5x² - x = -3x³ + 3x² - x + 5 (3x - 5)(2x + 1) = 6x² - 7x - 5 (2x - 1)(x³ - 2x² + 5x) = 2x⁴ - 5x³ + 12x² - 5x Use Pascal's Triangle to expand the binomial. 5. (x - 4)⁵ Pascal's Triangle: 1 5 10 10 5 1 = 1(x⁵) + 5(x⁴)(-4) + 10(x³)(-4)² + 10(x²)(-4)³ + 5(x)(-4)⁴ + 1(-4)⁵ = x⁵ - 20x⁴ + 160x³ - 640x² + 1280x - 1024 6. (x + 3)⁶ Pascal's Triangle: 1 6 15 20 15 6 1 = 1(x⁶) + 6(x⁵)(3) + 15(x⁴)(3)² + 20(x³)(3)³ + 15(x²)(3)⁴ + 6(x)(3)⁵ + 1(3)⁶ = x⁶ + 18x⁵ + 135x⁴ + 540x³ + 1215x² + 1458x + 729 4.3 Dividing Polynomials Divide using Long Division or Synthetic Division. (2x³ - 7x² - 7x + 130) ÷ (x - 4) 2x² + x - 3 + 11/(x - 4) (3x² + 7x - 20) ÷ (3x - 5) x + 4 (x³ - 3x² - 5x - 25) ÷ (x² + 2x + 5) x - 5 (x³ + 27) ÷ (x + 3) x² - 3x + 9 Use Synthetic Division to evaluate f(x) = 2x³ + 4x² - 10x - 9 for x = 3. f(3) = 51 4.4 Factoring Polynomials Factor the polynomial completely. p³ - 2p² - 15p p(p + 3)(p - 5) w³ - 3w² - 4w + 12 (w - 3)(w - 2)(w + 2) 6x³ - 24x 6x(x - 2)(x + 2) 27h³ + 8 (3h + 2)(9h² - 6h + 4) a⁴ - 8a² + 16 (a - 2)²(a + 2)² m⁴ - 64m m(m - 4)(m² + 4m + 16) Show that x - 1 is a factor of f(x) = 2x³ - 2x² + 3x - 3. Then factor completely. (x - 1)(2x² + 3)