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

2019
Views:

41

Pages:

2
Author:

Cody Bush

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. 5 11 4 -3 1) f(x) = x – 8x – 6x + √9 2) g(x) = x + 4x + 12x Graph the polynomial function. 3) f(x) = x4 – 7x2 + 5x + 3 Describe the End Behavior of the graph. 4.2 Adding, Subtracting, & Multiplying Polynomials 4) f(x) = -0.3x3 + 1.7x2 – 4x + 6 5) f(x) = -2x4 + 6x2 + 11 Simplify 1) (5x3 – 7x2 + 4) + (-2x3 + 5x2 +6x) 2) (x3 – 2x2 + 5) – (4x3 + 5x2 – x) 3) (3x – 5)(2x + 1) 4) (2x – 1)(x3 – 2x2 + 5x) Use Pascal’s Triangle to expand the binomial. 5) 4.3 Dividing Polynomials (x – 4)5 6) (2x + 3)6 Divide using Long Division or Synthetic Division. 1) (2x3 – 7x2 – 7x + 130) ÷ (x – 4) 3) (x3 – 3x2 – 5x – 25) ÷ (x2 + 2x + 5) 5) Use Synthetic Division to evaluate 2) (3x2 + 7x – 20) ÷ (3x – 5) 4) (x3 + 27) ÷ (x + 3) f(x) = 2x3 + 4x2 – 10x – 9 for x = 3 4.4 Factoring Polynomials Factor the polynomial completely. 3 2 3 1) p – 2p – 15p 2) w 4) 27h3 + 8 5) a4 – 8a2 + 16 x–1 7) Show that is a factor of Then factor completely. 4.5 Solving Polynomial Equations – 3w2 – 4w + 12 3) 6x3 – 24x 6) m4 – 64m f(x) = 2x3 – 2x2 + 3x – 3. Find all real solutions of the equation. 3 2 1) x – 5x + 2x + 8 = 0 2) 4x4 – 17x + 4 = 0 Write a polynomial function f of least degree that has rational coefficient, a leading coefficient of 1, and the given zeros. 3) 4.6 The Fundamental Theorem of Algebra -3, 5, √6 4) 9, 1 − √5 Write a polynomial function f of least degree that has rational coefficient, a leading coefficient of 1, and the given zeros. 1) -4, 0, 9 2) -2, i 3) 2, 7 +4i Determine the possible numbers of positive real zeros, negative real zeros, and imaginary zeros for the function. 3 4 2 5) f(x) = x – 2x + 4 6) f(x) = x + 3x – 4 4.7 Transformations of Polynomial Functions Describe the transformation of f represented by g. Then graph each function. 4 4 3 1) f(x) = x , g(x) = (-x – 7) 2) f(x) = x , g(x) = 2x3 + 8 Write a rule for g that represents the indicated transformations of the graph of f. 3) Let the graph of g be a translation 5 units left followed by a vertical stretch by a 3 factor of 4 of the graph of f(x) = x + x – 3 4) Let the graph of g be a horizontal shrink by a factor of 1/3, followed by a reflection in 3 3 the x-axis, and a translation 4 units down of the graph of f(x) = 6x – x + 1