Αποτελέσματα Αναζήτησης
The polynomial x x x k3 2+ + +4 7 , where k is a constant, is denoted by f x( ). a) Given that ( x +2 ) is a factor of f x ( ) , show that k = 6. b) Express f x ( ) as a product of a linear factor and a quadratic factor.
SOLVING POLYNOMIAL EQUATIONS Solve the following equations. You will need the Quadratic Formula on some. 1. 3x2 −27x+42 = 0 2. 25x2 4 3. 4x2 20 x+25 =0 4. x2 −16 48 5. 3y2 +y−4 =0 6. 5 2 14x 24 7. 10 2 + 3 =17 x 8 4x2 − 6 0 9.
Consider the polynomial W (x) = (x− a)k Q(x), where a 6= 0, Q is a nonzero polynomial, and k a natural number. Prove that W has at least k + 1 nonzero coefficients. 23.
† solving polynomial equations. † the zeros of polynomial functions. † modeling data with polynomial models. You can use the skills in this chapter † to solve problems in future math classes, including College Algebra and Trigonometry. † to solve real-life problems in physics and graphic arts. † to predict the value of stocks.
• Determine roots of polynomial equations. (Lessons 4-1, 4-4) • Solve quadratic, rational, and radical equations and rational and radical inequalities. (Lessons 4-2, 4-6, 4-7) • Find the factors of polynomials. (Lesson 4-3) • Approximate real zeros of polynomial functions. (Lesson 4-5) • Write and interpret polynomial functions that model
Answers to 6.4 PRACTICE - Factoring and Solving Polynomial Equations 1) ( 5 b 2 + 8 )( 4 b − 5 ) 2) ( 4 v 2 − 3 )( v + 8 ) 3) ( p 2 − 4 )( p − 4 )
f(x) = ax3 + bx2 + cx + d , and determined the roots of f(x) to be ±1 and 2. What is the value of b, if. = 1? 8 Which statement regarding polynomials and their zeros is true? f(x) = (x2 − 1)(x + a) has zeros of 1 and −a, only. f(x) = x3 − ax2 + 16x − 16a has zeros of 4 and a, only. f(x) = (x2 + 25)(x + a) has zeros of ±5 and −a.
