Explanation Division of a polynomial by binomial is done by long-division method. In this method to find the first quotient term, divide the first dividend term by the first divisor term. Multiply the divisor with the term obtained by dividing the first dividend term with the first quotient term. The product obtained is subtracted from the dividend. Repeat the same process to divide the other terms of the dividend. Calculation: Consider the expression 3 x 2 − 2 x − 7 x + 2 . The following steps are used to solve the problem. First multiply the divisor by 3 x and write the product 3 x 2 + 6 x under the dividend and subtract. The value obtained is equals to − 8 x . Now multiply the divisor by 8 and write the product − 8 x − 16 under the dividend and simplify. The polynomial is divided as follows, By using the long division it is written as follows, x + 2 3 x − 8 3 x 2 − 2 x − 7 3 x 2 + 6 x _ − 8 x − 7 − 8 x − 16 _

10th Edition

ISBN: 9781285195728

Author: Jerome E. Kaufmann, Karen L. Schwitters

Publisher: Cengage Learning

See similar textbooks

Videos

Question

Chapter 4.5, Problem 16PS

To determine

To Find:

The value of the polynomials by performing the indicated division by binomials.

Expert Solution & Answer

Want to see the full answer?

Check out a sample textbook solution

See solution

Chapter 4.5, Problem 15PS

Chapter 4.5, Problem 17PS

Students have asked these similar questions

1.2.19. Let and s be natural numbers. Let G be the simple graph with vertex set Vo... V„−1 such that v; ↔ v; if and only if |ji| Є (r,s). Prove that S has exactly k components, where k is the greatest common divisor of {n, r,s}.

Question 3 over a field K. In this question, MË(K) denotes the set of n × n matrices (a) Suppose that A Є Mn(K) is an invertible matrix. Is it always true that A is equivalent to A-¹? Justify your answer. (b) Let B be given by 8 B = 0 7 7 0 -7 7 Working over the field F2 with 2 elements, compute the rank of B as an element of M2(F2). (c) Let 1 C -1 1 [4] [6] and consider C as an element of M3(Q). Determine the minimal polynomial mc(x) and hence, or otherwise, show that C can not be diagonalised. [7] (d) Show that C in (c) considered as an element of M3(R) can be diagonalised. Write down all the eigenvalues. Show your working. [8]

R denotes the field of real numbers, Q denotes the field of rationals, and Fp denotes the field of p elements given by integers modulo p. You may refer to general results from lectures. Question 1 For each non-negative integer m, let R[x]m denote the vector space consisting of the polynomials in x with coefficients in R and of degree ≤ m. x²+2, V3 = 5. Prove that (V1, V2, V3) is a linearly independent (a) Let vi = x, V2 = list in R[x] 3. (b) Let V1, V2, V3 be as defined in (a). Find a vector v € R[×]3 such that (V1, V2, V3, V4) is a basis of R[x] 3. [8] [6] (c) Prove that the map ƒ from R[x] 2 to R[x]3 given by f(p(x)) = xp(x) — xp(0) is a linear map. [6] (d) Write down the matrix for the map ƒ defined in (c) with respect to the basis (2,2x + 1, x²) of R[x] 2 and the basis (1, x, x², x³) of R[x] 3. [5]

Chapter 4 Solutions

Intermediate Algebra

Ch. 4.1 - For Problems 1-10, answer true or false. When a...Ch. 4.1 - For Problems 1-10, answer true or false. A...Ch. 4.1 - For Problems 1-10, answer true or false. 3 is a...Ch. 4.1 - For Problems 1-10, answer true or false. A...Ch. 4.1 - For Problems 1-10, answer true or false. The...Ch. 4.1 - For Problems 1-10, answer true or false. The...Ch. 4.1 - Prob. 7CQ Ch. 4.1 - Prob. 8CQ Ch. 4.1 - Prob. 9CQ Ch. 4.1 - Prob. 10CQ

Knowledge Booster

$Algebra$

Learn more about

Need a deep-dive on the concept behind this application? Look no further. Learn more about this topic, algebra and related others by exploring similar questions and additional content below.

The value of the polynomials by performing the indicated division by binomials.

Solution Summary: The author explains the long-division method of division of a polynomial by binomials to find the first quotient term.

Videos

To Find: The value of the polynomials by performing the indicated division by binomials.

Want to see the full answer?

Chapter 4 Solutions

To Find:

The value of the polynomials by performing the indicated division by binomials.