Perform each division. See Examples 9 and 10. (p2+2p+20)/(p+6)

Ch. R - Review of Basic Concepts

Lial13th EditionCollege AlgebraISBN: 9780136881063Not the one you use?Change textbook

All textbooks

Lial 13th Edition

Ch. R - Review of Basic Concepts

Problem 93

Chapter 1, Problem 93

Perform each division. See Examples 9 and 10. (p²+2p+20)/(p+6)

Verified step by step guidance

Identify the division problem as a polynomial division: divide the polynomial \(p^{2} + 2p + 20\) by the binomial \(p + 6\).

Set up the long division by writing \(p^{2} + 2p + 20\) under the division symbol and \(p + 6\) outside.

Divide the leading term of the dividend \(p^{2}\) by the leading term of the divisor \(p\) to get the first term of the quotient: \(p\).

Multiply the entire divisor \(p + 6\) by this term \(p\) and subtract the result from the dividend to find the new remainder.

Repeat the process with the new remainder: divide its leading term by \(p\), multiply the divisor by this term, subtract again, and continue until the degree of the remainder is less than the degree of the divisor.

Verified video answer for a similar problem:

This video solution was recommended by our tutors as helpful for the problem above.

Video duration:

Was this helpful?

Key Concepts

Here are the essential concepts you must grasp in order to answer the question correctly.

Polynomial Division

Polynomial division is a process similar to long division with numbers, used to divide one polynomial by another. It helps simplify expressions or find quotients and remainders when dividing polynomials, especially when the divisor is a linear polynomial.

Long Division Method for Polynomials

The long division method involves dividing the leading term of the dividend by the leading term of the divisor, multiplying the divisor by this result, subtracting from the dividend, and repeating with the remainder. This step-by-step approach breaks down complex polynomial division into manageable parts.

Remainder and Quotient in Polynomial Division

When dividing polynomials, the result includes a quotient and possibly a remainder. The quotient is the polynomial result of the division, while the remainder is a polynomial of lower degree than the divisor. Understanding these helps interpret the division outcome correctly.

Recommended video:

Guided course

05:13

Introduction to Polynomials

Related Practice

Textbook Question

Simplify each expression. Write answers without negative exponents. Assume all variables represent positive real numbers. (64^5/3)/(64^4/3)

views

Textbook Question

Simplify each radical. Assume all variables represent positive real numbers. ⁶√√5³

views

Textbook Question

Add or subtract as indicated. 25.32 + 109.2 + 8.574

Textbook Question

Evaluate each expression. (4-2³)(-2+√25)

views

Textbook Question

Perform all indicated operations, and write each answer with positive integer exponents. [ (x^-2 + y^-2)/ (x^-2 - y^-2) ] * [ (x+y)/(x-y) ]

views

Textbook Question

Perform all indicated operations, and write each answer with positive integer exponents. {x- 9y^-1}/{ (x-3y^-1)(x+3y^-1)}