(a) Explanation Given: The rational expression is, z 2 + 5 z + 6 2 z 2 − 5 z − 3 ⋅ 2 z 2 − z − 1 z 2 + 2 z − 3 . Property used: Multiplication property, P Q ⋅ R S = P R Q S , for all mathematical expressions P , Q , R , and S , with Q ≠ 0 and S ≠ 0 . Calculation: Apply the Multiplication property, z 2 + 5 z + 6 2 z 2 − 5 z − 3 ⋅ 2 z 2 − z − 1 z 2 + 2 z − 3 = ( z 2 + 5 z + 6 ) ⋅ ( 2 z 2 − z − 1 ) ( 2 z 2 − 5 z − 3 ) ⋅ ( z 2 + 2 z − 3 ) . Obtain the factors as follows. z 2 + 5 z + 6 = z 2 + 3 z + 2 z + 6 = z ( z + 3 ) + 2 ( z + 3 ) = ( z + 3 ) ( z + 2 ) 2 z 2 − 5 z − 3 = 2 z 2 − 6 z + z − 3 = 2 z ( z − 3 ) + 1 ( z − 3 ) = ( z − 3 ) ( 2 z + 1 ) 2 z 2 − z − 1 = 2 z 2 − 2 z + z − 1 = 2 z ( z − 1 ) + 1 ( z − 1 ) = ( z − 1 ) ( 2 z + 1 ) z 2 + 2 z − 3 = z 2 + 3 z − z − 3 = z ( z (b) To determine To express: The rational expression a − 3 a 2 + 3 a + 2 + 5 a a 2 − 4 in lowest terms.

10th Edition

ISBN: 8220102020252

Author: RITCHEY

Publisher: PEARSON

See similar textbooks

Concept explainers

Percentage

A percentage is a number indicated as a fraction of 100. It is a dimensionless number often expressed using the symbol %.

Algebraic Expressions

In mathematics, an algebraic expression consists of constant(s), variable(s), and mathematical operators. It is made up of terms.

Numbers

Numbers are some measures used for counting. They can be compared one with another to know its position in the number line and determine which one is greater or lesser than the other.

Subtraction

Before we begin to understand the subtraction of algebraic expressions, we need to list out a few things that form the basis of algebra.

Addition

Before we begin to understand the addition of algebraic expressions, we need to list out a few things that form the basis of algebra.

Videos

Question

Chapter R.3, Problem 2YT

(a)

To determine

To perform: The indicated operations of z2+5z+62z2−5z−3⋅2z2−z−1z2+2z−3 .

(b)

To determine

To express: The rational expression a−3a2+3a+2+5aa2−4 in lowest terms.

Expert Solution & Answer

Want to see the full answer?

Check out a sample textbook solution

See solution

Chapter R.3, Problem 1YT

Chapter R.3, Problem 1E

Students have asked these similar questions

Inverse laplace transform H.w Find the Inverse Laplace t following:- 1- 1 $3/2 S 2- 52 +2 s²+2 3- tan-1 1 S 4- 3 8s-27 4s+12 5- s²+8s+16 6- 1 √2s+3

xux +yuy =2xy,withu =2 on y = x2

Q2/ verify that f grad = (h grad f- f grad h) h h₂ where and h are scalar factions. Solve in paper

Chapter R Solutions

EBK FINITE MATHEMATICS AND CALCULUS WIT

Ch. R.1 - Perform the operation 3(x24x5)4(3x25x7)Ch. R.1 - Perform the operation (3y+2)(4y22y5).Ch. R.1 - Find (2x+7)(3x1) using the FOIL method.Ch. R.1 - Find (3x+2y)3.Ch. R.1 - Perform the indicated operations....Ch. R.1 - Perform the indicated operations....Ch. R.1 - Perform the indicated operations....Ch. R.1 - Perform the indicated operations....Ch. R.1 - Perform the indicated operations....Ch. R.1 - Perform the indicated operations....

Knowledge Booster

$Calculus$

Learn more about

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

To perform: The indicated operations of z 2 + 5 z + 6 2 z 2 − 5 z − 3 ⋅ 2 z 2 − z − 1 z 2 + 2 z − 3 .

Solution Summary: The author explains how to perform the indicated operations of z2+5z+62.