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Intermediate Algebra

10th Edition
Jerome E. Kaufmann + 1 other
ISBN: 9781285195728

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BuyFindarrow_forward

Intermediate Algebra

10th Edition
Jerome E. Kaufmann + 1 other
ISBN: 9781285195728
Textbook Problem

Further Investigations

For problems 116-121, factor each trinomial and assume that all variables that appear as exponents represent positive integers.

x 2 a + 10 x a + 21

To determine

To factor:

The given trinomial x2a+10xa+21, where the exponent a is a positive integer.

Explanation

Procedure:

To factor trinomials of the form x2+mx+n, we use the following procedure:

Let us consider a product x+ax+b.

Using the distributive property of multiplication, we get

x+ax+b=xx+b+ax+b

=xx+xb+ax+ab

=x2+a+bx+ab

From the above, we find that the product of x+ax+b yields a trinomial of the form x2+a+bx+ab.

It must be noted that the middle term is the sum of a and b and the last term is the product of a and b.

These two relationships can be used for factoring trinomials of the form x2+mx+n.

Calculation:

Given expression: x2a+10xa+21.

We need to complete the following with two integers whose sum is 10 and whose product is 21

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P-48CRSect-3.CR P-49CRSect-3.CR P-50CRSect-3.CR P-51CRSect-3.CR P-52CRSect-3.CR P-53CRSect-3.CR P-54CRSect-3.CR P-55CRSect-3.CR P-56CRSect-3.CR P-57CRSect-3.CR P-58CRSect-3.CR P-59CRSect-3.CR P-60CRSect-3.CR P-61CRSect-3.CR P-62CRSect-3.CR P-63CRSect-3.CR P-64CRSect-3.CR P-65CRSect-3.CR P-66CRSect-3.CR P-67CRSect-3.CR P-68CRSect-3.CR P-69CRSect-3.CR P-70CRSect-3.CR P-71CRSect-3.CR P-72CRSect-3.CR P-73CRSect-3.CR P-74CRSect-3.CR P-75CRSect-3.CR P-76CRSect-3.CR P-77CRSect-3.CR P-78CRSect-3.CR P-79CRSect-3.CR P-80CRSect-3.CR P-81CRSect-3.CR P-82CRSect-3.CR P-83CRSect-3.CR P-84CRSect-3.CR P-85CRSect-3.CR P-86CRSect-3.CR P-87CRSect-3.CR P-88CRSect-3.CR P-89CRSect-3.CR P-90CRSect-3.CR P-91CRSect-3.CR P-92CRSect-3.CR P-93CRSect-3.CR P-94CRSect-3.CR P-95CRSect-3.CR P-96CRSect-3.CR P-97CRSect-3.CR P-98CRSect-3.CR P-99CRSect-3.CR P-100CRSect-3.CR P-101CRSect-3.CR P-102CRSect-3.CR P-103CRSect-3.CR P-104CRSect-3.CR P-105CRSect-3.CR P-106CRSect-3.CR P-107CRSect-3.CR P-108CRSect-3.CR P-109CRSect-3.CR P-110CRSect-3.CR P-111CRSect-3.CR P-112CRSect-3.CR P-113CRSect-3.CR P-114CRSect-3.CT P-1CTSect-3.CT P-2CTSect-3.CT P-3CTSect-3.CT P-4CTSect-3.CT P-5CTSect-3.CT P-6CTSect-3.CT P-7CTSect-3.CT P-8CTSect-3.CT P-9CTSect-3.CT P-10CTSect-3.CT P-11CTSect-3.CT P-12CTSect-3.CT P-13CTSect-3.CT P-14CTSect-3.CT P-15CTSect-3.CT P-16CTSect-3.CT P-17CTSect-3.CT P-18CTSect-3.CT P-19CTSect-3.CT P-20CTSect-3.CT P-21CTSect-3.CT P-22CTSect-3.CT P-23CTSect-3.CT P-24CTSect-3.CT P-25CT

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