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Intermediate Algebra

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

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Section
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.

4 x 2 a + 20 x a + 25

To determine

To factor:

The given trinomial 4x2a+20xa+25, where the exponent a is a positive integer.

Explanation

Procedure:

The following two are square binomials:

a+b2=a2+2ab+b2 and a-b2=a2-2ab+b2.

These patterns can be used for factoring purposes.

The trinomials on the left side are called perfect-square trinomials; they are the result of squaring a binomial.

The perfect-square trinomials can be factored as usual. However, the perfect-square trinomials can be easily recognized by the nature of their terms.

For example, 4x2+16x+16 is a perfect-square trinomial because

1. The first term 4x2 is a perfect-square. That is 2x2.

2. The last term 16 is a perfect-square. That is 42.

3. The middle term 16x is twice the product of the quantities being squared in the first and last terms.

Hence, the factored form of the trinomial 4x2+16x+16 is 2x+42

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