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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

For problems 1-30, factor completely each of the trinomials and indicate any that are not factorable using integers. (Objective 1)

x 2 - 11 x + 28 .

To determine

To factor:

The given expression x2-11x+28.

Explanation

Approach:

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:x2-11x+28.

We need to complete the following with two integers whose sum is -11 and whose product is 28.

x2-11x+28=x+___x+___

The following table shows the possible pairs of factors of 28 and whose sum is -11:

Factors Product of the factors Sum of the factors
1

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