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Intermediate Algebra

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

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Chapter
Section
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)

t 4 + 10 t 2 + 24 .

To determine

To factor:

The given expression t4+10t2+24.

Explanation

Procedure:

Step-1:

To factor trinomials of the form x4+mx2+n, we first assume x2=u.

Step-2: Rewrite the trinomial as u2+mu+n.

Let us consider a product u+au+b.

Using the distributive property of multiplication, we get

u+au+b=uu+b+au+b

=uu+ub+ax+ab

=u2+a+bu+ab

From the above, we find that the product of u+au+b yields a trinomial of the form u2+a+bu+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 u2+mu+n.

Step-3: Substitute u=x2 back to get the solution.

Calculation:

Given expression: t4+10t2+24

Let, u=t2.

Rewrite the given trinomial as

u2+10u+24.

We need to complete the following with two integers whose sum is 10 and whose product is 24

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