Chapter 6: Q 65E (page 589)

In the following exercises, factor each trinomial of the form $x^{2} + b x + c$ .
$a^{2} + 25 a + 100$

Short Answer

Expert verified

The factors are $(a + 5) (a + 20)$ .

Step by step solution

Step 1. Writing the expression

Write the factors as two binomials with first terms $a$ .

localid="1644544102479" $(a) (a)$ .

Step 2. Finding the factors

We need to find two numbers whose product is $100$ and sum is $25$ .

Factors of $100$	Sum of factors
$1, 100$	$101$
$2, 50$	$52$
$4, 25$	$29$
$5, 20$	$25$
$10, 10$	$20$

Thus, $5, 20$ are the correct factors.

Hence, the factorization of the trinomial is $(a + 5) (a + 20)$ .

Step 3. Check

Multiply the factorization to get the trinomial again.

$(a + 5) (a + 20) = a^{2} + 20 a + 5 a + 100 (a + 5) (a + 20) = a^{2} + 25 a + 100$

Thus, the obtained factorization is correct.

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In the following exercises, factor each trinomial of the form $x^{2} + b x + c$ .
$a^{2} + 25 a + 100$

Short Answer

Step by step solution

Step 1. Writing the expression

Step 2. Finding the factors

Step 3. Check

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In the following exercises, factor each trinomial of the formx2+bx+c.a2+25a+100

Short Answer

Step by step solution

Step 1. Writing the expression

Step 2. Finding the factors

Step 3. Check

One App. One Place for Learning.

Most popular questions from this chapter

Recommended explanations on Math Textbooks

Calculus

Statistics

Applied Mathematics

Geometry

Decision Maths

Mechanics Maths

Study anywhere. Anytime. Across all devices.

In the following exercises, factor each trinomial of the form $x^{2} + b x + c$ .
$a^{2} + 25 a + 100$