Chapter 6: Q 78E (page 589)

In the following exercises, factor each trinomial of the form
$x^{2} + b x + c$
$- 11 - 10 x + x^{2}$

Short Answer

Expert verified

The binomial factors of the equations are $(x + 11) (x - 1)$ .

Step by step solution

Step 1. Given information and rewriting the equation in general from

The given equation is

$- 11 - 10 x + x^{2}$

The general form is

$x^{2} - 10 x - 11$

Step 2. Writing factors as two binomial with n.

The factors should be written as two binomials with n as the first term.

$(n) (n)$

The product of the two numbers is 11,and their sum is 10. Because the third term sign is negative, the sum seems to be a difference.

$[\begin{matrix} Factors & 11 \\ 1 \\ Difference & 10 \end{matrix}]$

So form of binomial is $(x 11) (x 1)$ .

Step 3. Finding factors

The larger binomial second term is also positive because the second trinomial term is positive.

Because the third trinomial term is negative, the binomial signs are transposed.

The binomial factors are as follows:

$(x + 11) (x - 1)$

Step 4. Checking the factors

$Check : Multiply the factors . (x + 11) (x - 1) = x ² - x + 11 x - 11 [Multiply] = x ² + 10 x - 11 True [Group the like terms]$

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In the following exercises, factor each trinomial of the form
$x^{2} + b x + c$
$- 11 - 10 x + x^{2}$

Short Answer

Step by step solution

Step 1. Given information and rewriting the equation in general from

Step 2. Writing factors as two binomial with n.

Step 3. Finding factors

Step 4. Checking the factors

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In the following exercises, factor each trinomial of the form x2+bx+c-11-10x+x2

Short Answer

Step by step solution

Step 1. Given information and rewriting the equation in general from

Step 2. Writing factors as two binomial with n.

Step 3. Finding factors

Step 4. Checking the factors

One App. One Place for Learning.

Most popular questions from this chapter

Recommended explanations on Math Textbooks

Mechanics Maths

Decision Maths

Calculus

Theoretical and Mathematical Physics

Applied Mathematics

Probability and Statistics

Study anywhere. Anytime. Across all devices.

In the following exercises, factor each trinomial of the form
$x^{2} + b x + c$
$- 11 - 10 x + x^{2}$