Q. 358 Factor Trinomials of the Form x2... [FREE SOLUTION]

91影视

Intermediate Algebra

OPENSTAX

$Math Studyset 91影视 Explanations$ Math

OER 2017 Edition 路 1346 pages

ISBN: 9780998625720

Chapter 6: Q. 358 (page 634)

Factor Trinomials of the Form $x^{2} + b x + c$
In the following exercises, factor each trinomial of the form $x^{2} + b x + c$ .
$x^{2} - 3 x - 10$

Short Answer

Expert verified

The binomial factors of $x^{2} - 3 x - 10$ is $(x - 5) (x + 2)$

Step by step solution

Step 1. Given

The trinomial $x^{2} - 3 x - 10$

To factor the given trinomial

Step 2. Write as binomials with first term as x

Write two sets of parentheses and put $x$ as the first term.

$x^{2} - 3 x - 10 = (x) (x)$

Step 3. Find two numbers that multiply to c and add to b

Find two numbers that multiply to give $- 10$ and add to $- 3$ .

Factors of $- 10$	Addition of factors
$1, - 10$	$- 9$
$2, - 5$	$- 3$

Step 4. Use numbers as last number of factors.

So the factor that multiply to give $- 10$ and add to $- 3$ is $- 5, 2$ .

So the factor is $(x - 5) (x + 2)$

Step 5. Check the answer

The factors are $(x - 5) (x + 2)$

Multiply the factors

$(x - 5) (x + 2) = x^{2} + 2 x - 5 x - 10$

$= x^{2} - 3 x - 10$

Hence the multiplication of factors gives the trinomial.

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91影视

Factor Trinomials of the Form $x^{2} + b x + c$
In the following exercises, factor each trinomial of the form $x^{2} + b x + c$ .
$x^{2} - 3 x - 10$

Short Answer

Step by step solution

Step 1. Given

Step 2. Write as binomials with first term as x

Step 3. Find two numbers that multiply to c and add to b

Step 4. Use numbers as last number of factors.

Step 5. Check the answer

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91影视

Factor Trinomials of the Form x2+bx+cIn the following exercises, factor each trinomial of the form x2+bx+c.x2-3x-10

Short Answer

Step by step solution

Step 1. Given

Step 2. Write as binomials with first term as x

Step 3. Find two numbers that multiply to c and add to b

Step 4. Use numbers as last number of factors.

Step 5. Check the answer

One App. One Place for Learning.

Most popular questions from this chapter

Recommended explanations on Math Textbooks

Applied Mathematics

Discrete Mathematics

Logic and Functions

Geometry

Theoretical and Mathematical Physics

Statistics

Study anywhere. Anytime. Across all devices.

Factor Trinomials of the Form $x^{2} + b x + c$
In the following exercises, factor each trinomial of the form $x^{2} + b x + c$ .
$x^{2} - 3 x - 10$