# Factoring: b & c Positive

When factoring trinomials, you might encounter

^{2}+ bx + c

## How a trinomial is formed

First, we''ll examine how a trinomial (a polynomial with exactly 3 terms) is created with the following expression:

Use FOIL to complete the process:

y * y + y * 7 + 3 * y + 3 * 7

= y

^{2}+ 7y + 3y + 21

= y

^{2}+ 10y + 21

There is your trinomial. Now, let''s look at how to reverse the process by factoring it.

## How to factor a trinomial when b and c are positive

When factoring trinomials in which both b and c are positive, you''ll want to locate two numbers that, when multiplied together, yield the last term (the constant) of the trinomial and, when added together, yield the coefficient of the middle term.

Let''s factor the following trinomial:

^{2}+ 7x + 12

First, we''ll find two numbers whose sum is 7 and product is 12. Let''s list the pairs:

We''ve located the pair!

Now, let''s rewrite the expression:

^{2}+ 7x + 12

= x

^{2}+ 3x + 4x + 12

by re-writing

^{2}+ 3x) + (4x + 12)

Therefore, the trinomial:

^{2}+ 7x + 12

in factored form is:

It''s good to note that some trinomials cannot be factored. In other words, they are irreducible polynomials. For instance:

^{2 }+ 17x + 81

## Practice problems on factoring trinomials when b and c are positive

a. Factor

^{2}+ 13n + 36

^{2}+ 4n + 9n + 36 = (n

^{2}+ 4n) + (9n + 36) = n(n + 4) + 9(n + 4) = (n + 9)(n + 4)

b. Factor:

^{2}+ 17y + 52

Find our pair:

^{2}+ 4y + 13y + 52 = (y

^{2}+ 4y) + (13y + 52) = y(y + 4) + 13(y + 4) = (y + 13)(y + 4)

c. Factor:

^{2}+ 19x + 88

Find our pair:

^{2}+ 8x + 11x + 88 = (x

^{2}+ 8x) + (11x + 88) = x(x + 8) + 11(x + 8) = (x + 11)(x + 8)

## Topics related to the Factoring: b & c Positive

Quadratic Equations, Solving by Factoring

## Flashcards covering the Factoring: b & c Positive

## Practice tests covering the Factoring: b & c Positive

College Algebra Diagnostic Tests

## Delve deeper into factoring trinomials when b and c are positive

Students learning how to factor trinomials have a lot of challenging steps to remember. They might struggle with locating two numbers that multiply to create the constant and add to the coefficient -- or they could have trouble using the Distributive Property. Whether your student needs help grasping how to factor trinomials, or they want to boost their knowledge while studying for a test or working on assignments, tutoring can make a significant difference. Learn all about the perks of studying alongside a qualified private educator by reaching out to the Educational Directors at Varsity Tutors today.

- TACHS Test Prep
- CCNP - Cisco Certified Network Professional Test Prep
- BCABA - Board Certified Assistant Behavior Analyst Courses & Classes
- Series 99 Test Prep
- South Dakota Bar Exam Test Prep
- 4th Grade Social Studies Tutors
- Actuarial Exam STAM Courses & Classes
- Marketing Information Systems Tutors
- CSET - California Subject Examinations for Teachers Test Prep
- ISEE-Upper Level Writing Tutors
- Competition Math Tutors
- Advanced Geometry Tutors
- AU- Associate in Commercial Underwriting Test Prep
- VTNE - Veterinary Technician National Exam Test Prep
- IB Geography Tutors
- Certified Ethical Hacker Courses & Classes
- PCAT Test Prep
- Alaska Bar Exam Test Prep
- NCLEX Tutors
- Actuarial Exam PA Courses & Classes