Algebra Tutorials!

 Sunday 4th of August

 Home Calculations with Negative Numbers Solving Linear Equations Systems of Linear Equations Solving Linear Equations Graphically Algebra Expressions Evaluating Expressions and Solving Equations Fraction rules Factoring Quadratic Trinomials Multiplying and Dividing Fractions Dividing Decimals by Whole Numbers Adding and Subtracting Radicals Subtracting Fractions Factoring Polynomials by Grouping Slopes of Perpendicular Lines Linear Equations Roots - Radicals 1 Graph of a Line Sum of the Roots of a Quadratic Writing Linear Equations Using Slope and Point Factoring Trinomials with Leading Coefficient 1 Writing Linear Equations Using Slope and Point Simplifying Expressions with Negative Exponents Solving Equations 3 Solving Quadratic Equations Parent and Family Graphs Collecting Like Terms nth Roots Power of a Quotient Property of Exponents Adding and Subtracting Fractions Percents Solving Linear Systems of Equations by Elimination The Quadratic Formula Fractions and Mixed Numbers Solving Rational Equations Multiplying Special Binomials Rounding Numbers Factoring by Grouping Polar Form of a Complex Number Solving Quadratic Equations Simplifying Complex Fractions Algebra Common Logs Operations on Signed Numbers Multiplying Fractions in General Dividing Polynomials Polynomials Higher Degrees and Variable Exponents Solving Quadratic Inequalities with a Sign Graph Writing a Rational Expression in Lowest Terms Solving Quadratic Inequalities with a Sign Graph Solving Linear Equations The Square of a Binomial Properties of Negative Exponents Inverse Functions fractions Rotating an Ellipse Multiplying Numbers Linear Equations Solving Equations with One Log Term Combining Operations The Ellipse Straight Lines Graphing Inequalities in Two Variables Solving Trigonometric Equations Adding and Subtracting Fractions Simple Trinomials as Products of Binomials Ratios and Proportions Solving Equations Multiplying and Dividing Fractions 2 Rational Numbers Difference of Two Squares Factoring Polynomials by Grouping Solving Equations That Contain Rational Expressions Solving Quadratic Equations Dividing and Subtracting Rational Expressions Square Roots and Real Numbers Order of Operations Solving Nonlinear Equations by Substitution The Distance and Midpoint Formulas Linear Equations Graphing Using x- and y- Intercepts Properties of Exponents Solving Quadratic Equations Solving One-Step Equations Using Algebra Relatively Prime Numbers Solving a Quadratic Inequality with Two Solutions Quadratics Operations on Radicals Factoring a Difference of Two Squares Straight Lines Solving Quadratic Equations by Factoring Graphing Logarithmic Functions Simplifying Expressions Involving Variables Adding Integers Decimals Factoring Completely General Quadratic Trinomials Using Patterns to Multiply Two Binomials Adding and Subtracting Rational Expressions With Unlike Denominators Rational Exponents Horizontal and Vertical Lines
Try the Free Math Solver or Scroll down to Tutorials!

 Depdendent Variable

 Number of equations to solve: 23456789
 Equ. #1:
 Equ. #2:

 Equ. #3:

 Equ. #4:

 Equ. #5:

 Equ. #6:

 Equ. #7:

 Equ. #8:

 Equ. #9:

 Solve for:

 Dependent Variable

 Number of inequalities to solve: 23456789
 Ineq. #1:
 Ineq. #2:

 Ineq. #3:

 Ineq. #4:

 Ineq. #5:

 Ineq. #6:

 Ineq. #7:

 Ineq. #8:

 Ineq. #9:

 Solve for:

 Please use this form if you would like to have this math solver on your website, free of charge. Name: Email: Your Website: Msg:

# Factoring Quadratic Trinomials

A trinomial is a mathematical expression with 3 terms. A quadratic trinomial is a trinomial whose highest exponent is two. The general form of a quadratic trinomial is ax 2 + bx + c, where a is the leading coefficient (number in front of the variable with highest degree) and c is the constant (number with no variable).

## I. Types of Quadratic Trinomials

1. Quadratic trinomials with a leading coefficient of one.

Example: x 2 - 12x + 27

a = 1 b = -12 c = 27

2. Quadratic trinomials with a leading coefficient other than one.

Example: 2x 2 + 17x + 26

a = 2 b = 17 c = 26

## II. Factoring Quadratic Trinomials with Leading Coefficient of One (5 steps)

1. List all possible factors of the constant.

2. Determine which factors will add together to give the middle coefficient. (* see Sect IV Hints) Note: If no factors can be found, a different form of factoring must be used.

3. Write two sets of parentheses with x ' s on the left inside each set.

4. Place the factors inside the parentheses after the x's.

5. Check your answer using the FOIL method and compare to the original trinomial.

Example: x 2 - 12x + 27

Step 1) Factors of constant.

 1, 27 -1, -27 3, 9 -3, -9

Step 2) Sum of factors equals middle term.

 1 + 27 = 28 -1 - 27 = -28 3 + 9 = 12 -3 - 9 = -12

Step 3) Set up Parentheses.

Step 4) Place correct factors. (x - 3)(x - 9)

Step 5) FOIL and Compare.

(x - 3)(x - 9)

x 2 - 3x - 9x + 27

x 2 - 12x + 27

original: x 2 - 12x + 27

## III. Factoring Quadratic Trinomials with Leading Coefficient Other Than One

1. Multiply the leading coefficient and the constant together.

2. List all possible factors of the result from step one.

3. Determine which factors will add together to give the middle coefficient. (* see Sect IV Hints) Note: If no factors can be found, a different form of factoring must be used.

4. Write the middle coefficient as the sum of the factors using the results from step three and rewrite the polynomial.

5. Group the first two terms and the last two terms together.

6. Factor the Greatest Common Factor (GCF) from each group.

7. Factor the GCF again.

8. Check your answer using the FOIL method and compare to the original trinomial.

Example: 2x 2 + 17x + 26

Step 1) Multiply a & c.

2 * 26 = 52

Step 2) Factors of a * c.

 1, 52 -1, -52 2, 26 -2, -26 4, 13 -4, -13

Step 3) Sum of the factors equals middle term.

 1 + 52 = 53 -1 - 52 = -53 2 + 26 = 28 -2 - 26 = -28 4 + 13 = 17 -4 - 13 = -17

Step 4) Rewrite middle term as Sum of the factors.

17x = 4x + 13x

Now polynomial looks like 2x 2 + 4x + 13x + 26

Step 5) Group Terms.

(2x 2 + 4x) + (13x + 26)

Step 6) Factor GCF.

2x(x + 2) + 13(x + 2)

Step 7) Factor GCF again.

(x + 2)(2x + 13)

Step 8) FOIL and Compare to original trinomial.

(x + 2)(2x + 13)

2x 2 + 13x + 4x + 26

2x 2 + 17x + 26

original: 2x 2 + 17x + 26

## IV. Hints on Factoring Quadratic Trinomials

1. If both signs in the trinomial are positive, then both signs in the factored form will be positive.

x 2 + 6x + 8

positive

(x + 2) (x + 4)

2. If the first sign is negative and the second sign is positive, then both signs in the factored form will be negative.

x 2 - 16x + 39

negative positive

(x - 13) (x - 3)

3. If both signs are negative, then, in factored form, the larger factor will be negative, and the smaller factor will be positive.

x 2 - 8x - 33

negative positive

(x - 11) (x + 3)

4. If the first sign is positive and the second sign is negative, then, in factored form, the larger factor will be positive, and the smaller factor will be negative.

x 2 + 2x - 35

positive negative

(x + 7) (x - 5)

 Copyrights © 2005-2024