In other words, the standard form represents all quadratic equations. The standard form of a quadratic equation is ax 2 + bx + c = 0 when a ≠ 0 and a, b, and c are real numbers.Īll quadratic equations can be put in standard form, and any equation that can be put in standard form is a quadratic equation. Solve a quadratic equation by factoring.Ī quadratic equation is a polynomial equation that contains the second degree, but no higher degree, of the variable.Place a quadratic equation in standard form.Upon completing this section you should be able to: QUADRATICS SOLVED BY FACTORING OBJECTIVES You now have the necessary skills to solve equations of the second degree, which are known as quadratic equations. In previous chapters we have solved equations of the first degree. All skills learned lead eventually to the ability to solve equations and simplify the solutions. In these cases it is usually better to solve by completing the square or using the quadratic formula.Solving equations is the central theme of algebra. However, not all quadratic equations can be factored evenly. (1,180) (2,90) (3,60) (4,45) (5,36) (6,30) ģ.2: p = -180, a negative number, therefore one factor will be positive and the other negative.ģ.3: b = 24, a positive number, therefore the larger factor will be positive and the smaller will be negative.įactoring quadratics is generally the easier method for solving quadratic equations. Is negative then one factor will be positive and the other negative. This equation is already in the proper form where a = 15, b = 24 and c = -12. Step 1: Write the equation in the general form ax 2 + bx + c = 0. This equation is already in the proper form where a = 4, b = -19 and c = 12.ģ.2: p = 48, a positive number, therefore both factors will be positive or both factors will be negative.ģ.3: b = -19, a negative number, therefore both factors will be negative. Step 8: Set each factor to zero and solve for x.

Now that the equation has been factored, solve for x. Using the reverse of the distributive property we can write the outside expressions (shown in red in Step 6) as a second polynomial factor. If this does not occur, regroup the terms and try again. Notice that the parenthetical expression is the same for both groups. Step 7: Rewrite the equation as two polynomial factors. Step 6: Factor the greatest common denominator from each group. Step 4: Rewrite bx as a sum of two x -terms using the factor pair found in Step 3. If p is negative and b is positive, the larger factor will be positive and the smaller will be negative.ģ.2: p = 12, a positive number, therefore both factors will be positive or both factors will be negative.ģ.3: b = 7, a positive number, therefore both factors will be positive. If p is positive and b is negative, both factors will be negative. If both p and b are negative, the larger factor will be negative and the smaller will be positive. If both p and b are positive, both factors will be positive. If p is negative then one factor will be positive and the other negative.ģ.3: Determine the factor pair that will add to give b. If p is positive then both factors will be positive or both factors will be negative. Step 3: Determine the factor pairs of p that will add to b.įirst ask yourself what are the factors pairs of p, ignoring the negative sign for now.

c and find the factors of the result, let's call this p.

This equation is already in the proper form where a = 3, b = 7 and c = 4. Step 1: Write the equation in the general form

Solving quadratic equation by factoring