solve the quadratic equation by factoring

#Solve the quadratic equation by factoring how to#

Solve these linear equations and get two roots of the given quadratic equation. Put each linear factor equal to 0 0 (to apply the zero product rule). General Steps to solve by factoring Out of all of the factor pairs from step 1, look for the pair (if it exists) that add up to b. Step 4: Write out the factors and check using the distributive property. Factorize ax2+bx+c ax2 +bx+c into two linear factors. Step 3: Find the factors whose sum is – 7: We need to get the negative factors of 10 to get a negative sum. Step 2: Find the factors of ( x 2 – 7 x + 10) If there are many factors to consider you may want to use the quadratic formula instead.Įxample 1: Get the values of x for the equation 2 x 2 – 14 x + 20 = 0 Set each factor to zero (Remember: a product of factors is zero if and only if one or more of the factors is zero). Transform the equation using standard form in which one side is zero. When the coefficient of x 2 is greater than 1 and we cannot simplify the quadratic equation by finding common factors, we would need to consider the factors of the coefficient of x 2 and the factors of c in order to get the numbers whose sum is b. To solve an quadratic equation using factoring : 1 1. Step 2: Rewrite the equation with the substitution to put it in quadratic form. (If a 0 and b 0 then the equation is linear, not quadratic. Step 2: Now, find two numbers such that their product is equal to ac and sum equals to b. Step 1: Consider the quadratic equation ax 2 + bx + c 0.

This method is almost similar to the method of splitting the middle term. Solution: Step 1: Identify a substitution that will put the equation in quadratic form. In algebra, a quadratic equation (from Latin quadratus ' square ') is any equation that can be rearranged in standard form as 1 where x represents an unknown value, and a, b, and c represent known numbers, where a 0. Factoring Quadratic Equation using Formula. Click on the links below to learn more about these alternative methods to solving quadratic equations. But no need to worry, we include more complex examples in the next section. We simply must determine the values of r1 r1 and r2 r2. If this happens, you can solve it by using a method called completing the square, or by using the quadratic formula. In these cases, solving quadratic equations by factoring is a bit simpler because we know factored form, y (x-r1) (x-r2) y (xr1)(xr2), will also have no coefficients in front of x x. Put the quadratic expression on one side of the 'equals' sign, with zero on the other side.

#Solve the quadratic equation by factoring how to#

Sometimes the coefficient of x in quadratic equations may not be 1, but the expression can be simplified by first finding common factors. Example 9.4.1 How to Solve Equations in Quadratic Form. If you end up with a quadratic expression that cant be factored, youll need to solve it a different way. How to solve a quadratic equation by factoring. If the Coefficient of x 2 Is Greater Than 1 Good question! A quadratic equation is an equation in which the variable is raised to the second power.Perfect Square Trinomial (Square of a Sum or Square of a Difference) orįactoring Quadratic Equations where the coefficient of x 2 is 1.įactoring Quadratic Equations by Completing the Squareįactoring Quadratic Equations using the Quadratic Formula. The first step in solving a quadratic equation is to expand the equation and, if necessary, resolve any problems with fractions.

Then, by remembering the zero product property, we know the solutions of the equation are the solutions of linear equations. Really, it’s another shining moment for the distributive property of multiplication! We’re not using it to calculate the product, but we can use it to write an expression as a product.įactoring is often used when solving quadratic equations because, then, the quadratic expression is rewritten as a product of linear expressions. Just because math is getting more complicated doesn’t mean we can’t make it a little easier for ourselves! Factoring is one way we can make our calculations a little clearer and easier to follow.Īnd who wouldn’t want to make math easier? What does it mean to factor an expression?įactoring an expression means rewriting it as a product of two or more factors.