solving quadratic equations by factoring

#Solving quadratic equations by factoring how to

Believe it or not, for uncomplicated quadratic equations, one of the accepted means of factoring is simply to examine the problem, then just consider possible answers until you find the right one. Note: the numbers in the blanks can be fractions or decimals.If it is in the form x 2-bx-c, you answer is in the form (x + _)(x - _).If it is in the form x 2+bx+c, your answer looks like this: (x + _)(x + _).If the quadratic equation is in the form x 2-bx+c, your answer is in this form: (x - _)(x - _).Slight variations on this basic shortcut exist for slight variations in the equation itself:.3 and 2 multiply together to make 6 and also add up to make 5, so we can simplify this equation to (x + 3)(x + 2). For example, let's consider the quadratic equation x 2 + 5x + 6 = 0.These two terms, when multiplied together, produce your quadratic equation - in other words, they are your quadratic equation's factors. Once you find these two numbers d and e, place them in the following expression: (x+d)(x+e). Find two numbers that both multiply to make c and add to make b. If your quadratic equation it is in the form x 2 + bx + c = 0 (in other words, if the coefficient of the x 2 term = 1), it's possible (but not guaranteed) that a relatively simple shortcut can be used to factor the equation. In quadratic equations where a = 1, factor to (x+d )(x+e), where d × e = c and d + e = b. x/2 + 4, for instance, can be simplified to 1/2(x + 8), and -7x + -21 can be factored to -7(x + 3). This process also applies to equations with negatives and fractions.6 is the biggest number that divides evenly into both 12x and 6, so we can simplify the equation to 6(2x + 1). To factor the algebraic equation 12 x + 6, first, let's try to find the greatest common factor of 12x and 6. This simplification process is possible because of the distributive property of multiplication, which states that for any numbers a, b, and c, a(b + c) = ab + ac. Usually, to make the equation as simple as possible, we try to search for the greatest common factor.

#Solving quadratic equations by factoring how to

Using your knowledge of how to factor both lone numbers and variables with coefficients, you can simplify simple algebraic equations by finding factors that the numbers and variables in an algebraic equation have in common.

This article has been viewed 662,027 times.Īpply the distributive property of multiplication to factor algebraic equations. This article has been fact-checked, ensuring the accuracy of any cited facts and confirming the authority of its sources. There are 7 references cited in this article, which can be found at the bottom of the page. Additionally, David has worked as an instructor for online videos for textbook companies such as Larson Texts, Big Ideas Learning, and Big Ideas Math. After attaining a perfect 800 math score and a 690 English score on the SAT, David was awarded the Dickinson Scholarship from the University of Miami, where he graduated with a Bachelor’s degree in Business Administration. With over 10 years of teaching experience, David works with students of all ages and grades in various subjects, as well as college admissions counseling and test preparation for the SAT, ACT, ISEE, and more. David Jia is an Academic Tutor and the Founder of LA Math Tutoring, a private tutoring company based in Los Angeles, California. Step 4: Write out the factors and check using the distributive property.This article was co-authored by David Jia. 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 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. Sometimes the coefficient of x in quadratic equations may not be 1, but the expression can be simplified by first finding common factors. If the Coefficient of x 2 Is Greater Than 1

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.