Factor quadratic equation how to#

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.

Factor quadratic equation 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 is known as a quadratic equation or the square-like equation.Apply the distributive property of multiplication to factor algebraic equations. Furthermore, the area of a square of side length x is such that it is given by x2, a polynomial equation consisting of an exponent. Question 6: Why the quadratic equation is known by the name quadratic?Īnswer: Quadratum is the Latin word for square. Furthermore, such an operation is known as squaring. Question 5: How does a problem become quadratic?Īnswer: A quadratic refers to a type of problem that deals with a variable multiplied by itself. Moreover, a, b, and c are representative of the known numbers. Question 4: In maths, what is meant by quadratic equations?Īnswer: In maths, a quadratic equation is an equation that one can rearrange in the standard form. One can check by inserting answer in the original equation.Put all terms on one side of the equal sign such that zero is left on the other side.Question 3: How should one solve the quadratic equation by factoring?Īnswer: One can solve the quadratic equation by the following steps: Solving it for x, we get the following two solutions:

The general form of the quadratic equation can be written as ax 2 + bx + c = 0. So a quadratic equation, which is a polynomial equation of order 2, must have 2 solutions. “A polynomial equation of degree n, has n roots” The fundamental theorem of algebra, when applied to polynomial equations of this form, provide an important result, which is: “A polynomial equation has at least one solution”Īny equation of the form a 1x (n-1) + a 2x (n-2) + a 3x (n-3) + … + a n = 0 is a polynomial equation of degree n. How many solutions must it have? How many solutions does any equation have? The answer is provided by the Fundamental Theorem of Algebra: Modulus and Conjugate of a Complex NumberĪ quadratic equation is an equation of degree 2.

Browse more Topics under Complex Numbers And Quadratic Equations The most effective way to solve a quadratic equation is to use the quadratic formula. The equation has two solutions which may be identical or different. We say that any equation that has the form ax 2 + bx + c = 0, or an equation that we can reduce to this form is a quadratic equation. In earlier classes, you read about the quadratic equations.