Step 4: Going back to the original equationħ x 2 + 18 x + 11= 0 Factorize the left hand side of the equationĮxample 3: Get the values of x for the equation 4 x 2 + 26 x + 12 = 0 Step 2: Write down the different combinations of the factors and perform the distributive property to check. Since 7 and 11 are prime numbers there are only two possibilities to try out. Step 5: Going back to the original equationĢ x 2 – 14 x + 20 = 0 Factorize the left hand side of the equationĮxample 2: Get the values of x for the equation 7 x 2 + 18 x + 11 = 0 Step 4: Write out the factors and check using the distributive property.Ģ( x – 2) ( x – 5) = 2( x 2 – 5 x – 2 x + 10) 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 finding common factors. X - 4 = 0 ⇒ x = 4 If the Coefficient of x 2 Is Greater Than 1 X 2 – 6 x + 8 = 0 Factorize the left hand side of the equation Step 2: Find the factors whose sum is – 6: We need to get the negative factors of 8 to get a negative sum. Get the values of x for the equation: x 2 – 6 x + 8 = 0 X 2 – 5 x – 6 = 0 Factorize the left hand side of the equationĮxample 4:* (b is negative and c is positive)* Step 2: Find the factors whose sum is –5: Get the values of x for the equation: x 2 – 5 x – 6 X 2 + 4 x – 5 = 0 Factorize the left hand side of the equation Get the values of x for the equation: x 2 + 4 x – 5 = 0 X 2 + 7 x + 10 = 0 Factorize the left side of the quadratic equationĮxample 2: (b is positive and c is negative) Step 4: Going back to the original quadratic equation Step 3: Write out the factors and check using the distributive property. Solve the quadratic equation: x 2 + 7 x + 10 = 0 To factorize quadratic equations of the form: x 2 + bx + c, you will need to find two numbers whose product is c and whose sum is b. In other cases, you will have to try out different possibilities to get the right factors for quadratic equations. For example: Square of Sum, Square of Difference and Difference of Two Squares. We try to find common factors, and then look for patterns that will help you to factorize the quadratic equation. When factoring Quadratic Equations, of the form:Īx 2* + bx + c* = 0 where *a*, *b* and *c* are numbers and *a* ≠ 0.
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