Solving Quadratic Equations by Factoring Examples with Answers

SOLVING QUADRATIC EQUATIONS BY FACTORING EXAMPLES WITH ANSWERS

Solving Quadratic Equations by Factoring Examples with Answers :

In this section, we will see how to solve a quadratic equation by factoring.

We follow the steps provided below to factor a quadratic equation.

Step 1 :

Write the equation in form ax² + bx + c = 0.

Step 2 :

If the coefficient of x² is 1, we have to take the constant term and split it into two factors such that the product of those factors must be equal to the constant term and simplified value must be equal to the middle term.

If the coefficient of x² is not 1, we have to multiply the constant term along with the coefficient of x².Split the product into two factors.

Step 3 :

Rewrite the middle with those numbers.

Step 4 :

Factor the first two and last two separately.

Step 5 :

Equate the linear factors to zero and solve for x.

Solving Quadratic Equations by Factoring Examples with Answers

Example 1 :

Solve x² + 17x + 60 = 0

Solution :

x² + 17x + 60 = 0

60 = 12 ⋅ 5 and 17 = 12 + 5

Factors of 60 are 12 and 5. By multiplying 12 and 5, we get 60 and simplifying 12 and 5, we get 17.

x² + 12x + 5x + 60 = 0

x(x + 12) + 5(x + 12) = 0

(x + 5) (x + 12) = 0

x + 5 = 0

x = -5

x + 12 = 0

x = -12

Hence the solution is {-5, -12}.

Example 2 :

Solve x² - 5x - 36 = 0

Solution :

x² - 5x - 36 = 0

-36 = -9 ⋅ 4 and -5 = -9 + 4

Factors of -36 are -9 and 4. By multiplying -9 and 4, we get -36 and simplifying -9 and 4, we get -5.

x² - 9x + 4x - 36 = 0

x(x - 9) + 4(x - 9) = 0

(x - 9) (x + 4) = 0

x - 9 = 0

x = 9

x + 4 = 0

x = -4

Hence the solution is {-4, 9}.

Example 3 :

Solve x² - 14x + 48 = 0

Solution :

x² - 14x + 48 = 0

48 = -8 ⋅ (-6) and -14 = -8 - 6

Factors of 48 are -8 and -6. By multiplying -8 and -6, we get 48 and simplifying -8 and -6, we get -14.

x² - 8x - 6x + 48 = 0

x(x - 8) - 6(x - 8) = 0

(x - 8) (x - 6) = 0

x - 8 = 0

x = 8

x - 6 = 0

x = 6

Hence the solution is {6, 8}.

Example 4 :

Solve x² + 2x - 24 = 0

Solution :

x² + 2x - 24 = 0

-24 = 6 ⋅ (-4) and 2 = 6 - 4

Factors of -24 are 6 and -4. By multiplying 6 and -4, we get -24 and simplifying 6 and -4, we get 2.

x² + 6x - 4x - 24 = 0

x(x + 6) - 4(x + 6) = 0

(x + 6) (x - 4) = 0

x + 6 = 0

x = -6

x - 4 = 0

x = 4

After having gone through the stuff given above, we hope that the students would have understood how to solve quadratic equations using factoring method.

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