# SOLVING QUADRATIC EQUATIONS BY FACTORING - FACTORING, ROOTS, EXAMPLES, EXERCISE

if you have not already done so.

There, we gave introduction to Quadratic polynomial,
Equations and about Method of Solving by Factoring.

That knowledge is a prerequisite here.

Here, we apply the Method to solve problems.
Solved Examples and Exercise problems are given.

### Example 1 : Solving Quadratic Equations by Factoring

Solve 9x2 + 26x + 16 = 0

Solution of Example 1 of Solving Quadratic Equations by Factoring :

The Factoring of the LHS of the above Equation is given below.

-*-*-*-*-*-*

Let P = 9x2 + 26x + 16

Step 1: Coefficient of x2 x constant term
= 9 x 16 = 144

Step 2: We have to express 144 as two factors whose sum
= coefficient of x = 26;
144 = 2 x 72 = 2 x 2 x 36 = 2 x 2 x 2 x 18 = 8 x 18; (8 + 18 = 26)

Step 3: P = 9x2 + 26x + 16 = 9x2 + 8x + 18x+ 16

Step 4: P = x(9x + 8) + 2(9x + 8)

Step 5: P = (9x + 8)(x + 2)

Thus, Factoring the Quadratic Polynomial, 9x2 + 26x + 16,
we get the Factors as (9x + 8)(x + 2).

-*-*-*-*-*-*

9x2 + 26x + 16 = 0 ⇒ (9x + 8)(x + 2) = 0
⇒ (9x + 8) = 0 or (x + 2) = 0
(9x + 8) = 0 ⇒ 9x = -8 ⇒ x = -8⁄9
(x + 2) = 0 ⇒ x = -2
Thus, x = -8⁄9, -2 are the two roots of the given Quadratic equation. Ans.

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### Example 2 : Solving Quadratic Equations by Factoring

Solve 2 - 5x - 18x2 = 0

Solution of Example 2 of Solving Quadratic Equations by Factoring :

The Factoring of the LHS of the above Equation is given below.

-*-*-*-*-*-*

Let P = 2 - 5x - 18x2 = -18x2 - 5x + 2

Step 1: Coefficient of x2 x constant term
= -18 x 2 = -36

Step 2: We have to express -36 as two factors whose sum
= coefficient of x = -5 ;
-36 = -2 x 18 = -2 x 2 x 9 = 4 x -9; [4 + (-9) = -5]

Step 3: P = -18x2 - 5x + 2 = -18x2 + 4x - 9x+ 2

Step 4: P = 2x(-9x + 2) + 1(-9x + 2)

Step 5: P = (-9x + 2)(2x + 1)

Thus, Factoring of Quadratic Polynomial,2 - 5x - 18x2,
we get the Factors as (-9x + 2)(2x + 1).

-*-*-*-*-*-*

2 - 5x - 18x2 = 0 ⇒ (-9x + 2)(2x + 1) = 0
⇒ (-9x + 2) = 0 or (2x + 1) = 0
(-9x + 2) = 0 ⇒ -9x = -2 ⇒ x = -2⁄-9 = 2⁄9
(2x + 1) = 0 ⇒ 2x = -1 ⇒ x = -1⁄2
Thus, x = 2⁄9, -1⁄2 are the two roots of the given Quadratic equation. Ans.

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## Exercise : Solving Quadratic Equations by Factoring

Solve the following problems on

1. Solve 8x2 + 25x + 18 = 0.
2. Solve 3 - 2x - 21x2 = 0.

For Answers See at the bottom of the Page.

NOTE: You may solve these problems of Exercise
using Quadratic Formula, after learning it.

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