**Solving Quadratic Equations by Factoring Worksheet :**

Worksheet given in this section will be much useful for the students who would like to practice problems on solving quadratic equations by factoring.

Before look at the worksheet, if you would like to learn how to solve quadratic equations by factoring,

**Problem 1 :**

Solve the quadratic equation by factoring :

x^{2} – 5x – 24 = 0

**Problem 2 :**

Solve the quadratic equation by factoring :

3x^{2} – 5x – 12 = 0

**Problem 3 :**

Solve the quadratic equation by factoring :

(x + 4)^{2} = 2x + 88

**Problem 4 :**

Solve the quadratic equation by factoring :

√5x^{2} + 2x – 3√5 = 0

**Problem 5 :**

Solve the quadratic equation by factoring :

x - 18/x = 3

**Problem 1 :**

Solve the quadratic equation by factoring :

x^{2} – 5x – 24 = 0

**Solution :**

In the given quadratic equation, the coefficient of x^{2} is 1.

Decompose the constant term -24 into two factors such that the product of the two factors is equal to -24 and the addition of two factors is equal to the coefficient of x, that is 5.

Then, the two factors of -24 are

+3 and -8

Factor the given quadratic equation using and +3 and solve for x.

(x + 3)(x - 8) = 0

x + 3 = 0 or x - 8 = 0

x = -3 and x = 8

So, the solution is {-3, 8}.

**Problem 2 :**

Solve the quadratic equation by factoring :

3x^{2} – 5x – 12 = 0

**Solution :**

In the given quadratic equation, the coefficient of x^{2} is not 1.

**So, m****ultiply the coefficient of x ^{2} and the constant term "-12". **

**3 **⋅ (-12) = -36

Decompose -36 into two factors such that the product of two factors is equal to -36 and the addition of two factors is equal to the coefficient of x, that is -5.

Then, the two factors of -36 are

+4 and -9

Now we have to divide the two factors 4 and -3 by the coefficient of x^{2}, that is 3.

Now, factor the given quadratic equation and solve for x as shown below.

(3x + 4)(x - 3) = 0

3x + 4 = 0 or x - 3 = 0

x = -4/3 or x = 3

So, the solution is {-4/3, 3}.

**Problem 3 :**

Solve the quadratic equation by factoring :

(x + 4)^{2} = 2x + 88

**Solution :**

Write the given quadratic equation in the form

ax^{2} + bx + c = 0

Then,

(x + 4)^{2} = 2x + 88

(x + 4)(x + 4) = 2x + 88

x^{2} + 4x + 4x + 16 = 2x + 88

x^{2} + 8x + 16 = 2x + 88

x^{2} + 6x - 72 = 0

In the quadratic equation above, the coefficient of x^{2} is 1.

Decompose the constant term -72 into two factors such that the product of the two factors is equal to -72 and the addition of two factors is equal to the coefficient of x, that is +6.

Then, the two factors of -72 are

+12 and -6

Factor the given quadratic equation using +12 and -6 and solve for x.

(x + 12)(x - 6) = 0

x + 12 = 0 or x - 6 = 0

x = -12 and x = 6

So, the solution is {-12, 6}.

**Problem 4 :**

Solve the quadratic equation by factoring :

√5x^{2} + 2x – 3√5 = 0

**Solution :**

In the given quadratic equation, the coefficient of x^{2} is not 1.

**So, m****ultiply the coefficient of x ^{2} and the constant term "-3**√5

√5** ⋅ (-3**√5

Decompose -15 into two factors such that the product of two factors is equal to -15 and the addition of two factors is equal to the coefficient of x, that is +2.

Then, the two factors of -15 are

+5 and -3

Now we have to divide the two factors +5 and -3 by the coefficient of x^{2}, that is √5.

Now, factor the given quadratic equation and solve for x as shown below.

(x + √5)(√5x - 3) = 0

x + √5 = 0 or √5x - 3 = 0

x = -√5 or x = 3/√5

So, the solution is {-√5, 3/√5}.

**Problem 5 :**

Solve the quadratic equation by factoring :

x - 18/x = 3

**Solution :**

Write the given quadratic equation in the form

ax^{2} + bx + c = 0

Then,

x - 18/x = 3

x^{2}/x - 18/x = 3

(x^{2} - 18)/x = 3

x^{2} - 18 = 3x

x^{2} - 3x - 18 = 0

In the quadratic equation above, the coefficient of x^{2} is 1.

Decompose the constant term -18 into two factors such that the product of the two factors is equal to -18 and the addition of two factors is equal to the coefficient of x, that is -3.

Then, the two factors of -18 are

+3 and -6

Factor the given quadratic equation using +3 and -6 and solve for x.

(x + 3)(x - 6) = 0

x + 3 = 0 or x - 6 = 0

x = -3 and x = 6

So, the solution is {-3, 6}.

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

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