## SOLVING QUADRATIC EQUATIONS BY FACTORING WORKSHEET

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,

## Solving Quadratic Equations by Factoring Worksheet - Problems

Problem 1 :

Solve the quadratic equation by factoring :

x2 – 5x – 24  =  0

Problem 2 :

Solve the quadratic equation by factoring :

3x2 – 5x – 12  =  0

Problem 3 :

Solve the quadratic equation by factoring :

(x + 4)2  =  2x + 88

Problem 4 :

Solve the quadratic equation by factoring :

√5x2 + 2x – 3√5  =  0

Problem 5 :

Solve the quadratic equation by factoring :

x - 18/x  =  3 ## Solving Quadratic Equations by Factoring Worksheet - Solutions

Problem 1 :

Solve the quadratic equation by factoring :

x2 – 5x – 24  =  0

Solution :

In the given quadratic equation, the coefficient of x2 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 :

3x2 – 5x – 12  =  0

Solution :

In the given quadratic equation, the coefficient of x2 is not 1.

So, multiply the coefficient of x2 and the constant term "-12".

⋅ (-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 x2, 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

ax2 + bx + c  =  0

Then,

(x + 4)2  =  2x + 88

(x + 4)(x + 4)  =  2x + 88

x2 + 4x + 4x + 16  =  2x + 88

x2 + 8x + 16  =  2x + 88

x2 + 6x - 72  =  0

In the quadratic equation above, the coefficient of x2 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 :

√5x2 + 2x – 3√5  =  0

Solution :

In the given quadratic equation, the coefficient of x2 is not 1.

So, multiply the coefficient of x2 and the constant term "-3√5".

√5 ⋅ (-3√5)  =  -15

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 x2, 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

ax2 + bx + c  =  0

Then,

x - 18/x  =  3

x2/x - 18/x  =  3

(x2 - 18)/x  =  3

x2 - 18  =  3x

x2 - 3x - 18  =  0

In the quadratic equation above, the coefficient of x2 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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