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

Before look at the worksheet, if you would like to learn how to factor quadratic polynomials,

## Factoring Quadratic Polynomials Worksheet - Problems

Problem 1 :

Factor :

x2 + 6x + 5

Solution :

In the quadratic expression above, the coefficient of x2 is 1.

Decompose the constant term +5 into two factors such that the product of the two factors is equal to +5 and the addition of two factors is equal to the coefficient of x, that is +6.

Then, the two factors of +5 are

+1 and +5

Factor the given quadratic expression using +1 and +5.

x2 + 6x + 5  =  (x + 1)(x + 5)

Therefore, the factors of the given quadratic expression are

(x + 1) and (x + 5)

Problem 2 :

Factor :

x2 + 2x - 35

Solution :

In the quadratic expression above, the coefficient of x2 is 1.

Decompose the constant term -35 into two factors such that the product of the two factors is equal to -35 and the addition of two factors is equal to the coefficient of x, that is +2.

Then, the two factors of -35 are

-5 and +7

Factor the given quadratic expression using -5 and +7.

x2 + 2x - 35  =  (x - 5)(x + 7)

Therefore, the factors of the given quadratic expression are

(x - 5) and (x + 7)

Problem 3 :

Factor :

x2 - 6x - 7

Solution :

In the quadratic expression above, the coefficient of x2 is 1.

Decompose the constant term -7 into two factors such that the product of the two factors is equal to -7 and the addition of two factors is equal to the coefficient of x, that is -6.

Then, the two factors of -7 are

-7 and +1

Factor the given quadratic expression using -7 and +1.

x2 - 6x - 7  =  (x - 7)(x + 1)

Therefore, the factors of the given quadratic expression are

(x - 7) and (x + 1)

Problem 4 :

Factor :

x2 - 18x + 65

Solution :

In the quadratic expression above, the coefficient of x2 is 1.

Decompose the constant term +65 into two factors such that the product of the two factors is equal to +65 and the addition of two factors is equal to the coefficient of x, that is -18.

Then, the two factors of +65 are

-5 and -13

Factor the given quadratic expression using -5 and -13.

x2 - 18x + 65  =  (x - 5)(x - 13)

Therefore, the factors of the given quadratic expression are

(x - 5) and (x - 13)

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

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