FACTORING TRINOMIALS WHEN A IS 1

The general form any quadratic equation will be in the form

ax2 + bx + c

To factorize a quadratic polynomial, we have to check whether the coefficient of x2 is 1 or not equal to 1. 

Here we see examples on factoring quadratic polynomial when the coefficient x2 is, that is a = 1.

Write each trinomial in factored form (as the product of two binomials).

Problem 1 :

p² + 14p + 48

Solution :

Factors of 48

1 and 48

2 and 24

3 and 16

4 and 12

6 and 8

Sum

49

26

19

16

14

Product

48

48

48

48

48

= (p + 6) (p + 8)

Problem 2 :

n² + 10n + 16

Solution :

Factors of 16

1 and 16

2 and 8

4 and 4

Sum

17

10

8

Product

16

16

16

= (n + 2) (n + 8)

Problem 3 :

p² + 14p + 40

Solution :

Factors of 40

1 and 40

2 and 20

4 and 10

Sum

41

22

14

Product

40

40

40

= (p + 4) (p + 10)

Problem 4 :

r² + 9r + 18

Solution :

Factors of 18

1 and 18

2 and 9

3 and 6

Sum

19

11

9

Product

18

18

18

= (r + 3) (r + 6)

Problem 5 :

p² - 8p + 7

Solution :

Factors of 7

-1 and -7

Sum

-8

Product

7

= (p - 1) (p - 7)

Problem 6 :

b² - 9b + 14

Solution :

Factors of 14

-1 and -14

-2 and -7

Sum

-15

-9

Product

14

14

= (b - 2) (b - 7)

Problem 7 :

b² - 8b + 15

Solution :

Factors of 15

-1 and -15

-3 and -5

Sum

-16

-8

Product

15

15

= (b - 3) (b - 5)

Problem 8 :

m² - 16m + 63

Solution :

Factors of 63

-1 and -63

-3 and -21

-7 and -9

Sum

-64

-24

-16

Product

63

63

63

= (m - 7) (m - 9)

Problem 9 :

k² - 4k – 60

Solution :

Factors of -60

1 and -60

2 and -30

3 and -20

5 and -12

6 and -10

Sum

-59

-28

-17

-7

-4

Product

-60

-60

-60

-60

-60

= (k + 6) (k - 10)

Problem 10 :

m² + m – 6

Solution :

Factors of -6

1 and -6

-2 and 3

Sum

5

1

Product

-6

-6

= (m - 2) (m + 3)

Problem 11 :

p² - 2p – 15

Solution :

Factors of -15

1 and -15

3 and -5

Sum

-14

-2

Product

-15

-15

= (p + 3) (p - 5)

Problem 12 :

r² + r – 20

Solution :

Factors of -20

-1 and 20

-4 and 5

Sum

19

1

Product

-20

-20

= (r - 4) (r + 5)

Recent Articles

  1. Solving Word Problems on Numbers Worksheet

    Feb 25, 24 07:44 AM

    Solving Word Problems on Numbers Worksheet

    Read More

  2. Solving Word Problems on Numbers

    Feb 24, 24 11:07 PM

    Solving Word Problems on Numbers

    Read More

  3. Reducing Ratios to Lowest Terms Worksheet

    Feb 24, 24 08:49 PM

    Reducing Ratios to Lowest Terms Worksheet

    Read More