# 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 481 and 482 and 243 and 164 and 126 and 8 Sum4926191614 Product4848484848

= (p + 6) (p + 8)

Problem 2 :

n² + 10n + 16

Solution :

 Factors of 161 and 162 and 84 and 4 Sum17108 Product161616

= (n + 2) (n + 8)

Problem 3 :

p² + 14p + 40

Solution :

 Factors of 401 and 402 and 204 and 10 Sum412214 Product404040

= (p + 4) (p + 10)

Problem 4 :

r² + 9r + 18

Solution :

 Factors of 181 and 182 and 93 and 6 Sum19119 Product181818

= (r + 3) (r + 6)

Problem 5 :

p² - 8p + 7

Solution :

 Factors of 7-1 and -7 Sum-8 Product7

= (p - 1) (p - 7)

Problem 6 :

b² - 9b + 14

Solution :

 Factors of 14-1 and -14-2 and -7 Sum-15-9 Product1414

= (b - 2) (b - 7)

Problem 7 :

b² - 8b + 15

Solution :

 Factors of 15-1 and -15-3 and -5 Sum-16-8 Product1515

= (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 Product636363

= (m - 7) (m - 9)

Problem 9 :

k² - 4k – 60

Solution :

 Factors of -601 and -602 and -303 and -205 and -126 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 -61 and -6-2 and 3 Sum51 Product-6-6

= (m - 2) (m + 3)

Problem 11 :

p² - 2p – 15

Solution :

 Factors of -151 and -153 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 Sum191 Product-20-20

= (r - 4) (r + 5)

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