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)
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