# FACTORING TRINOMIALS WHEN A IS NOT 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 is not equal to 1.

If the quadratic polynomial is in the form,

ax2 + bx + c ---> Both factors are positive

ax2 - bx + c ---> Both factors are negative

ax2 - bx - c ---> The large factor will be negative

ax2 + bx - c ---> The small factor will be negative

Factoring trinomials when a is not 1.

Problem 1:

7m² + 6m - 1

Solution :

= 7m² + 6m - 1

 Factors of -7-1 and 7 Sum6 Product-7

= 7m² + 7m – m – 1

= 7m (m + 1) – 1 (m + 1)

= (7m - 1) (m + 1)

Problem 2 :

3k² - 10k + 7

Solution :

 Factors of 21-3 and -7 Sum-10 Product21

= 3k² - 10k + 7

= 3k² - 3k - 7k + 7

= 3k(k - 1) - 7(k - 1)

= (3k - 7) (k - 1)

Problem 3 :

5x² - 36x - 81

Solution :

 Factors of -405-45 and 9 Sum-36 Product-405

= 5x² - 36x - 81

= 5x² - 45x + 9x – 81

= 5x(x - 9) + 9(x - 9)

= (5x + 9) (x - 9)

Problem 4 :

2x² - 9x - 81

Solution :

 Factors of -162-18 and 9 Sum-9 Product-162

= 2x² - 9x - 81

= 2x² - 18x + 9x - 81

= 2x(x - 9) + 9(x - 9)

= (2x + 9) (x - 9)

Problem 5 :

3n² - 16n + 20

Solution :

 Factors of 60-10 and -6 Sum-16 Product60

= 3n² - 16n + 20

= 3n² - 6n – 10n + 20

= 3n(n - 2) – 10(n - 2)

= (3n - 10) (n - 2)

Problem 6 :

2r² + 7r - 30

Solution :

 Factors of 6012 and -5 Sum-60 Product7

= 2r² + 7r - 30

= 2r² +12r – 5r – 30

= 2r(r + 6) – 5(r + 6)

= (2r - 5) (r + 6)

Problem 7 :

5k² + 8k + 80

Solution :

5k² + 8k + 80 is not factorable.

Problem 8 :

5x² - 14x + 8

Solution :

 Factors of 60-10 and -4 Sum-14 Product40

= 5x² - 14x + 8

= 5x² - 10x – 4x + 8

= 5x(x - 2) – 4(x - 2)

= (5x - 4) (x - 2)

Problem 9 :

7p² - 20p + 12

Solution :

 Factors of 84-14 and -6 Sum-20 Product84

= 7p² - 20p + 12

= 7p² - 14p – 6p + 12

= 7p(p - 2) – 6(p - 2)

= (7p - 6) (p - 2)

Problem 10 :

3v² + 14v - 49

Solution :

= 3v² + 14v - 49

= 3v² + 21v – 7v – 49

= 3v(v + 7) – 7(v + 7)

= (3v - 7) (v + 7)

Problem 11 :

7x² - 26x - 45

Solution :

= 7x² - 26x - 45

= 7x² - 35x + 9x – 45

= 7x(x - 5) + 9(x - 5)

= (7x + 9) (x - 5)

Problem 12 :

5p² - 52p + 20

Solution :

= 5p² - 52p + 20

= 5p² - 50p – 2p + 20

= 5p(p - 10) – 2(p - 10)

= (5p - 2) (p - 10)

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