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Middle/High School Algebra, Geometry, and Statistics (AGS)
4.3 Factorization of any Quadratic Polynomial - I

Method of Factorization:

1. Multiply the coefficient of x2 by the constant term.

2. Resolve this product into two factors such that their sum is the coefficient of x.

3. Rewrite the x term as the term of two terms with these coefficients.

4. Then we can find the factors.

Example:
Factorize, 6x2+19x+15.

Solution:
Given that, 6x2+19x+15.
Here x2 coefficient is 6 and constant term is 15,
the product of these terms is = 6 * 15 = 90
19 = 10 + 9 = 10 * 9 = 90.
Therefore, 6x2+19x+15 = (6x2+10x)+(9x+15).
Take 2x and 3 as common, we get
= 2x(3x+5)+3(3x+5)
Take (3x+5) as common, we get
= (3x+5)(2x+3)

Directions: Solve the following problems. Also write at least ten examples of your own.
Q 1: Factorize, 8x2+42x+10.
(8x+2)(x+5)
(2x+3)(2x+1)
(8x+2)(x+4)
(3x+2)(x+7)

 Q 2: Factorize, 3x2+23x+14.
(8x+2)(x+5)
(7x+5)(x+3)
(3x+2)(x+7)
(2x+5)(x+3)

Q 3: Factorize, 6x2+25x+21.
(2x+3)(2x+1)
(6x+7)(x+3)
(8x+2)(x+5)
(2x+5)(x+6)

 Q 4: Factorize, 4x2+8x+3.
(2x+3)(2x+1)
(3x+2)(x+7)
(2x+5)(x+6)
(8x+2)(x+5)

Q 5: Factorize, 7x2+26x+15.
(2x+5)(x+3)
(7x+5)(x+3)
(2x+5)(x+6)
(3x+2)(x+7)

 Q 6: Factorize, 2x2+17x+30.
(8x+2)(x+5)
(2x+5)(x+6)
(3x+2)(x+7)
(2x+3)(2x+1)

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