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### Middle/High School Algebra, Geometry, and Statistics (AGS)4.6 Factoring Quadratic Equations with Two Variables

Example:
x2 + 9xy + 14y2
To factor quadratic equation with two variables, you must find factors of the form x + py and x + qy.

First, find the signs of the factors needed.
In this example b = 9 and c = 14.
Because both b and c are positive, you must find two positve factors of 14 that have a sum of 9.

 Factors of 14 Sum of factors 14,1 14+1 =15 7,2 7+2=9 Correct sum

The factors 7 and 2 have a sum of 9, so 7 and 2 are the correct values of p and q
x + 9xy + 14y
= x +7xy + 2xy + 14y
= x (x + 7y) + 2y ( x + 7y)
= (x+7y)(x+2y)

Directions: Answer the following questions. Also write at least 5 examples of your own.
 Q 1: r2 + 15rs + 50s2(r+3s)(r+12s)(r+7s)(r+8s)(r+5s)(r+10s) Q 2: m2 - mn - 42n2(m-7n)(m+6n)(m-5n)(m+4n)(m-8n)(m+7n) Q 3: c2 + 13cd + 36d2(c+9d)(c-4d)(c+3d)2(c+9d)(c+4d) Q 4: g2 + 4gh - 60h2(g+6)(g+10h)(g-5h)(g-9h)(g-6h)(g+10h) Q 5: u2 - 3uv -108v2(u-10v)(u+7v)(u-12v)(u+9v)(u+11v)(u+9v) Q 6: x2 + 9xy + 14y2(x+4)(x+6y)(x+7y)(x+2y)(x+5y)(x+4y) Q 7: x2 + 8xy - 65y2(x-13y)(x-5y)(x+13y)(x-5y)(x-13y)(x+5y) Q 8: x2 - 4xy + 4y2 (x-2y)(x-2y)(x-2y)2(x-2y)(x+2y) Question 9: This question is available to subscribers only! Question 10: This question is available to subscribers only!