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Online Quiz (Worksheet A B C D)

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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: c2 + 13cd + 36d2
(c+3d)2
(c+9d)(c-4d)
(c+9d)(c+4d)

Q 2: x2 + 8xy - 65y2
(x-13y)(x+5y)
(x-13y)(x-5y)
(x+13y)(x-5y)

Q 3: u2 - 3uv -108v2
(u-12v)(u+9v)
(u-10v)(u+7v)
(u+11v)(u+9v)

Q 4: y2 - 6yz + 5z2
(y-z)(y+5z)
(y-z)(y-5z)
(y-z)2

Q 5: r2 + 15rs + 50s2
(r+5s)(r+10s)
(r+3s)(r+12s)
(r+7s)(r+8s)

Q 6: a2 + 2ab - 15b2
(a-3b)(a+5b)
(a-5b)(a+3b)
(a-b)(a+b)

Q 7: x2 + 9xy + 14y2
(x+4)(x+6y)
(x+7y)(x+2y)
(x+5y)(x+4y)

Q 8: g2 + 4gh - 60h2
(g+6)(g+10h)
(g-5h)(g-9h)
(g-6h)(g+10h)

Question 9: This question is available to subscribers only!

Question 10: This question is available to subscribers only!


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