Factors Of Polynomials

Factors of Polynomials

In the following, the left side is equal to the right side.

Left Side	Right Side
A2 + B2	(A + i B) (A - i B), i=sqrt(-1), i2=-1
A2 - B2	(A + B) (A - B)
A2 + 2 A B + B2	(A + B)2
A2 - 2 A B + B2	(A - B)2
A3 + B3	(A + B) (A2 - A B + B2)
A3 - B3	(A - B) (A2 + A B + B2)
A3 + 3 A2B + 3 A B2 + B3	(A + B)3
A3 - 3 A2B + 3 A B2 - B3	(A - B)3
A3 - A2B - A B2 + B3	(A - B)2 (A + B)
A3 + A2B - A B2 - B3	(A + B)2 (A - B)
A2+B2+C2+2(AB+BC+CA)	(A + B + C)2
A3+B3+C3+6ABC+ 3[A2(B+C)+B2(C+A)+C2(A+B)]	(A + B + C)3
	memorize

 

Left Side	Right Side
A x2 + B x + C	A (x+[B+sqrt(B2-4AC)]/[2A]) (x+[B-sqrt(B2-4AC)]/[2A])
A x2 + B x + C	(2Ax+[B+sqrt(B2-4AC)]) (2Ax+[B-sqrt(B2-4AC)]) / (4A)
x2 + (A + B) x + A B	(x + A) (x + B)
x2 + (A - B) x - A B	(x + A) (x - B)
x2 - (A - B) x - A B	(x - A) (x + B)
x2 - (A + B) x + A B	(x - A) (x - B)
	memorize

 

Left Side	Right Side
x2 + 7 x + 12	(x + 3) (x + 4)
x2 - x - 12	(x + 3) (x - 4)
x2 + x - 12	(x - 3) (x + 4)
x2 - 7 x + 12	(x - 3) (x - 4)
x2 + 8 x + 12	(x + 2) (x + 6)
x2 - 4 x - 12	(x + 2) (x - 6)
x2 + 4 x - 12	(x - 2) (x + 6)
x2 - 8 x + 12	(x - 2) (x - 6)
x2 + 13 x + 12	(x + 1) (x + 12)
x2 - 11 x - 12	(x + 1) (x - 12)
x2 + 11 x - 12	(x - 1) (x + 12)
x2 - 13 x + 12	(x - 1) (x - 12)
	memorize

 

Left Side	Right Side
x2 + 4 sqrt(3) x + 12	(x + 2 sqrt(3)) (x + 2 sqrt(3))
x2 - 12	(x + 2 sqrt(3)) (x - 2 sqrt(3))
x2 - 4 sqrt(3) x + 12	(x - 2 sqrt(3)) (x - 2 sqrt(3))
x2 + 7.3 x + 12	(x + 2.5) (x + 4.8)
x2 - 2.3 x - 12	(x + 2.5) (x - 4.8)
x2 + 2.3 x - 12	(x - 2.5) (x + 4.8)
x2 - 7.3 x + 12	(x - 2.5) (x - 4.8)
x2 + 7.4 x + 12	(x + 2.4) (x + 5)
x2 - 2.6 x - 12	(x + 2.4) (x - 5)
x2 + 2.6 x - 12	(x - 2.4) (x + 5)
x2 - 7.4 x + 12	(x - 2.4) (x - 5)
x2 + 24.5 x + 12	(x + 0.5) (x + 24)
x2 - 23.5 x - 12	(x + 0.5) (x - 24)
x2 + 23.5 x - 12	(x - 0.5) (x + 24)
x2 - 24.5 x + 12	(x - 0.5) (x - 24)
	memorize

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