Lesson 2 · from §49 of the 1910 text
Common Monomial Factors
The simplest form is ab + ac - ad = a(b + c - d).
Rule. Find by inspection the greatest monomial that divides every term. Divide the polynomial by it, and write the quotient in parentheses after the monomial.
Example. In 9x^2y - 36y^2, every term contains 9y. Dividing gives x^2 - 4y, so 9x^2y - 36y^2 = 9y(x^2 - 4y).
Typing tip: write a factored answer like 9y(x^2 - 4y). Take out the greatest factor; if something common is left inside the parentheses, the checker will tell you.
Quick check
6a^2b + 9ab^2
Exercises
How to type math
Use ^ for powers (a^2), / for fractions ((a+b)/2), sqrt(x) for square roots, and cbrt(x) for cube roots. You can leave out the multiplication sign: 3ab means 3 \cdot a \cdot b. Mixed numbers like 4 1/2 work too. The preview under each box shows how your answer was read.
Factor out the greatest common monomial.
3x + 6
x^3 - x^2
8x - 2x^4
xy + y^2
5b^3 - 15b^6
c^3 - c^2y
x^3 - x + x^2
c^5 - c^3 + c^2
3y - 9y^4 + 12
c^2 + 2bc - c
3y^2 - 15y + 6y^3
10ab - 14bc - 8b^2
y^5 + 3y^4z + 6y^3z^2
4a^2x^2 - 6a^3y^3 + 12a^4x^2y^2
12z^3 + 30a^4z^7 - 18c^3z^5
6c^6 + 10c^10 - 20c^2
8y^8 - 4y^4 - 12y^12
x^4 + x^3 - x^2 + x
-8y^6 - 4y^9 + 12y^3 + 6y^5
14b^5 - 49b^7 + 21b^2 - 7b^3
-a^2x^2y^3 - 3a^4x^3y^2 - 2a^3x^5y^6z^3 + 5a^4x^4y^4z
-18a^3b^3c^4 - 45a^4cy^2 - 36a^3c^2xz - 63a^4cxy
32c^7x^2 + 80c^10bx - 112c^6b + 48c^12x
56a^4b^3x^2 - 28a^3x + 112a^5x^2y^2 - 196a^6x^3