Subtracting Polynomials
If you know how to add polynomials, then you already know how to subtract
them. You just need to add the opposite of the polynomial that follows
the minus sign. Take a look at the following examples.
a) (2c^{2} +10c 9)  (5c^{2} 8c + 2) 
Watch the signs. 
= (2c^{2} +10c 9) + (1)(5c^{2} 8c + 2) 
Change to (1) times polynomial. 
= (2c^{2} +10c 9) + (5c^{2} +8c  2) 
Distribute the (1) over the 2nd polynomial. 
= [(2c^{2 }) +(5c^{2} )] + (10c + 8c)
+[(9) + ( 2)] 
Apply associative and commutative properties. 
= ( 7c^{2} + 18c 11) 
Add coefficients. 
b) (9x^{3}  3x^{2} 7)  (6x^{3}
+ 4x + 9) 
Note that the middle terms arenâ€™t â€œsimilarâ€. 
= (9x^{3}  3x^{2} 7) +(1)(6x^{3}
+ 4x + 9) 
Watch the signs. Change to (1) times polynomial. 
= (9x^{3}  3x^{2} 7) +(+6x^{3} 
4x  9) 
Distribute the (1) over the 2nd polynomial. 
= (9x^{3} + 6x^{3} ) +(3x^{2} )
+( 4x) + (7  9) 
Apply the associative and commutative properties. 
= (9 + 6)x^{3} + (3)x^{2}  4x +
(7  9) 
Apply the distributive property. 
= 15x^{3}  3x^{2}  4x  16 
Add coefficients. 
