Adding and subtracting operations with polynomials – a quick review
When we are adding or subtracting 2 or more polynomials, we have to first group the same variables (arguments) that have the sameand then add or subtract them. For example, if we have ax3 in one polynomial (where a is some real number), we have to group it with bx3 from the other polynomial (where b is also some real number). Here is one example with adding polynomials:</p>
We remove the brackets, and since we have a plus in front of every bracket, the signs in the polynomials don’t change.
We group variables with the same: red is for second degree, and there we have -1+2, which is 1 and that’s how we got x2. Blue is for the first degree where we have 2+4 which is 6, and the green is for the constants (real numbers) where we have 3-5 which is -2.
The principle is the same with subtracting, only we have to keep in mind that a minus in front of the polynomial changes all signs in that polynomial. Here is one example:
<p>We remove the brackets, and since wtation”>e have a minus in front of the second polynomial, all signs in that polynomial change. We have -3x2and with minus in front, it becomes a plus and same goes for -10 (red pluses).
Now we group the variables with same: there is no variable with the third degree in the second polynomial, so we just write 4x3. We group other variables the same way when we were adding polynomials.
Adding and Subtracting Polynomials Practice Questions
1. Add polynomials -3x2+2x+6 and -x2-x-1.
2. Subtract polynomials 4x3-2x2-10 and 5x3+x2+x+5.
Dividing Operations with Polynomials
3. Divide x3-3x2+3x-1 by x-1.
4. Divide x2-y2 by x-y.
(-3x2+2x+6) + (-x2-x-1)=
We remove the brackets and we group the variables by.
We remove the brackets, but we change all signs in the second polynomial because of the minus. Now we group the variables by.
(x3-3x2+3x-1) : (x-1)= x2-2x+1
(x2-y2) : (x-y) =x+y