How is the process for adding two polynomials like the process for how adding two integers? How is it different?
Adding two polynomials is similar to adding two integers in terms of the basic concept of combining values. However, the process differs in terms of how the addition is performed.
To add two integers, you simply add the values together and obtain the sum. For example, if you have the integers 3 and 5, their sum would be 3 + 5 = 8.
On the other hand, adding two polynomials involves the addition of variables raised to different powers. Each term of the polynomial consists of a coefficient multiplied by a variable raised to a certain power. To add two polynomials, you combine like terms, which means that you add the coefficients of the terms with the same power of the variable.
Here's a step-by-step process to add two polynomials:
1. Arrange the polynomials with like terms lined up vertically. For example, if you want to add the polynomials (2x^2 + 3x + 1) and (4x^2 - 2x + 5), place them in the following format:
2x^2 + 3x + 1
+4x^2 - 2x + 5
2. Start by adding the coefficients of the terms with the highest power of the variable, in this case, the terms with x^2. Add 2x^2 and 4x^2 together, which gives you 6x^2.
2x^2 + 3x + 1
+4x^2 - 2x + 5
---------------
6x^2
3. Proceed to add the coefficients of the terms with the next highest power, in this case, the terms with x. Add 3x and -2x together, which gives you 1x or simply x.
2x^2 + 3x + 1
+4x^2 - 2x + 5
---------------
6x^2 + x
4. Finally, add the constant terms of the polynomials. Add 1 and 5 together, which gives you 6.
2x^2 + 3x + 1
+4x^2 - 2x + 5
---------------
6x^2 + x + 6
So, the sum of the two polynomials (2x^2 + 3x + 1) and (4x^2 - 2x + 5) is 6x^2 + x + 6.
add 423 + 26
4*10^2 + 2*10^1 + 3 *10^0 + 2*10^1 + 6*10^0
combine like terms
= 4*10^2 + 4*10^1 + 9 *10^0
now if it is just numbers, we can say 10^2 = 100 and 10^1 = 10 and 10^0=1
so you have
400 + 40 + 9 = 149
however if it were
4 x^2 + 2 x + 3 + 2 x + 6
combine like terms
4 x^2 + 4 x + 9
I can not take that next step expressing x^2 = something times x
because the first problem had x^2 = 100 , x = 10 so x^2 = 10 x