Add polynomials
0.15x^4 + 0.10x^3
- 0.01x^3 + 0.01x^2 + x
1.25x^4 + 0.11x^2 + 0.01
027x^3 + 0.99
-0.35x^4 + 15x^2 - 0.03
I don't understand PLEASE PLEASE HELP!!
Just as you have to line up the decimal places with numbers, you can only add like powers with polynomials.
So, add up all the terms with x^4: (0.15 + 1.25 - 0.35) = 1.05
Add up all the x^3 terms: (0.10 -0.01 + 0.27) = 0.36 (assuming 027x^3 should be 0.27)
Add up the x^2 terms: (0.01 + 0.11 + 0.15) = 0.27 (assuming 15x^2 should be .15)
Add up all the x terms: (1) = 1
Add up the plain numbers: (0.01 + 0.99 - 0.03) = 0.97
Put it all together to get
1.05x^4 + 0.36x^3 + 0.15x^2 + x + 0.97
If my assumptions about decimal places are wrong, adjust things as needed.
Of course! Adding polynomials involves combining like terms with the same degree of the variable. Let's go through the steps to add these polynomials:
Step 1: Combine the terms with the same degree of the variable.
Starting with the degree 4 terms:
- We have 0.15x^4 + 1.25x^4 - 0.35x^4. Combine these terms to get x^4 terms: 0.15x^4 + 1.25x^4 - 0.35x^4 = 1.05x^4.
Next, let's move on to the degree 3 terms:
- We have 0.10x^3 - 0.01x^3 + 0.27x^3. Combine these terms to get x^3 terms: 0.10x^3 - 0.01x^3 + 0.27x^3 = 0.36x^3.
Now, let's combine the degree 2 terms:
- We have 0.01x^2 + 0.11x^2 + 15x^2. Combine these terms to get x^2 terms: 0.01x^2 + 0.11x^2 + 15x^2 = 15.12x^2.
Finally, let's combine the degree 1 (x) terms:
- We have x. There are no more x terms to combine, so x remains as it is.
Also, consider the constants:
- We have 0.01 + 0.01. Combine these terms to get constants: 0.01 + 0.01 = 0.02.
Step 2: Write out the final answer by combining the terms we obtained in Step 1.
The final answer to the addition of the polynomials is:
1.05x^4 + 0.36x^3 + 15.12x^2 + x + 0.02.
I hope this explanation helps you understand the process of adding polynomials! Let me know if you have any more questions.