Essay show all work. Add the following polynomials; (1/5x^2-1/5x-3/4)+(1/10x^2-1/2x+1/2)
I really need help and I am thankful for your time, some tutors just mess with your head and make you more confused,if I did not need you guys I would not be here so thanks again
remember we can add or subtract only "like" terms
so we have to form common denominators for each type
(1/5)x^2 + (1/10)x^2 which is (3/10)x^2 ...... 1/5 + 1/10 =2/10+1/10
then
(-1/5)x - (1/2)x
= (-2/10)x - (5/10)x = (-7/10)x
and finally
-3/4 + 1/2
= -3/4 + 2/4
= -1/4
(1/5x^2-1/5x-3/4)+(1/10x^2-1/2x+1/2)
= (3/10)x^2 - (7/10)x - 1/4
thank you once again
No problem! I'm here to help you out. To add these two polynomials, you need to combine like terms.
Let's start with the first polynomial: (1/5x^2 - 1/5x - 3/4)
Now, let's look at the second polynomial: (1/10x^2 - 1/2x + 1/2)
To add these polynomials, you just need to add the coefficients of the like terms.
Terms with the same variable and exponent (like x^2, x, and the constant term) are called "like terms."
The like terms in these polynomials are:
- x^2 terms: 1/5x^2 and 1/10x^2 (you can add these by combining the coefficients)
- x terms: -1/5x and -1/2x
- constant terms: -3/4 and 1/2
Now let's add these like terms one by one:
For the x^2 terms:
1/5x^2 + 1/10x^2 = (1/5 + 1/10)x^2 = 3/10x^2
For the x terms:
-1/5x - 1/2x = (-1/5 - 1/2)x = -7/10x
For the constant terms:
-3/4 + 1/2 = (-3/4 + 2/4) = -1/4
Therefore, when you add these two polynomials, you get:
(1/5x^2 - 1/5x - 3/4) + (1/10x^2 - 1/2x + 1/2) = 3/10x^2 - 7/10x - 1/4
Make sure to double check the calculations and units of each term to ensure accuracy.