Add or Subtract for #3-4
3. (2x2 + 6x + 1) + (–7x2 + 2x – 3)
5x2 – 4x – 2
–5x2 + 8x – 2
5x2 – 8x + 2
–9x2 – 8x + 2
4. (3x2 – 7x – 4) – (6x2 – 6x + 1)
–3x2 – x –5
–3x2 –13x + 5
9x2 – x + 5
3x2 – 13x – 5
My answers:
3. 5x2 – 8x + 2
4. –3x2 – x –5
#4 is correct, but #3 is not
#3.
(2x2 + 6x + 1) + (–7x2 + 2x – 3)
= 2x^2 + 6x + 1 - 7x^2 + 2x - 3 , the brackets were not needed because a +1 was understood in front of them
= -5x^2 + 8x -2
To add or subtract polynomial expressions, we need to combine like terms by adding or subtracting the coefficients of the same variables.
Let's go through each question and explain how to find the correct answers:
3. (2x^2 + 6x + 1) + (-7x^2 + 2x - 3)
To add these two polynomial expressions, we combine like terms. We add the coefficients of the terms with the same exponent.
For the x^2 terms:
2x^2 + (-7x^2) = -5x^2
For the x terms:
6x + 2x = 8x
For the constant terms:
1 + (-3) = -2
Putting it all together, the answer is: -5x^2 + 8x - 2
So, the correct answer to question 3 is: -5x^2 + 8x - 2
4. (3x^2 - 7x - 4) - (6x^2 - 6x + 1)
To subtract these two polynomial expressions, we follow a similar process. We combine like terms by subtracting the coefficients of the terms with the same variables.
For the x^2 terms:
3x^2 - 6x^2 = -3x^2
For the x terms:
- 7x - (-6x) = -7x + 6x = -x
For the constant terms:
- 4 - 1 = -5
Putting it all together, the answer is: -3x^2 - x - 5
So, the correct answer to question 4 is: -3x^2 - x - 5