Question
How to Subtract Polynomials Horizontally
Steps
1.
i Answer
I-----
2. i Answer
(5x'-3x+4)-(2x'+6x-1)
(5x7-3X+4) +1-1)12x7+6x
- 1)
(5x'-3x+4)+1-2x'+-6x+
1)
(5x*-2x1) +(-3x-6x)+(4+
1)
3x2-9x+5
Options:
•: Solve it like an addition problem
¿ Use the distributive property to change the subtracted polynomial to an added polynomial.
Steps
1.
i Answer
I-----
2. i Answer
(5x'-3x+4)-(2x'+6x-1)
(5x7-3X+4) +1-1)12x7+6x
- 1)
(5x'-3x+4)+1-2x'+-6x+
1)
(5x*-2x1) +(-3x-6x)+(4+
1)
3x2-9x+5
Options:
•: Solve it like an addition problem
¿ Use the distributive property to change the subtracted polynomial to an added polynomial.
Answers
GPT-4o mini
To subtract polynomials horizontally, you can follow these steps:
1. **Rewrite the Problem**: Write down the polynomials in the subtraction format. For example, if you are subtracting \((2x^2 + 6x - 1)\) from \((5x^2 - 3x + 4)\), you will have:
\[
(5x^2 - 3x + 4) - (2x^2 + 6x - 1)
\]
2. **Use the Distributive Property**: Change the subtraction of the second polynomial into addition by distributing a negative sign across the second polynomial:
\[
(5x^2 - 3x + 4) + (-2x^2 - 6x + 1)
\]
This means you will take each term in the second polynomial and change its sign.
3. **Combine Like Terms**: Now, combine the like terms by adding the coefficients of the same powers of \(x\):
- For \(x^2\): \(5x^2 - 2x^2 = 3x^2\)
- For \(x\): \(-3x - 6x = -9x\)
- For the constant terms: \(4 + 1 = 5\)
Putting it all together, you will get:
\[
3x^2 - 9x + 5
\]
### Summary of Steps
- Change subtraction to addition by distributing the negative sign.
- Combine like terms to simplify the expression.
### Example Solution
\[
(5x^2 - 3x + 4) - (2x^2 + 6x - 1) = 3x^2 - 9x + 5
\]
### Conclusion
To perform the subtraction of polynomials successfully, rewrite the problem as an addition by applying the distributive property, and then combine like terms.
1. **Rewrite the Problem**: Write down the polynomials in the subtraction format. For example, if you are subtracting \((2x^2 + 6x - 1)\) from \((5x^2 - 3x + 4)\), you will have:
\[
(5x^2 - 3x + 4) - (2x^2 + 6x - 1)
\]
2. **Use the Distributive Property**: Change the subtraction of the second polynomial into addition by distributing a negative sign across the second polynomial:
\[
(5x^2 - 3x + 4) + (-2x^2 - 6x + 1)
\]
This means you will take each term in the second polynomial and change its sign.
3. **Combine Like Terms**: Now, combine the like terms by adding the coefficients of the same powers of \(x\):
- For \(x^2\): \(5x^2 - 2x^2 = 3x^2\)
- For \(x\): \(-3x - 6x = -9x\)
- For the constant terms: \(4 + 1 = 5\)
Putting it all together, you will get:
\[
3x^2 - 9x + 5
\]
### Summary of Steps
- Change subtraction to addition by distributing the negative sign.
- Combine like terms to simplify the expression.
### Example Solution
\[
(5x^2 - 3x + 4) - (2x^2 + 6x - 1) = 3x^2 - 9x + 5
\]
### Conclusion
To perform the subtraction of polynomials successfully, rewrite the problem as an addition by applying the distributive property, and then combine like terms.