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Answer :
Sure! Let's perform the operation step-by-step to find the sum of the polynomials [tex]\((6x^2 - 4x + 11)\)[/tex] and [tex]\((4 - x^2 - 3x)\)[/tex], and express the result in descending powers of [tex]\(x\)[/tex].
1. Write down the polynomials:
- First polynomial: [tex]\(6x^2 - 4x + 11\)[/tex]
- Second polynomial: [tex]\(4 - x^2 - 3x\)[/tex]
2. Arrange the second polynomial in standard form:
- [tex]\(4 - x^2 - 3x\)[/tex] can be rewritten as [tex]\(-x^2 - 3x + 4\)[/tex] for easier addition.
3. Add the corresponding terms from both polynomials:
- [tex]\(x^2\)[/tex] terms:
- [tex]\(6x^2\)[/tex] from the first polynomial, [tex]\(-x^2\)[/tex] from the second polynomial.
- [tex]\(6x^2 + (-x^2) = 5x^2\)[/tex]
- [tex]\(x\)[/tex] terms:
- [tex]\(-4x\)[/tex] from the first polynomial, [tex]\(-3x\)[/tex] from the second polynomial.
- [tex]\(-4x + (-3x) = -7x\)[/tex]
- Constant terms:
- [tex]\(11\)[/tex] from the first polynomial, [tex]\(4\)[/tex] from the second polynomial.
- [tex]\(11 + 4 = 15\)[/tex]
4. Combine the results:
- The resulting polynomial is [tex]\(5x^2 - 7x + 15\)[/tex].
So, the final answer in descending powers of [tex]\(x\)[/tex] is:
[tex]\[ 5x^2 - 7x + 15 \][/tex]
1. Write down the polynomials:
- First polynomial: [tex]\(6x^2 - 4x + 11\)[/tex]
- Second polynomial: [tex]\(4 - x^2 - 3x\)[/tex]
2. Arrange the second polynomial in standard form:
- [tex]\(4 - x^2 - 3x\)[/tex] can be rewritten as [tex]\(-x^2 - 3x + 4\)[/tex] for easier addition.
3. Add the corresponding terms from both polynomials:
- [tex]\(x^2\)[/tex] terms:
- [tex]\(6x^2\)[/tex] from the first polynomial, [tex]\(-x^2\)[/tex] from the second polynomial.
- [tex]\(6x^2 + (-x^2) = 5x^2\)[/tex]
- [tex]\(x\)[/tex] terms:
- [tex]\(-4x\)[/tex] from the first polynomial, [tex]\(-3x\)[/tex] from the second polynomial.
- [tex]\(-4x + (-3x) = -7x\)[/tex]
- Constant terms:
- [tex]\(11\)[/tex] from the first polynomial, [tex]\(4\)[/tex] from the second polynomial.
- [tex]\(11 + 4 = 15\)[/tex]
4. Combine the results:
- The resulting polynomial is [tex]\(5x^2 - 7x + 15\)[/tex].
So, the final answer in descending powers of [tex]\(x\)[/tex] is:
[tex]\[ 5x^2 - 7x + 15 \][/tex]
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