Answer :
To add and simplify the given polynomials [tex]\(9x^3 - 3x^2 - 9x + 18\)[/tex] and [tex]\(7x - 29\)[/tex], follow these steps:
1. Write down both polynomials clearly:
- First polynomial (P1): [tex]\(9x^3 - 3x^2 - 9x + 18\)[/tex]
- Second polynomial (P2): [tex]\(7x - 29\)[/tex]
2. Add the polynomials:
Combine like terms from both polynomials. This means adding together the terms that have the same power of [tex]\(x\)[/tex].
- Cubic term: [tex]\(9x^3\)[/tex] (This appears only in P1, so it remains [tex]\(9x^3\)[/tex].)
- Quadratic term: [tex]\(-3x^2\)[/tex] (This appears only in P1, so it remains [tex]\(-3x^2\)[/tex].)
- Linear term: [tex]\(-9x + 7x = -2x\)[/tex]
- Constant term: [tex]\(18 - 29 = -11\)[/tex]
3. Write the result after combining like terms:
The resulting polynomial after addition is:
[tex]\[
9x^3 - 3x^2 - 2x - 11
\][/tex]
Therefore, the simplified result of adding the two polynomials is [tex]\(9x^3 - 3x^2 - 2x - 11\)[/tex], which matches option (b).
1. Write down both polynomials clearly:
- First polynomial (P1): [tex]\(9x^3 - 3x^2 - 9x + 18\)[/tex]
- Second polynomial (P2): [tex]\(7x - 29\)[/tex]
2. Add the polynomials:
Combine like terms from both polynomials. This means adding together the terms that have the same power of [tex]\(x\)[/tex].
- Cubic term: [tex]\(9x^3\)[/tex] (This appears only in P1, so it remains [tex]\(9x^3\)[/tex].)
- Quadratic term: [tex]\(-3x^2\)[/tex] (This appears only in P1, so it remains [tex]\(-3x^2\)[/tex].)
- Linear term: [tex]\(-9x + 7x = -2x\)[/tex]
- Constant term: [tex]\(18 - 29 = -11\)[/tex]
3. Write the result after combining like terms:
The resulting polynomial after addition is:
[tex]\[
9x^3 - 3x^2 - 2x - 11
\][/tex]
Therefore, the simplified result of adding the two polynomials is [tex]\(9x^3 - 3x^2 - 2x - 11\)[/tex], which matches option (b).
