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Answer :
Certainly! Let's solve the expression step by step and then classify the resulting polynomial.
First, let's simplify the given expression:
[tex]\[ 2(-9x^6 - 7x^5 - 16) + (3x^6 - 7x^5 + 14). \][/tex]
### Step 1: Distribute the 2 into the first polynomial
Multiply each term in the first parentheses by 2:
[tex]\[ 2 \cdot (-9x^6) = -18x^6, \][/tex]
[tex]\[ 2 \cdot (-7x^5) = -14x^5, \][/tex]
[tex]\[ 2 \cdot (-16) = -32. \][/tex]
After distribution, the expression becomes:
[tex]\[ -18x^6 - 14x^5 - 32 + 3x^6 - 7x^5 + 14. \][/tex]
### Step 2: Combine like terms
Now, group and add the like terms together:
- The [tex]\(x^6\)[/tex] terms: [tex]\(-18x^6 + 3x^6 = -15x^6\)[/tex],
- The [tex]\(x^5\)[/tex] terms: [tex]\(-14x^5 - 7x^5 = -21x^5\)[/tex],
- The constant terms: [tex]\(-32 + 14 = -18\)[/tex].
So, the simplified polynomial is:
[tex]\[ -15x^6 - 21x^5 - 18. \][/tex]
### Step 3: Classify the polynomial
- Degree: The degree of the polynomial is the highest power of [tex]\(x\)[/tex], which is 6.
- Number of terms: There are 3 terms in the polynomial [tex]\(-15x^6 - 21x^5 - 18\)[/tex].
### Final answer:
The polynomial in standard form is [tex]\(-15x^6 - 21x^5 - 18\)[/tex]. It is classified as a 6th degree polynomial with 3 terms.
First, let's simplify the given expression:
[tex]\[ 2(-9x^6 - 7x^5 - 16) + (3x^6 - 7x^5 + 14). \][/tex]
### Step 1: Distribute the 2 into the first polynomial
Multiply each term in the first parentheses by 2:
[tex]\[ 2 \cdot (-9x^6) = -18x^6, \][/tex]
[tex]\[ 2 \cdot (-7x^5) = -14x^5, \][/tex]
[tex]\[ 2 \cdot (-16) = -32. \][/tex]
After distribution, the expression becomes:
[tex]\[ -18x^6 - 14x^5 - 32 + 3x^6 - 7x^5 + 14. \][/tex]
### Step 2: Combine like terms
Now, group and add the like terms together:
- The [tex]\(x^6\)[/tex] terms: [tex]\(-18x^6 + 3x^6 = -15x^6\)[/tex],
- The [tex]\(x^5\)[/tex] terms: [tex]\(-14x^5 - 7x^5 = -21x^5\)[/tex],
- The constant terms: [tex]\(-32 + 14 = -18\)[/tex].
So, the simplified polynomial is:
[tex]\[ -15x^6 - 21x^5 - 18. \][/tex]
### Step 3: Classify the polynomial
- Degree: The degree of the polynomial is the highest power of [tex]\(x\)[/tex], which is 6.
- Number of terms: There are 3 terms in the polynomial [tex]\(-15x^6 - 21x^5 - 18\)[/tex].
### Final answer:
The polynomial in standard form is [tex]\(-15x^6 - 21x^5 - 18\)[/tex]. It is classified as a 6th degree polynomial with 3 terms.
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