Answer :
Sure! Let's find the coefficient of [tex]\(x^4\)[/tex] in the given polynomial [tex]\(2x^5 - 4x^4 + 2x^3 + 6x - 9\)[/tex].
To do this, we need to identify the term in the polynomial that contains [tex]\(x^4\)[/tex] and then determine its coefficient.
1. Write down the polynomial:
[tex]\[
2x^5 - 4x^4 + 2x^3 + 6x - 9
\][/tex]
2. Look at each term in the polynomial to find the term that has [tex]\(x^4\)[/tex]:
- The first term is [tex]\(2x^5\)[/tex], which has [tex]\(x^5\)[/tex].
- The second term is [tex]\(-4x^4\)[/tex], which has [tex]\(x^4\)[/tex].
- The third term is [tex]\(2x^3\)[/tex], which has [tex]\(x^3\)[/tex].
- The fourth term is [tex]\(6x\)[/tex], which has [tex]\(x\)[/tex].
- The fifth term is [tex]\(-9\)[/tex], which is a constant.
3. The term that includes [tex]\(x^4\)[/tex] is [tex]\(-4x^4\)[/tex].
4. The coefficient of [tex]\(x^4\)[/tex] in [tex]\(-4x^4\)[/tex] is [tex]\(-4\)[/tex].
Therefore, the coefficient of [tex]\(x^4\)[/tex] in the polynomial [tex]\(2x^5 - 4x^4 + 2x^3 + 6x - 9\)[/tex] is [tex]\(-4\)[/tex].
To do this, we need to identify the term in the polynomial that contains [tex]\(x^4\)[/tex] and then determine its coefficient.
1. Write down the polynomial:
[tex]\[
2x^5 - 4x^4 + 2x^3 + 6x - 9
\][/tex]
2. Look at each term in the polynomial to find the term that has [tex]\(x^4\)[/tex]:
- The first term is [tex]\(2x^5\)[/tex], which has [tex]\(x^5\)[/tex].
- The second term is [tex]\(-4x^4\)[/tex], which has [tex]\(x^4\)[/tex].
- The third term is [tex]\(2x^3\)[/tex], which has [tex]\(x^3\)[/tex].
- The fourth term is [tex]\(6x\)[/tex], which has [tex]\(x\)[/tex].
- The fifth term is [tex]\(-9\)[/tex], which is a constant.
3. The term that includes [tex]\(x^4\)[/tex] is [tex]\(-4x^4\)[/tex].
4. The coefficient of [tex]\(x^4\)[/tex] in [tex]\(-4x^4\)[/tex] is [tex]\(-4\)[/tex].
Therefore, the coefficient of [tex]\(x^4\)[/tex] in the polynomial [tex]\(2x^5 - 4x^4 + 2x^3 + 6x - 9\)[/tex] is [tex]\(-4\)[/tex].
