Answer :
We start with the polynomial
[tex]$$5x - 6x^4 + 3 - 7x^3.$$[/tex]
Step 1: Identify each term and its exponent
- The term [tex]$-6x^4$[/tex] has an exponent of 4.
- The term [tex]$-7x^3$[/tex] has an exponent of 3.
- The term [tex]$5x$[/tex] has an exponent of 1.
- The constant [tex]$3$[/tex] is equivalent to [tex]$3x^0$[/tex] (exponent 0).
Step 2: Rearrange the terms in descending order of exponents
The term with the highest exponent is [tex]$-6x^4$[/tex], followed by [tex]$-7x^3$[/tex], then [tex]$5x$[/tex], and finally the constant [tex]$3$[/tex]. When arranged in descending order, the polynomial becomes:
[tex]$$-6x^4 - 7x^3 + 5x + 3.$$[/tex]
Thus, the polynomial in standard form is:
[tex]$$-6x^4 - 7x^3 + 5x + 3.$$[/tex]
[tex]$$5x - 6x^4 + 3 - 7x^3.$$[/tex]
Step 1: Identify each term and its exponent
- The term [tex]$-6x^4$[/tex] has an exponent of 4.
- The term [tex]$-7x^3$[/tex] has an exponent of 3.
- The term [tex]$5x$[/tex] has an exponent of 1.
- The constant [tex]$3$[/tex] is equivalent to [tex]$3x^0$[/tex] (exponent 0).
Step 2: Rearrange the terms in descending order of exponents
The term with the highest exponent is [tex]$-6x^4$[/tex], followed by [tex]$-7x^3$[/tex], then [tex]$5x$[/tex], and finally the constant [tex]$3$[/tex]. When arranged in descending order, the polynomial becomes:
[tex]$$-6x^4 - 7x^3 + 5x + 3.$$[/tex]
Thus, the polynomial in standard form is:
[tex]$$-6x^4 - 7x^3 + 5x + 3.$$[/tex]
