Choose the polynomial that is written in standard form. Select one:
a. -3x³y² + 4x³y + 10x²
b. -8xy² + 4x^y² + 3x³
c. x¹y² + 4x³y² + 10x^4
d. x^6y^2 + 4x³y + 10x^7
AAAaannndd the bot gets it wrong yet again!
a. -3x³y² + 4x³y + 10x²
The polynomial that is written in standard form is:
c. x¹y² + 4x³y² + 10x^4
To determine which polynomial is written in standard form, we need to understand what standard form for polynomials means. In standard form, a polynomial is arranged in decreasing order of the exponents.
Let's analyze each option and see which one satisfies the requirement:
a. -3x³y² + 4x³y + 10x²
b. -8xy² + 4x^y² + 3x³
c. x¹y² + 4x³y² + 10x^4
d. x^6y^2 + 4x³y + 10x^7
Let's break down the exponent terms for each option:
a. -3x³y² + 4x³y + 10x²
Exponents: 3 (x), 2 (y), and 3 (x)
b. -8xy² + 4x^y² + 3x³
Exponents: 1 (x), 2 (y), y, and 3 (x)
c. x¹y² + 4x³y² + 10x^4
Exponents: 1 (x), 2 (y), 3(x), and 4 (x)
d. x^6y^2 + 4x³y + 10x^7
Exponents: 6 (x), 2 (y), 3(x), and 7 (x)
Among these options, option c. x¹y² + 4x³y² + 10x^4 is the only one written in standard form since the exponents decrease from left to right: 4 (x), 3 (x), 2 (y), and 1 (x).
Therefore, the polynomial written in standard form is c. x¹y² + 4x³y² + 10x^4.