Question

Choose the polynomial that is written in standard form.

−3x5 + 4x3 + 10x2
−8x + 4x4 + 3x3
x4 + 4x3 + 10x4
x6 + 4x3 + 10x7

Answer 1

Answer:

• A. −3x⁵ + 4x³ + 10x²

Step-by-step explanation:

• The standard form means that the terms are ordered from biggest exponent to lowest exponent.

Verify the answer options

A. −3x⁵ + 4x³ + 10x²

• 5, 3, 2 - correct order  

B. −8x + 4x⁴ + 3x³

• 1, 4, 3 - incorrect order

C. x⁴ + 4x³ + 10x⁴

• 4, 3, 4 - incorrect order

D. x⁶ + 4x³ + 10x⁷

• 6, 3, 7 - incorrect order

Answer 2

Answer:

${ - 3x}^{5} + {4x}^{3} + {10x}^{2}$

Step-by-step explanation:

For a polynomial to be in standard form, it must satify the conditions below:

1) It must not contain like terms

2) The exponents (powers) must be written in descending order

That is, the polynomial must be of the form

$f(x) = {ax}^{n} + {bx}^{n - 1} + {cx}^{n - 2} + . \: . \: . \: . \: . \: mx + n$

Where a, b, c, m, n, are coefficients/constants

The only option that satifies the above conditions, and follows the pattern f(x) shown is:

${ - 3x}^{5} + {4x}^{3} + {10x}^{2}$