Question

I need help ASPA with these two questions!!! <3 GIVE THANKS

1. Classify the expression: 5x3 + 2x − 3


Quadratic expression

Linear expression

Cubic expression

Exponential expression


2. Choose the expression that represents a quadratic expression.


12x4 − 2x3 + 5x2 − 9x − 6

2x3 + 5x2 − 9x − 6

12x2 + 8x − 1

−8x − 1

Answer 1

1. Cubic expression

2.
`12x^2+8x-1`

Explanation:

1. We have the expression
`5x^3+2x-3` and we have to classify it.

A quadratic expression has the form
`ax^2+bx+c,a\\eq 0`.

We can see that the first term is squared. And in the expression that we have to classify the first term is raised to the cubic, then it isn't a quadratic expression.

A linear expression has the form
`ax+b`.

We can see that it only has two terms and the first term has exponent 1. The expression
`5x^3+2x-3` has 3 terms and the first term has exponent 2 then it isn't a linear expression.

A cubic expression has the form
`ax^3+bx^2+cx+d`.

We can see that the first term is raised to the cubic. And
`5x^3+2x-3` is raised to the cubic.

We can rewrite it:
`5x^3+2x-3=5x^3+0x^2+2x-3`

`a=5\\b=0\\c=2\\d=-3`

The expression
`5x^3+2x-3` agrees with the definition of a cubic expression. Then it's a cubic expression.

An Exponential expression has the form
`y=ab^x, a>0`

2. We said that a quadratic expression has the form
`ax^2+bx+c,a\\eq 0`.

Then the expression that agrees with the definition is
`12x^2+8x-1,a\\eq 0`

With,

`a=12\\b=8\\c=1`

Answer 2

Part 1) Is a cubic expression

Part 2) The quadratic expression is 12x² + 8x − 1

Explanation:

Part 1) Classify the expression: 5x³ + 2x − 3

we know that

Polynomials can be classified two different ways - by the number of terms and by their degree.

so

a) By the number of terms is a trinomial, because has three terms

b) By their degree The degree of the polynomial is found by looking at the term with the highest exponent on its variable

The highest exponent is 3 so this is a 3rd degree trinomial

therefore

Is a cubic expression

Part 2) Choose the expression that represents a quadratic expression

we know that

If the expression is a quadratic equation , then the highest exponent of the variable is 2

therefore

The quadratic expression is 12x² + 8x − 1