Answer:
Part 1) Is a cubic expression
Part 2) The quadratic expression is 12x² + 8x − 1
Step-by-step 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
Answer:
1. Cubic expression
2. [tex]12x^2+8x-1[/tex]
Step-by-step explanation:
1. We have the expression [tex]5x^3+2x-3[/tex] and we have to classify it.
A quadratic expression has the form [tex]ax^2+bx+c,a\neq 0[/tex].
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 [tex]ax+b[/tex].
We can see that it only has two terms and the first term has exponent 1. The expression [tex]5x^3+2x-3[/tex] has 3 terms and the first term has exponent 2 then it isn't a linear expression.
A cubic expression has the form[tex]ax^3+bx^2+cx+d[/tex].
We can see that the first term is raised to the cubic. And [tex]5x^3+2x-3[/tex] is raised to the cubic.
We can rewrite it: [tex]5x^3+2x-3=5x^3+0x^2+2x-3[/tex]
[tex]a=5\\b=0\\c=2\\d=-3[/tex]
The expression [tex]5x^3+2x-3[/tex] agrees with the definition of a cubic expression. Then it's a cubic expression.
An Exponential expression has the form [tex]y=ab^x, a>0[/tex]
2. We said that a quadratic expression has the form [tex]ax^2+bx+c,a\neq 0[/tex].
Then the expression that agrees with the definition is [tex]12x^2+8x-1,a\neq 0[/tex]
With,
[tex]a=12\\b=8\\c=1[/tex]
