Use complete sentences to explain how to use linear factors to determine the equation of a polynomial function
2 answers:
Answer with Step-by-step explanation:
First we find the degree of polynomial.
Consider two linear factors
(x-a) and (x-b)
Multiplying these two factors to get the polynomial.
There are two linear factors .
Therefore, the degree of polynomial is 2 and the polynomial is quadratic.
Degree of polynomial=Number of linear factors
If the linear factors are three then the polynomial formed by multiplying theses factors .
Then, we get the polynomial of degree 3 and the polynomial is cubic polynomial.
It we have four linear factors.
After multiplying these four factors, we get a polynomial of degree 4.
The polynomial is bi quadratic.
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Option A: z + 1
Option B: 6 + w
Option D:
Solution:
Let us first define the polynomial.
A polynomial can have constants, variables, exponents and fractional coefficients.
A polynomial cannot have negative exponents, fractional exponents and never divided by a variable.
<u>To find which expressions are polynomial:</u>
Option A: z + 1
By the definition, z + 1 is a polynomial.
It is polynomial.
Option B: 6 + w
By the definition, 6 + w is a polynomial.
It is polynomial.
Option C:
Here, y have fractional exponent.
So, it is not a polynomial.
Option D:
By the definition, is a polynomial.
It is polynomial.
Hence z + 1, 6 +w and are polynomials.