Let's go through each question step-by-step:
Question 16:
[tex]\(\sqrt{2}\)[/tex] is not a polynomial function. Polynomials are expressions involving variables raised to non-negative integer powers, and [tex]\(\sqrt{2}\)[/tex] does not fit this definition. Therefore, it does not have a degree.
Answer:
None of the options provided is correct because [tex]\(\sqrt{2}\)[/tex] is not a polynomial and hence does not have a degree. The best approximation for this case is "not applicable," often represented mathematically as NaN (Not a Number).
Question 17:
We need to find the number of terms in the polynomial [tex]\(4x^3 + 3x^2 - 6x + 7\)[/tex].
A polynomial's terms are the separate elements that are added or subtracted.
- The first term is [tex]\(4x^3\)[/tex]
- The second term is [tex]\(3x^2\)[/tex]
- The third term is [tex]\(-6x\)[/tex]
- The fourth term is [tex]\(7\)[/tex]
Counting these, we find there are 4 terms in this polynomial.
Answer:
c) 4
Question 18:
We need to evaluate the polynomial [tex]\(p(x) = x^2 - 2\sqrt{2}x + 1\)[/tex] at [tex]\(x = 2\sqrt{2}\)[/tex].
Substitute [tex]\(2\sqrt{2}\)[/tex] into [tex]\(p(x)\)[/tex]:
[tex]\[ p(2\sqrt{2}) = (2\sqrt{2})^2 - 2\sqrt{2} \cdot 2\sqrt{2} + 1 \][/tex]
Now calculate each term:
[tex]\[ (2\sqrt{2})^2 = 4 \times 2 = 8 \][/tex]
[tex]\[ - 2\sqrt{2} \cdot 2\sqrt{2} = -2 \times 2 \times 2 = -8 \][/tex]
[tex]\[ 8 - 8 + 1 = 1 \][/tex]
Answer:
b) 1
Question 19:
We need to determine the number of zeros a cubic polynomial can have.
A cubic polynomial is a polynomial of degree 3. A fundamental theorem of algebra states that a polynomial of degree [tex]\(n\)[/tex] can have at most [tex]\(n\)[/tex] real roots.
Therefore, a cubic polynomial can have at most 3 zeros.
Answer:
c) 3
