Polynomial Vocabulary: Problems with Solutions

Solution:
We order the exponents from the largest exponent to the smallest.
$-3x^{5}+5x^{2}+2x-5$
Grade $5$

Solution:
Number of terms 3.

Solution:
We order the exponents from the largest exponent to the smallest.

$5x^{4}-3x^{2} -x+\left( \frac{1}{2}+\frac{5}{2}\right)$
Sum the constants.
$5x^{4}-3x^{2} -x+3$

Grade 4.

Solution:
Certainly, the polynomial has 4 terms, but its grade is 5.
We observe it better if we order its terms.

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

Solution:
False
A trinomial is a polynomial that has 3 terms.

Solution:
We order and simplify: $5x^{2}-x^{4}+(3-5)= -x^{4}+5x^{2}-2$

Solution:
$y$ is the only one polynomial of grade 1, main coefficient 1, that has an independent term 0, and its variable is y.

Solution:
A binomial has 2 terms, for example,
$x^{2}-4$

Solution:
Answer: $\sqrt{2}x^{3}-\sqrt[3]{7}x+\frac{3}{2}$

This is the only expression that is a polynomial, its coefficient can be any real number. Here the coefficients are
$\sqrt{2};-\sqrt[3]{7};\frac{3}{2}$
Grade $3$,
Independent term $\frac{3}{2}$

Solution:
Correct answer: All of these are polynomials.
$\frac{1}{2}x^{3}+x^{2}-\pi $
Grade $3$,
Variable $x$,
Number of terms $3$

$\sqrt{5}x^{5}+2$
Grade $5$,
Variable $x$,
Number of terms $2$

$\pi y^{4}-ey^{3}+(\sqrt{2}-\sqrt{3})y+1$
Grade $4$,
Variable $y$,
Number of terms $4$