Is the expression ${x^{10}} + {y^3} + {t^{50}}$, polynomial in one variable or not? State the reason for your answer.
Answer
${x^{10}} + {y^3} + {t^{50}}$ We can observe that in the polynomial ${x^{10}} + {y^3} + {t^{50}}$, we have x, y and t as the variables and the powers of x, y and t in each term is a whole number. Therefore, we conclude that ${x^{10}} + {y^3} + {t^{50}}$ is a polynomial but not a polynomial in one variable.
Is the expression $y + \frac{2}{y}$, polynomial in one variable or not? State the reason for your answer.
Answer
$y + \frac{2}{y}$ We can observe that in the polynomial $y + \frac{2}{y}$ ,we have y as the only variable and the powers of y in each term are not a whole number. Therefore, we conclude that $y + \frac{2}{y}$ is not a polynomial in one variable.
Is the expression $3\sqrt t + t\sqrt 2$, polynomial in one variable or not? State the reason for your answer.
Answer
$3\sqrt t + t\sqrt 2$ We can observe that in the polynomial $3\sqrt t + t\sqrt 2 $ we have t as the only variable and the powers of t in each term are not a whole number. Therefore, we conclude that $3\sqrt t + t\sqrt 2$ is not a polynomial in one variable.
Is the expression ${y^2} + \sqrt 2$, polynomial in one variable or not? State the reason for your answer.
Answer
${y^2} + \sqrt 2$ We can observe that in the polynomial ${y^2} + \sqrt 2 $, we have y as the only variable and the powers of y in each term are a whole number. Therefore, we conclude that ${y^2} + \sqrt 2$ is a polynomial in one variable.
Is the expression $4{x^2} - 3x + 7{\text{ }}$, polynomial in one variable or not? State the reason for your answer.
Answer
$4{x^2} - 3x + 7{\text{ }}$ We can observe that in the polynomial $4{x^2} - 3x + 7{\text{ }}$ we have x as the only variable and the powers of x in each term are a whole number. Therefore, we conclude that $4{x^2} - 3x + 7{\text{ }}$ is a polynomial in one variable.
Finding a zero of p(x), is the same as solving the equation p(x) = 0 Now, 2x + 1 = 0 gives us $x=-\frac{1}{2}$ So, $-\frac{1}{2}$ is a zero of the polynomial 2x + 1 $$ $$ $$
Check whether –2 and 2 are zeroes of the polynomial x + 2
Answer
We have, p(x) = x + 2 Then p(2) = 2 + 2 = 4, p(–2) = –2 + 2 = 0 Therefore, –2 is a zero of the polynomial x + 2, but 2 is not the zero of the polynomial.
Find the value of $p(x) = 5x^2 – 3x + 7$ at $x = 1$
Answer
The given polynomial is, $p(x) = 5x^2 – 3x + 7$
The value of the polynomial $p(x)$ at $x = 1$ is given by
$p(1) = 5(1)^2 – 3(1) + 7$
$= 5 – 3 + 7$
$= 9$