Question

which expressions are polynomials.If not give reason:
$\frac{1x { + 3x - 4 = = }^{2} }{?} }^{2} }{?}$
​

Answer 1

Step-by-step explanation:

(i) In 4x2−3x+7. all the indies of x are whole numbers. So, it is a polynomial in one variable x.

(ii) In y2+2 the index of y is a whole number. So, it is a polynomial in one variable y.

(iii) In 3t+t2=3t21+2 t, here the exponent of first term is 21, which is not whole number therefore is it not a polynomial.

(iv) In y+y2=y+2y−1, here the exponent of first term is −1, which is not whole number, therefore, is it not a polynomial.

(v) In x10+y3+t50 is not a polynomial in one variable as three variable x,y and t occur in it.

Answer 2

Step-by-step explanation:

(i)4x

2

+5x−2=4x

2

+5x

1

−2x

0

Here power of the equation is 2,1 and 0

Since all powers are whole number, it is a polynomial.

Now, since there is only one variable x,

it is a polynomial in one variable.

(ii)y

2

Here power of the equation is 2

Since all powers are whole number, it is a polynomial.

Now, since there is only one variable y,

it is a polynomial in one variable.

(iii)5=5x

0

Here power of the equation is 0

Now, since there is only no variable or power of the variable is zero which is a whole number

it is a polynomial and known as constant polynomial.

(iv)2x

2

+

x

3

−5=2x

2

+3x

−1

−5x

0

Here power of the equation is 2,−1 and 0

Since −1 is not a whole number, it is not a polynomial.