Question

state true or false
i)the degree of the polynomial 2 x³+6x⁴y²+9y³+11 is 6
ii)1/x +3x1is a polynomial
iii)-x and + x are not like term
iv)the algebraic from of decreased by 9 gives 2y is 3 x + 9 = 2y​

Answer 1

(I) TRUE

The degree of a polynomial is the highest degree of a single term.

Degrees of the terms:

$\sf \: 2 {x}^{3} \: \: is \: 3$

$\sf \: 6 {x}^{4} {y}^{2} \: is \: 4 + 2 = 6$

$\sf \: 9{y}^{3} \: is \: 3$

$\sf 11 = 11 {x}^{0} \: \: is \: 0$

here, 6 is the greatest of all the degrees of the terms .

so, the statement is true.

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(ii) FALSE

$\sf \dfrac{1}{x} + 3{x}^{1} \: is \: not \: a \: polynomial$

$\sf \: here \: \: \: \dfrac{1}{x} = {x}^{ - 1}$

A polynomial should have variables with power as whole numbers only. x is raise to the power of -1, which is not a whole number.

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(iii) FALSE

x and -x are like terms

Like terms should have same variable and power. Coefficient doesn't matter.

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(iv) FALSE

The algebraic form of 3 x decreased by 9 gives 2y is 3x - 9 = 2y

But in the above statement it's given that 9 is being added to 3x

so, the statement is incorrect.