The degree of polynomial in $ P(x)=5 x^{3}+4 x^{2}+7 x $

A) 1
B) 2
C) 3
D) 0

Academic Mathematics NCERT Class 9

To do: Find the degree of the polynomial $P(x)=5x^3+4x^2+7x$

Solution:

Degree of a polynomial is the highest power of $x$ in the given polynomial.

So, the degree of the polynomial $P(x)=5x^3+4x^2+7x$ is '3'

Tutorialspoint

Simply Easy Learning

Updated on: 10-Oct-2022

26 Views

Find the zeroes of the polynomial: $4 x^{4}+0 x^{3}+0 x^{2}+500+7$.
Find the zero of the polynomial in each of the following cases:(i) \( p(x)=x+5 \)(ii) \( p(x)=x-5 \)(iii) \( p(x)=2 x+5 \)(iv) \( p(x)=3 x-2 \)(v) \( p(x)=3 x \)(vi) \( p(x)=a x, a ≠ 0 \)(vii) \( p(x)=c x+d, c ≠ 0, c, d \) are real numbers.
Divide the polynomial $p(x)$ by the polynomial $g(x)$ and find the quotient and remainder, in each of the following:(i) $p(x) = x^3 - 3x^2 + 5x -3, g(x) = x^2-2$(ii) $p(x) =x^4 - 3x^2 + 4x + 5, g(x) = x^2 + 1 -x$(iii) $p(x) = x^4 - 5x + 6, g(x) = 2 -x^2$
Find the degree of the polynomial $( x + 1)( x^2-x-x^4+1)$.
divide the polynomial $p( x)$ by the polynomial $g( x)$ and find the quotient and remainder in each of the following: $( p(x)=x^{3}-3 x^{2}+5 x-3$, $g(x)=x^{2}-2$.
Find the value of the polynomial \( 5 x-4 x^{2}+3 \) at(i) \( x=0 \)(ii) \( x=-1 \)(iii) \( x=2 \)
Verify whether the following are zeroes of the polynomial, indicated against them.(i) \( p(x)=3 x+1, x=-\frac{1}{3} \)(ii) \( p(x)=5 x-\pi, x=\frac{4}{5} \)(iii) \( p(x)=x^{2}-1, x=1,-1 \)(iv) \( p(x)=(x+1)(x-2), x=-1,2 \)(v) \( p(x)=x^{2}, x=0 \)(vi) \( p(x)=l x+m, x=-\frac{m}{l} \)(vii) \( p(x)=3 x^{2}-1, x=-\frac{1}{\sqrt{3}}, \frac{2}{\sqrt{3}} \)(viii) \( p(x)=2 x+1, x=\frac{1}{2} \)
Simplify the following :$( 3 x^2 + 5 x - 7 ) (x-1) - ( x^2 - 2 x + 3 ) (x + 4)$
What is the degree of the following polynomial?$x^6 - 3 x^2+x^7 - 5x^3 + 6$
For which values of \( a \) and \( b \), are the zeroes of \( q(x)=x^{3}+2 x^{2}+a \) also the zeroes of the polynomial \( p(x)=x^{5}-x^{4}-4 x^{3}+3 x^{2}+3 x+b \) ? Which zeroes of \( p(x) \) are not the zeroes of \( q(x) \) ?
Find if the second polynomial is a factor of the first polynomial. \( 8 x^{4}+10 x^{3}-5 x^{2}-4 x+1,2 x^{2}+x-1 \)
Write the degree of the polynomial $3 x+4 x y-15$.
Write the degree of each of the following polynomials:(i) \( 5 x^{3}+4 x^{2}+7 x \)(ii) \( 4-y^{2} \)(iii) \( 5 t-\sqrt{7} \)(iv) 3
Factorise:(i) \( 12 x^{2}-7 x+1 \)(ii) \( 2 x^{2}+7 x+3 \)(iii) \( 6 x^{2}+5 x-6 \)(iv) \( 3 x^{2}-x-4 \)
Divide the polynomial $p(x)$ by the polynomial $g(x)$ and find the quotient and remainder, in each of the following:$p(x) =x^4 - 3x^2 + 4x + 5, g(x) = x^2 + 1 -x$

Kickstart Your Career

Get certified by completing the course

Get Started

Advertisements