Mathematics
Polynomials in one variable
एक चर वाले बहुपद
In this Class 10 Mathematics topic from the chapter “Polynomials,” students study algebraic expressions involving a single variable, such as x. They learn to identify a polynomial and its degree, understand constant, linear, quadratic, and cubic forms, and find its zeroes or roots. The topic also develops understanding of the relationship between zeroes and coefficients, helping students interpret polynomial equations and solve related problems accurately.
Practice questions
What is the sum of all the coefficients of the polynomial \(p(x)=7x^3-4x^2-2x-1\)?HardLevel 48If the sum of all coefficients of p(x)=3x^3+kx^2-7x+2 is 5, what is k?MediumLevel 48What is the sum of the coefficients of the odd-power terms in the polynomial p(x) = 5x^5 - 3x^4 + 2x^3 - x + 6?HardLevel 48What is the constant term of the polynomial \\(3x-2)(x^2+5x-1)\\)?HardLevel 48What is the simplified polynomial form of (x+6)^2-(x-2)^2?MediumLevel 48If the polynomial \(p(x)=x^3+ax+b\) satisfies \(p(1)=6\) and \(p(-1)=-4\), what is the value of \(a\)?HardLevel 48If \(p(x)=2x^3+rx^2+s\), \(p(0)=-3\), and \(p(1)=4\), what is the value of \(r\)?HardLevel 48For what value of (n) can ((n-2)x^2+(n+1)x+5) become a constant polynomial?HardLevel 48If \(p(x)=x^2+3x-10\), what is the value of \(p(4)-p(-2)\)?HardLevel 48Which calculation correctly proves that p(-3)=0 for the polynomial p(x)=x^3+27?HardLevel 48If \(p(x)=x^3-x^2+x-1\), what is the value of \(p(1)\)?HardLevel 48If \(p(x)=3x^2+bx+c\), \(p(0)=7\), and \(p(1)=2\), what is the value of \(b\)?HardLevel 48If (p(x)=x^2-7x+12), what is the value of (p(3)+p(4))?HardLevel 48If \(p(x)=x^2-25\), which of the following is the positive value of \(a\) for which \(p(a)=0\)?HardLevel 48Which of the following values of \(x\) is a zero of the polynomial \(p(x)=9x^2+12x+4\)?HardLevel 48If (x=1) and (x=-3) are both zeros of (p(x)=x^3+ax^2+bx+12), what is (a+b)?HardLevel 48If (x=1) and (x=2) are both zeros of (p(x)=x^3+ax^2+bx-6), what is (a)?HardLevel 48What is the expanded form of (x^2-4)(x^2+4)?HardLevel 48What is the coefficient of x^3 in the polynomial p(x) = 3x^5 - 2x^4 + 7x - 6?HardLevel 48If the degree of (p(x)=mx^4+(m+2)x^3+5x+1) is (3), what is (m)?HardLevel 48