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Subjects

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

If a=0 and b≠0 in p(x)=ax³+bx²+cx+d, what is the degree of p(x)?EasyLevel 47If \(p(x)=5x^3-2x^2+x-4\), what is the sum of all the coefficients of \(p(x)\)?HardLevel 47If the sum of all coefficients of p(x)=2x³+kx²−8x+3 is 0, what is k?MediumLevel 47If \(p(x)=3x^4-5x^2+2x-7\), what is the sum of the coefficients of the terms with odd powers of \(x\)?HardLevel 47What is the constant term of the polynomial (2x-3)(x^2+x+1)?HardLevel 47Which of the following expressions is a polynomial in one variable of degree 4, although it is not written in expanded form?HardLevel 47If the polynomial \(f(x)=x^3+ax+b\) satisfies \(f(1)=4\) and \(f(-1)=-2\), what is the value of \(a\)?HardLevel 47If the polynomial \(p(x)=x^3+rx^2+s\) satisfies \(p(0)=5\) and \(p(1)=9\), what is the value of \(r\)?HardLevel 47For what value of (m) can ((m+1)x^2+(m-2)x+7) become a constant polynomial?HardLevel 47If \(p(x)=x^2+2x-8\), what is the value of \(p(3)-p(-2)\)?HardLevel 47For the polynomial \(p(x)=x^3-8\), which calculation proves that \(p(2)=0\)?HardLevel 47If p(x)=x^3+x^2+x+1, what is the value of p(-1)?HardLevel 47If \(p(x)=2x^2+bx+c\), \(p(0)=5\), and \(p(1)=1\), what is the value of \(b\)?HardLevel 47If \(p(x)=x^2-5x+6\), what is the value of \(p(2)+p(3)\)?HardLevel 47If (p(x)=x^2-9ig), which is the positive value of (aig) for which (p(a)=0ig)?HardLevel 47Which of the following values is a zero of the polynomial \(p(x)=4x^2-12x+9\)?HardLevel 47If (x=1) and (x=-2) are both zeros of (p(x)=x^3+ax^2+bx+6), what is (a-b)?HardLevel 47If (x=1) and (x=-1) are both zeros of (p(x)=x^3+ax^2+bx+4), what is (a)?HardLevel 47If x − 2 is a factor of the polynomial p(x) = x³ + kx² − 4x − 12, what is the value of k?HardLevel 47What is the coefficient of x² in the polynomial p(x) = 2x⁴ − 3x³ + 5x − 9?HardLevel 47