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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 p(x) = 8x⁴ − 3x³ − 4x + 2, what is the sum of all the coefficients of p(x)?ExpertLevel 47If the sum of all coefficients of (p(x)=4x^4+kx^3-6x+1) is (5), what is (k)?ExpertLevel 47In the polynomial p(x) = 6x^6 − 5x^5 + 4x^3 − 2x^2 + x − 7, what is the sum of the coefficients of the odd-power terms?ExpertLevel 47What is the constant term of the polynomial \\(4x+3)(x^2-2x+5)\\)?ExpertLevel 47What is the simplified polynomial form of (2x + 5)^2 - (2x - 1)^2?MediumLevel 48If (p(x)=x^3+ax+b), (p(2)=13), and (p(-1)=-7), what is the value of (a+b)?ExpertLevel 47If \(p(x)=x^3+ax+b\), \(p(1)=6\), and \(p(-2)=-9\), what is the value of \(a\)?ExpertLevel 47For what value of (r) can ((r+4)x^3+(r-1)x^2+9) become a constant polynomial?ExpertLevel 47If \(p(x)=x^2-4x-12\), what is the value of \(p(6)-p(-2)\)?ExpertLevel 47Which calculation correctly proves that \(p(4)=0\) for the polynomial \(p(x)=x^3-64\)?ExpertLevel 47If \(p(x)=x^4-x^3+x^2-x+1\), what is the value of \(p(1)\)?ExpertLevel 47If \(p(x)=5x^2+bx+c\), \(p(0)=-4\), and \(p(1)=3\), what is the value of \(b\)?ExpertLevel 47Which of the following expressions is a quadratic polynomial in one variable?ExpertLevel 47If \(p(x)=x^2-49\), which of the following is one value of \(a\) for which \(p(a)=0\)?ExpertLevel 47Which of the following is a zero of the polynomial \(p(x)=16x^2-24x+9\)?ExpertLevel 47If x = 1 and x = -2 are both zeros of p(x) = x^3 + ax^2 + bx + 18, what is a + b?HardLevel 48If (x=1) and (x=5) are both zeros of (p(x)=x^3+ax^2+bx-10), what is (a)?ExpertLevel 47What is the expanded form of (x^2-9)(x^2+9)?ExpertLevel 47What is the coefficient of \(x^5\) in the polynomial \(p(x)=4x^6-5x^4+2x^2-11\)?ExpertLevel 47If the degree of p(x) = mx^5 + (m - 4)x^4 + 3x^2 + 1 is 4, what is m?HardLevel 48