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Cancellation Of Terms

Class 9 Mathematics के इस tag से जुड़े questions। हर question के साथ chapter, topic, level और difficulty दी गई है।

MathematicsLet the non-zero polynomials \(p(x)\) and \(q(x)\) both have degree \(n\), and suppose that \(p(x)+q(x)\) is also non-zero. Which condition is necessary and sufficient for the degree of \(p(x)+q(x)\) to be less than \(n\)?Class 9Introduction to PolynomialsDegree of a PolynomialHard MathematicsA student says that if two polynomials have degree 6, then the degree of their sum will always be 6. If \(p(x)=x^6-3x^2\) and \(q(x)=-x^6+5x\), which conclusion is correct?Class 9Introduction to PolynomialsDegree of a PolynomialHard MathematicsIf (F(x)=7x^{13}-7x^{13}+8x^9-8x^9+10x^6-5), what is the degree of (F(x))?Class 9Introduction to PolynomialsDegree of a PolynomialExpert MathematicsA student says that the polynomial \(p(x)=(x^3+2x^2-x)-(x^3-5x+4)\) has degree 3 because an \(x^3\) term is visible. What is the correct conclusion?Class 9Introduction to PolynomialsDegree of a PolynomialExpert MathematicsRima claims that the polynomial \(P(x)=(x^4+2x^2+1)-(x^4-3x^2+5)\) has degree 4 because both brackets contain an \(x^4\) term. Which is the correct evaluation of her claim?Class 9Introduction to PolynomialsDegree of a PolynomialExpert MathematicsIf (F(x)=6x^{12}-6x^{12}+7x^8-7x^8+9x^5-4), what is the degree of (F(x))?Class 9Introduction to PolynomialsDegree of a PolynomialExpert MathematicsIf (F(x)=4x^{10}-4x^{10}+5x^6-5x^6+7x^3-2), what is the degree of (F(x))?Class 9Introduction to PolynomialsDegree of a PolynomialHard MathematicsA student says that the degree of the polynomial \(P(x)=5x^6-5x^6+3x^4-x+1\) is 6 because an \(x^6\) term appears in it. Which conclusion is correct?Class 9Introduction to PolynomialsDegree of a PolynomialHard MathematicsIf (A(x)=x^5+4) and (B(x)=-x^5+3x^2), what is the degree of (A(x)+B(x))?Class 9Introduction to PolynomialsDegree of a PolynomialHard MathematicsIf (g(x)=2x^6-2x^6+x^4-x^2), what is the degree of (g(x))?Class 9Introduction to PolynomialsDegree of a PolynomialMedium