Polynomials Class 10 Maths Formulas

The List of Important Formulas for Class 10 Polynomials is provided on this page. We have everything covered right from basic to advanced concepts in Polynomials. Make the most out of the Maths Formulas for Class 10 prepared by subject experts and take your preparation to the next level. Access the Formula Sheet of Polynomials Class 10 covering numerous concepts and use them to solve your Problems effortlessly.

• “Polynomial” comes from the word ‘Poly’ (Meaning Many) and ‘nomial’ (in this case meaning Term)-so it means many terms.
• A polynomial is made up of terms that are only added, subtracted or multiplied.
• A quadratic polynomial in x with real coefficients is of the form ax² + bx + c, where a, b, c are real numbers with a ≠ 0.
• Degree – The highest exponent of the variable in the polynomial is called the degree of polynomial. Example: 3x³ + 4, here degree = 3.
• Polynomials of degrees 1, 2 and 3 are called linear, quadratic and cubic polynomial respectively.
• A polynomial can have terms which have Constants like 3, -20, etc., Variables like x and y and Exponents like 2 in y².
• These can be combined using addition, subtraction and multiplication but NOT DIVISION.
• The zeroes of a polynomial p(x) are precisely the x-coordinates of the points, where the graph of y = p(x) intersects the x-axis.

If α and β are the zeroes of the quadratic polynomial ax² + bx + c, then
\(sum\quad of\quad zeros,\alpha +\beta =\frac { -b }{ a } =\frac { -coefficient\quad of\quad x }{ coefficient\quad of\quad { x }^{ 2 } } \)
\(product\quad of\quad zeros,\alpha \beta =\frac { c }{ a } =\frac { constant\quad term }{ coefficient\quad of\quad { x }^{ 2 } } \)

If α, β, γ are the zeroes of the cubic polynomial ax³ + bx² + cx + d = 0, then
\(\alpha +\beta +\gamma =\frac { -b }{ a } =\frac { -coefficient\quad of\quad { x }^{ 2 } }{ coefficient\quad of\quad { x }^{ 3 } } \)
\(\alpha \beta +\beta \gamma +\gamma \alpha =\frac { c }{ a } =\frac { coefficient\quad of\quad { x } }{ coefficient\quad of\quad { x }^{ 3 } } \)
\(\alpha \beta \gamma =\frac { -d }{ a } =\frac { -constant\quad term }{ coefficient\quad of\quad { x }^{ 3 } } \)

Zeroes (α, β, γ) follow the rules of algebraic identities, i.e.,
(α + β)² = α² + β² + 2αβ
∴(α² + β²) = (α + β)² – 2αβ

DIVISION ALGORITHM:
If p(x) and g(x) are any two polynomials with g(x) ≠ 0, then
p(x) = g(x) × q(x) + r(x)
Dividend = Divisor x Quotient + Remainder

Remember this!

• If r (x) = 0, then g (x) is a factor of p (x).
• If r (x) ≠ 0, then we can subtract r (x) from p (x) and then the new polynomial formed is a factor of g(x) and q(x).