A polynomial is an expression consisting of variables (also called indeterminates) raised to various powers, combined using addition, subtraction, and multiplication. The general form of a polynomial is:
p(x) = aₙxⁿ + aₙ₋₁xⁿ⁻¹ + ... + a₁x + a₀
Where the aₙ, aₙ₋₁, ..., a₀ are constants (called coefficients), and x is the variable. The exponent (n) is a non-negative integer.
To add polynomials, combine like terms (terms that have the same variable raised to the same power).
To subtract polynomials, distribute the negative sign and combine like terms.
To multiply polynomials, use the distributive property (multiply each term in the first polynomial by each term in the second polynomial).
Add the polynomials 2x² + 3x + 4 and x² - x + 1:
(2x² + 3x + 4) + (x² - x + 1) = (2x² + x²) + (3x - x) + (4 + 1)
= 3x² + 2x + 5
Subtract (3x² + 4x - 2) from (5x² - 2x + 7):
(5x² - 2x + 7) - (3x² + 4x - 2) = (5x² - 3x²) + (-2x - 4x) + (7 + 2)
= 2x² - 6x + 9
Multiply (x + 2) and (x - 3):
(x + 2)(x - 3) = x² - 3x + 2x - 6
= x² - x - 6
Now, try adding and subtracting these polynomials:
2x³ + x² - 3x + 5 and x³ + 4x² - x - 1Click here for the solution