Adding and subtracting polynomials
Add and subtract polynomials in Grade 10 algebra by combining like terms with matching variables and exponents, arranging results in standard descending order.
Key Concepts
To add polynomials, combine like terms. To subtract a polynomial, add the opposite of each of its terms.
Add: $(3x^2 + 2x 1) + (x^2 5x + 6) = 3x^2 + x^2 + 2x 5x 1 + 6 = 4x^2 3x + 5$. Subtract: $(4y^3 y) (2y^3 + 3y 2) = 4y^3 y 2y^3 3y + 2 = 2y^3 4y + 2$.
Adding and subtracting polynomials is all about matching! You can only combine 'like terms'—those with the exact same variables and exponents. When you subtract, you must first flip the sign of every single term in the second polynomial. Then it becomes a simple game of sorting, matching, and combining the similar pieces together.
Common Questions
What are like terms in polynomials?
Like terms have the same variable(s) raised to the same exponent(s). For example, 3x² and -7x² are like terms; 3x² and 3x³ are not.
How do you subtract polynomials like (3x²+2x-1) - (x²-4x+5)?
Distribute the negative sign: 3x²+2x-1-x²+4x-5. Then combine like terms: (3-1)x²+(2+4)x+(-1-5) = 2x²+6x-6.
What is standard form for a polynomial?
Standard form lists terms in descending order of degree, from highest exponent to lowest. For example: 4x³-2x²+x-7.