Factoring Polynomials: A polynomial is a mathematical expression consisting of variables raised to different powers. Factoring a polynomial involves finding...
Factoring Polynomials:
A polynomial is a mathematical expression consisting of variables raised to different powers. Factoring a polynomial involves finding its factors, which are the expressions that divide the original polynomial evenly. The factors of a polynomial can be expressed as polynomials as well.
Remainder Theorem:
The remainder theorem states that when a polynomial f(x) is divided by x - a, the remainder is equal to f(a). This theorem can be used to find the value of f(a) by evaluating the polynomial f(x) at x = a.
Examples:
Factoring Polynomials:
2x^2 + 5x + 6 = (2x + 3)(x + 2)
x^3 - 4x + 3 = (x - 3)(x - 1)(x - 1)
Remainder Theorem:
When 12 is divided by 3, the remainder is 0, according to the remainder theorem.
If f(x) = x^2 + 1, then f(3) = 9, which is the remainder when 3 is divided by 2