Factoring Trinomials Formula
A trinomial is a polynomial with three terms and has the general form (ax2 + bx + c), where (a), (b), and (c) are constants. Here are some key formulas related to trinomials:
Quadratic Formula: x =
Used to find the roots (solutions) of a quadratic trinomial (ax2 + bx + c).
Discriminant Formula: Δ = b2 – 4ac
Discriminant (Δ) helps determine the nature of the roots. If (Δ > 0), there are two real and distinct roots. If (Δ = 0), there is one real root (a repeated root). If (Δ < 0), there are two complex conjugate roots.
Formula for factoring a quadratic trinomial in the form (ax2 + bx + c) involves expressing it as the product of two binomials. General factored form is given by:
ax2 + bx + c = a(x – m)(x – n)
where (m) and (n) are values that, when multiplied, give (ac) and when added (or subtracted in the parentheses), give (b).
For example, factorize (x2 – 5x + 6)
x2 – 5x + 6
= x2 – 3x -2x + 6
= x(x – 3) -2(x – 3)
= (x – 2)(x – 3)
Trinomials
A trinomial is a type of polynomial that consists of three terms. These terms are usually written as ax² + bx + c, where a, b, and c are constants, and x is the variable. Trinomials are common in algebra, particularly when dealing with quadratic equations, which can often be expressed or factored into trinomial form.
It is the expression that consist of three terms, the common form of trinomial is ax2 + bx + c. Trinomials in algebra, are essential for solving quadratic equations and analyzing various mathematical models.
Let’s know more about Trinomials definition, formula and examples in detail.