This online factoring trinomials calculator is intended to represent a trinomial with integer coefficients as a product of two binomials with integer coefficients. Enter the values of three coefficients in the input fields of the calculator and get the factored form of the trinomial.
ax2 + bx + c = (px + q) (rx + s)
Factoring Trinomials
A trinomial is a quadratic polynomial (or a polynomial of degree 2) which generally consists of three terms:
$$a{ x }^{ 2 } + bx + c,$$
where \(a \neq 0\). In many cases a trinomial can be factored or represented as a product of two binomials:
$$a{ x }^{ 2 } + bx + c = (px + q)(rx + s).$$
The process of factoring of polynomials is essential to the simplification of many algebraic expressions and is a useful tool in solving higher degree equations. This process is widely used in the case of polynomials with integer coefficient. So our online calculator deals with trinomials with integer coefficients only.
The algorithm, used in our factoring trinomials calculator, assumes representation of the trinomial in the form:
$$a{ x }^{ 2 } + bx + c = a{ x }^{ 2 } + mx +nx + c,$$
where integers \(m\) and \(n\) satisfy the following conditions: \(m + n = b\), \(mn = ac.\)
Once \(m\) and \(n\) are found, we use grouping and the distributive property to finally factor the trinomial.
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