Trinomials Factoring Calculator

Method 1 : Factoring perfect square trinomial

Example 01: Factor $4a^2-12a+9$

Step1: Verify that both the first and third terms are perfect squares.

$4a^2$ is perfect square because $4a^2={\left(2a\right)}^2$

$9$ is perfect square because $9={\left(3\right)}^2$

Step2: Check if middle term is twice the product of $2a$ and $3$

Step3: Put $2a$ and $3$ inside parentheses. Because the middle term's coefficient is negative, we'll insert a minus sign inside parenthesis.

Method 2 : Leading coefficient $a=1$

In this case, the trinomial has the following form $x^2+bx+c$.

Example 02: Factor $x^2+7x+10$

To factor this trinomial we need to find two integers ( $p$ and $q$ ) such that $p+q=b$ and $p\cdot q=c$.

In this example $p+q=7$ and $p\cdot q=10$

After some trials and errors we get $p=2$ and $q=5$

The factored form is

Method 4 : Special Cases

Example 04: Factor $3x^2+5x$

This is special case where $c=0$.

To solve this one we just need to factor $x$ out of $3x^2+5x$

Example 05: Factor $25x^2-4$

This is special case where $b=0$.

We'll need to use the difference of squares formula to factor this one.

Method 3 : Leading coefficient $a\ne 1$

In this case, the trinomial has the following form: $a{x}^2+bx+c$.

Example 03: Factor $3x^2-5x+2$

Step 1: Identify constants $a$ , $b$ and $c$

Step 2: Find out two numbers ( $p$ and $q$) that multiply to $a\cdot c=6$ and add up to $b=-5$.

After some trials and errors we get $p=-2$ and $q=-3$

Step 3:Replace middle term ( $-5x$ ) with $-2x-3x$

Step 4:Factor out x from the first two terms and -1 from the last two terms.