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Factoring Trinomials Calculator
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Trinomial Expressions are in the form of ax2 + bx + c. Factoring trinomials calculator ( known as factor trinomials calculator) is a trinomial calculator to find factors of trinomial expressions. It makes calculation easy and fun. Trinomial factoring calculator is a online tool that find the factors of that expression if any trinomial equation is given.

Below is given a default trinomial expression, click "Submit". It will find the factors of the given trinomial expression.

Steps for Factoring Trinomials

Step 1 :

Observe the values of a, b, and c; a is the coefficient of x2, b is the coefficient of x, and c is the constant.

Step 2 :

If a = 1, then find all the factor pairs(including negative factors also) for the term c, else multiply a(coefficient of x2) with c(constant term) and then find the factor pairs.

Step 3 :

Now, determine which factor pairs sums up to the middle term b.

Step 4 :

Make the expression into two binominals.

Examples on Factoring Trinomials

1. Factor x2+ 5x+ 6

Step 1 :

Here in the given equation,

a(coefficient of x2) = 1,

b(coefficient of x) = 5,

And c(constant) = 6.

Step 2 :

6 Factor pairs $\Rightarrow$ (1, 6), (2, 3), (-1, 6), (1, -6), (-1, -6), (-2, 3), (2, -3), (-2, -3)

Step 3 :

Factor pairs which sums up to 5 $\Rightarrow$ (2, 3)

So, x2+ 5x+ 6 $\Rightarrow$ x2+ 3x + 2x + 6

Step 4 :

$\Rightarrow$ x2+ 3x + 2x + 6

$\Rightarrow$ x(x + 3) + 2 (x + 3)

$\Rightarrow$ (x + 2)(x + 3)

(x + 2)(x + 3)

2. Factor 2x2 - 3x - 5

Step 1 :

Here in the given equation,

a(coefficient of x2) = 2,

b(coefficient of x) = -3,

And c(constant) = -5

Step 2 :

(2 $\times$ -5) = -10

-10 factor pairs $\Rightarrow$ (1, -10), (2, -5), (1, 10), (-1, -10), (-1, 10), (-2, -5), (-2, 5), (2, 5)

Step 3 :

Factor pairs which sums up to -10 $\Rightarrow$ (2, -5)

So, 2x2 - 3x - 5 $\Rightarrow$ 2x2 + 2x -5x - 5

Step 4 :

$\Rightarrow$ 2x2 + 2x -5x - 5

$\Rightarrow$ 2x(x + 1) -5(x + 1)

$\Rightarrow$ (2x - 5)(x + 1)

(2x - 5)(x + 1)

3. Jame and Criss have two credit cards of different shapes. Jame's card is square shaped and Criss has rectangular credit card, but both cards have same area. The length of the rectangular card is five inches more than twice the length of the side of the square card. The width of the Criss's credit card is 6 inches less than the side of the James's credit card. Find the side length of the James's card.

Step 1 :

Let s be the side length of the Jame's credit card.

Step 2 :

Since Area of both the credit cards is same. Let us convert given statement into equation form.
(s - 6)(2s + 5) = s$^2$

Step 3 :

2s$^2$ + 5s - 12s - 30 = s$^2$
s$^2$ - 7s - 30 = 0
s$^2$ - 10s + 3s - 30 = 0 (Using factorization method)
s(s - 10) + 3(s - 10) = 0
(s + 3)(s - 10) = 0
s + 3 = 0 and s - 10 = 0
s = -3 and s = 10

Step 4 :

Side length cannot be negative, so neglect s = -3.

The side length of James's card is 10 inches.

4. A business man wants to know when the sale of a particular item reaches a profit level of 20,000 dollars. The revenue equation is R = 600x - 1.5y$^2$, and the cost to produce y items is determined with C = 10,000 + 150y. How many items have to be produced and sold to net a profit of 20,000 dollars?

Step 1 :

Given: P = 20,000, R = 600y - 1.5y$^2$ and C = 10,000 + 150y

Step 2 :

The relationship between profit, cost and revenue is given as: P = R - C.
Substitute the given values, we get
20,000 = (600y - 1.5y$^2$) - (10,000 + 150y)

Step 3 :

20,000 = 600y - 1.5y$^2$ - 10,000 – 150 y
20,000 = 450 y - 1.5 y$^2$ - 10,000
30,000 = 450 y - 1.5y$^2$
or 1.5y$^2$ - 450 y + 30,000 = 0
1.5 y$^2$ - 450 y + 30,000 = 0
1.5( y$^2$ - 300y + 20,000) = 0
y$^2$ - 300y + 20,000 = 0
y$^2$ - 200 y – 100 y + 20,000 (Factorized the trinomial)
y ( y - 200) - 100( y - 200) = 0
(y - 100)(y - 200) = 0
y = 100 and  y = 200

Step 4 :

When y = 100 or y = 200, the profit is 20,000 dollars. At either level, the difference between the revenue and cost is 20,000 dollars.