On this page "factoring quadratic equations shortcuts",we are going to see how to factor a quadratic equations in a simple and easy way.

A equation which is in the form of ax² + bx + c is known as quadratic equation. Here a,b and c are just numbers. The highest power of this kind of equation will be 2.

Before going to find factors we have to notice whether the coefficient of x² is 1 or not. If it is 1 we have to follow the below steps.

(i) If it is 1 we have to take the constant term and we have to split it as two parts.

(ii) The product of two parts must be equal to the constant term and the simplified value must be equal to the middle term (or) x term.

(iii) Now we have to write these numbers in the form of (x + a) and (x +b)

## Factoring trinomials with leading coefficient 1

Example 1:

Factor x² + 17 x + 60

Solution:

Now we have to split the constant term (60) as two terms. The product of two terms must be equal to 60 and the simplified value must be equal to the middle term (17).

All terms are positive.So,we have to put positive sign for both factors.

(x + 12) (x + 5) are the factors of x² + 17 x + 60.

Let us see the next example of the topic "factoring quadratic equations shortcuts".

Example 2:

Factor x² -  14 x + 48

Solution:

Now we have to split the constant term (48) as two terms. The product of two terms must be equal to 48 and the simplified value must be equal to the middle term (-14).

The middle term is negative.So,we have to put negative sign for both factors.

(x - 8) (x - 6) are the factors of x² - 14 x + 48.

Let us see the next example of the topic "factoring quadratic equations shortcuts".

Example 3:

Factor x² -  x - 6

Solution:

Now we have to split the constant term (-6) as two terms. The product of two terms must be equal to -6 and the simplified value must be equal to the middle term (-1).

The middle and last term are negative.So,we have to put negative sign for large number.

(x + 2) (x - 3) are the factors of x² - x - 6.

Let us see the next example of the topic "factoring quadratic equations shortcuts".

Example 4:

Factor  x² + 2 x - 24

Solution:

Now we have to split the constant term (-24) as two terms. The product of two terms must be equal to -24 and the simplified value must be equal to the middle term (2).

The last term are negative.So,we have to put negative sign for small number.

(x + 6) (x - 4) are the factors of x² + 2x - 24.

## Factoring quadratic equations when a isn't 1

Before going to find factors we have to notice whether the coefficient of x² is 1 or not. If it is not 1 we have to follow the below steps.

(i) Multiply the coefficient of x² by the constant term and we have to split it as two parts.

(ii) The product of two parts must be equal to the constant term and the simplified value must be equal to the middle term (or) x term.

(iii) Divide the factors by the coefficient of x². Simplify the factors by the coefficient of x² as much as possible.

(iv) Write the remaining number along with x.

Let us see some examples for better understanding.

Example 1:

Factor 2 x² + x - 6

Solution:

To factor this quadratic equation we have to multiply the coefficient of x²  by the constant term

So that we get -12, now we have to split -12 as the multiple of two numbers.

Since the last term is having negative sign.So we have to put negative sign for the least number.

Now we have to divide the two numbers 4 and -3 by the coefficient of x² that is 2..If it is possible we can simplify otherwise we have to write the numbers along with x.

So (x + 2) (2x - 3) are the factors of 2 x² + x - 6

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