Factorize 2x2 + x – 6

Mathematics is not only about numbers but it is about dealing with different calculations involving numbers and variables. This is what basically is known as Algebra. Algebra is defined as the representation of calculations involving mathematical expressions that consist of numbers, operators, and variables. Numbers can be from 0 to 9, operators are the mathematical operators like +, -, ×, ÷, exponents, etc, variables like x, y, z, etc.

Exponents and Powers

Exponents and powers are the basic operators used in mathematical calculations, exponents are used to simplifying the complex calculations involving multiple self multiplications, self multiplications are basically numbers multiplied by themselves. For example, 7 × 7 × 7 × 7 × 7, can be simply written as 7⁵. Here, 7 is the base value and 5 is the exponent and the value is 16807. 11 × 11 × 11, can be written as 11³, here, 11 is the base value and 3 is the exponent or power of 11. The value of 11³ is 1331.

Exponent is defined as the power given to a number, the number of times it is multiplied by itself. If an expression is written as cx^y where c is a constant, c will be the coefficient, x is the base and y is the exponent. If a number say p, is multiplied n times, n will be the exponent of p. It will be written as

p × p × p × p … n times = pⁿ

What are Factors?

Factors are defined as the smaller numbers in multiplication that give the bigger product known as the divisor and the smaller numbers are known to be the factors of the divisor. In a mathematical equation, a factor is that number which after substituting satisfies that entire equation, for instance, x² – 4 = 0. In the given equation, by solving, the factor of the equation can be easily solved which is also the value of x here,

x² = 4

x = +4, -4

Factorize 2x² + x – 6

Solution:

The expression has a square term and therefore, cannot be factorized directly. Let’s break the middle expression into two parts and observe if some terms can be taken out common. Here, the expression 2x² + x – 6 can be broken as,

2x² + 4x – 3x -6

Taking 2x common from the first part and -3 common from the second part. The expression shall look like this,

= 2x (x + 2) – 3 (x + 2)

= (x + 2)(2x – 3)

Equating this to 0 and finding the roots,

Therefore, x = 3/2, x = -2

Similar Questions

Question 1: Factorize x² – 49.

Solution:

Using exponents, write x² – 49 as x² – 7²

Using identity, (x² – y²) = (x + y)(x – y)

= (x² – 7²)

= (x + 7)(x – 7)

Therefore, x = -7, x = 7

Question 2: Factorize x³ + 7x² – 7x – 49.

Solution:

The expression x³ + 7x² – 7x – 49 can be broken as,

• x³ + 7x²
• -7x – 49

Taking x² common from the first part and -7 common from the second part. The expression shall look like this,

= x² (x + 7) – 7 (x + 7)

= (x² – 7)(x + 7)

= (x² – (√7)²)(x + 7)

Using identity, (x² – y²) = (x + y)(x – y)

= (x + √7)(x – √7)(x + 7)

Therefore, x = -√7, x = √7, x = 7

Question 3: Factorize x² + x – 30

Solution:

x² + 6x – 5x – 30

Taking x common from the first part and -5 common from the second part. The expression shall look like this,

= x (x + 6) – 5 (x + 6)

= (x + 6)(x – 5)

Equating this to 0 and finding the roots,

Therefore, x = 5, x = -6