# How do you factorize 2x^{2} + 3x + 1?

**Exponents and powers** are a method to express repeated multiplication of the same number. For eg- 5×5×5×5 can be written as 54 where is the base and 4 is the exponent. It is most commonly used to express the powers of 10 to write a very large number in a convenient manner. For eg- 1000 can be written as 10^{3}.

### Laws of Exponents

- To multiply two exponential numbers with the same bases, the exponents are added and the base remains the same. For eg- a
^{m}×a^{n}=a^{m+n}. - When the exponent has another exponent, the base remains the same but the powers are multiplied. For eg- (a
^{m})^{n}=a^{m×n}. - To divide two exponential numbers with the same bases, the exponents are subtracted and the base remains the same. For eg- a
^{m}/a^{n}=a^{m-n}.

### What is a Quadratic Equation?

The **quadratic equations** are 2-degree polynomial equations with one variable. The general form of a quadratic equation is given as f(x) = ax^{2 }+ bx + c where a, b and c are real numbers and a≠0. In the general form, ‘a’ is the leading coefficient and ‘c’ is the absolute term. The values of x that satisfy the polynomial equation are known as the roots of the quadratic equation.

When a quadratic polynomial is equated to zero, it becomes a quadratic equation. The general form of the equation is ax^{2 }+ bx + c = 0.

For eg- 2x^{2}+3x+6=0, 4x^{2}+7x+3=0, x^{2}+2x=0.

**Quadratic Equation Formula**

The roots or solution of a quadratic equation are calculated by the formula given below:

(α, β) = (-b±√(b

^{2}-4ac))/2awhere,

α and β are the roots of the equation.

**Steps to solve a quadratic equation**

**Step 1: **Write the quadratic equation and equate it to zero.

**Step 2:** Identify the values of ‘a’, ‘b’, and ‘c’ from the equation.

**Step 3:** Substitute the values in the quadratic equation formula and solve for the values of the roots.

**Step 4:** Make sure the calculation is correct.

### How do you factor 2x^{2} + 3x + 1?

**Solution:**

Given that the quadratic equation is 2x

^{2 }+ 3x + 1Equate the quadratic equation to zero.

2x

^{2 }+ 3x + 1 = 0Here, a = 2, b = 3 and c = 1.

Substitute the values in the quadratic equation formula.

x = (-3±√(3

^{2}-4×2×1))/2×2x = (-3±√1)/4

x = (-3±1)/4

x = -1/2, -1

Hence, the factors of the equation as -1/2 and -1.

### Similar Questions

**Question 1: What are the factors of x ^{2 }+ 3x + 2?**

**Solution:**

Given that the quadratic equation is x

^{2}+3x+2.Equate the quadratic equation to zero.

x

^{2 }+ 3x + 2 = 0Here, a = 1, b = 3 and c = 2.

Substitute the values in the quadratic equation formula.

x = (-3±√(3

^{2}-4×1×2))/2×1x = (-3±√1)/2

x = (-3±1)/2

x = -1, -2

Hence, the factors of the equation as -1 and -2.

**Question 2: What are the factors of x ^{2 }+ 7x + 12.**

**Solution:**

Given that the quadratic equation is x

^{2 }+ 7x + 12.Equate the quadratic equation to zero.

x

^{2 }+ 7x + 12 = 0Here, a = 1, b = 7 and c = 12.

Substitute the values in the quadratic equation formula.

x = (-7±√(7

^{2}-4×1×12))/2×1x = (-7±√1)/2

x = (-7±1)/2

x = -4, -3

Hence, the factors of the equation as -4 and -3.