**Introduction :**

In mathematics, algebra is the one of the important branch in mathematics. Algebra includes polynomials, inequalities and matrices. Factoring is the process of the given polynomial expression can be factored by using the greatest common factor method. Factoring algebra solver is used to different types of expressions in algebra which can besolved the expression in the factorization form. Let us solve some example problems in factoring algebra.

Different steps for factoring are,

* Given polynomial expression is in the form of ax2 + bx + c = 0.

* Determine the greatest common factor.

* Each factor is set to zero.

* Solve the terms.

Some example problems for factoring algebra are,

**Example 1:**

Factor the given polynomial expression

7x^{2} + 28 – 53x = 0

**Solution:**

** **By using the factoring algebra solver, we enter into a, b and coefficients in the expression like in the solver.

** **

** **If we hit the calculate button, it will display the factorization form for the given expression like in the solver.

Given polynomial expression

7x^{2} + 28 – 53x = 0

Given polynomial is in the standard form ax^{2} + bx + c = 0

7x^{2 }– 53x + 28 = 0

Greatest common factor for the expression

7x^{2 }– 49x – 4x + 28 = 0

7x (x – 7) – 4(x – 7) = 0

(x – 7) (7x – 4) = 0

Solve the terms.

x – 7 = 0 and 7x – 4 = 0

x = 7 and 4/7

**Solution:** x = 7 and 4/7

**Example 2:**

Factor the given polynomial expression

a^{2} – 14 – 5a = 0

**Solution:**

Given polynomial expression

a^{2} – 14 – 5a = 0

Given polynomial is in the standard form ax^{2} + bx + c = 0.

a^{2 }– 5a – 14 = 0

Greatest common factor for the expression

a^{2 }– 7a + 2a – 14 = 0

a (a – 7) + 2(a – 7) = 0

(a – 7) (a + 2) = 0

Solve the terms.

a – 7 = 0 and a + 2 = 0

a = 7 and – 2.

**Solution:** a = 7 and – 2.

**Example 3:**

Factor the given polynomial expression

10m^{2} + 89m – 9 = 0

**Solution:**

Given polynomial expression

10m^{2} + 89m – 9 = 0

Given polynomial is in the standard form ax^{2} + bx + c = 0.

10m^{2 }+ 89m – 9 = 0

Greatest common factor for the expression

10m^{2 }+ 90m – m – 9 = 0

10m (m + 9) – 1 (m + 9) = 0

(10m – 1) (m + 9) = 0

Solve the terms.

10m – 1 = 0 and m + 9 = 0

m = 1/10 and – 9

**Solution:** m = 1/10 and – 9.

**Practice problem 1:**

Factor the given expression

a^{2} – 12 – 4a = 0

**Solution:**

**a = - 2 and 6.**

**Practice problem 2:**

Factor the given expression

a^{2} – 32 – 4a = 0

**Solution:**

**a = - 4 and 8.**