Chapter A.4, Problem 25E

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6th Edition

Daniel C. Alexander + 1 other

ISBN: 9781285195698

Textbook Problem

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*In Exercises 25 to 32, solve each quadratic equation by factoring.*

To determine

The quadratic equation by factorization.

Explanation

**Approach:**

Solving an equation is to find the value of the unknown variables in the equation, such that the obtained value or values of the unknown should satisfy the equation from which it was derived. Such a value is said to be the solution for the equation. In general a quadratic equation has two solutions for the variable in the equation as the degree of the equation is two.

**Calculation:**

Given,

The above equation is in the standard form of a quadratic equation.

Now, we shall proceed with the factorization of the quadratic expression in the left of the equation.

First look for the common factor

Terms | Prime factors |

But, the

Hence, factor the expression

First factorize the product of the coefficient of the first tern and the constant, such that the sum of the factors gives the coefficient of the middle term.

Thus, factorize

So that the sum of the factors

Now, split the middle term

Hence, the given equation

Becomes.

Factor out the common factors form the first two terms and form the last two terms of the above expression

Sect-A.1 P-1ESect-A.1 P-2ESect-A.1 P-3ESect-A.1 P-4ESect-A.1 P-5ESect-A.1 P-6ESect-A.1 P-7ESect-A.1 P-8ESect-A.1 P-9ESect-A.1 P-10E

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