Learn Before
Solving by Factoring
Solve the polynomial equation by converting it to standard form and applying factoring techniques.
Step 1 — Write in standard form. Subtract and add to both sides to bring all terms to one side:
Step 2 — Factor the greatest common factor. The three terms share a common factor of . Factor it out:
Step 3 — Factor the trinomial. The remaining trinomial is a perfect square trinomial:
Step 4 — Apply the Zero Product Property. Set each variable factor to zero:
Step 5 — Solve each equation:
The distinct solutions are and .
0
1
Tags
OpenStax
Intermediate Algebra @ OpenStax
Ch.6 Factoring - Intermediate Algebra @ OpenStax
Algebra
Related
Solving
Solving
Solving
Solving
Solving
Solving
Solving by Factoring
Solving by Factoring
Solving by Factoring
Finding the Dimensions of a Rectangular Bedroom with Area Square Feet
Finding the Dimensions of a Rectangular Sign with Area Square Feet
Finding the Dimensions of a Rectangular Patio with Area Square Feet
Finding the Zeros and Specific Heights for
Finding the Zeros and Specific Heights for
Finding the Zeros and Specific Heights for
To determine the required clearance for a new machine installation, a technician must solve a quadratic equation using the factoring method. Arrange the following steps in the correct order to successfully solve the equation.
A warehouse manager is calculating the required floor space for a new conveyor system using the quadratic equation , where represents the system's capacity. According to the standard five-step procedure for solving by factoring, what is the required first step the manager must perform?
A technical supervisor is training new staff on how to solve quadratic equations for equipment calibration. Match each procedural term with the correct action required when solving by the factoring method.
Workflow Verification for Equipment Calibration
A quality control technician is using the factoring method to solve a quadratic equation for a material stress analysis. According to the five-step procedure, the technician's very first step must be to write the equation in standard form, , before attempting to factor the expression.
Learn After
A technical designer is solving the equation to find the stabilization point for a new mechanical component. After rewriting the equation in standard form as , the designer must factor out the Greatest Common Factor (GCF). Which of the following is the correct GCF for the expression ?
An industrial engineer is using the polynomial equation to model the vibration frequencies of a new engine component. Arrange the following steps in the correct order to solve for using factoring techniques.
A structural analyst is evaluating a load-bearing model defined by the equation . Match each mathematical expression from the solution process to its correct functional role.
An automotive engineer is analyzing a vibration frequency model given by the equation . After factoring the equation into the complete form , the engineer applies the Zero Product Property. True or False: This process reveals that the equation has exactly two distinct numerical solutions: and x = rac{3}{2}.
Initiating the Factoring Process for a Growth Model