Examkin

Question

Difficulty: MediumFactoring Polynomials

During an analysis of a parabolic trajectory, an engineer must factor the polynomial 4x2−4x−484x^2 - 4x - 48 completely to determine its zero points. What is the correctly factored form of this polynomial?

  1. 4(x−4)(x+3)4(x - 4)(x + 3)Answer
  2. B
    4(x+4)(x−3)4(x + 4)(x - 3)
  3. C
    (4x−16)(x+3)(4x - 16)(x + 3)
  4. D
    4(x−6)(x+2)4(x - 6)(x + 2)

Answer

The completely factored form of the polynomial is 4(x−4)(x+3)4(x - 4)(x + 3).
To factor completely, first factor out the GCF of 4 to get 4(x2−x−12)4(x^2 - x - 12). Then, factor the resulting trinomial by finding two numbers that multiply to -12 and add to -1. Those numbers are -4 and 3, yielding the final form 4(x−4)(x+3)4(x - 4)(x + 3).

Step-by-Step Solution

1
Extract the greatest common factor (GCF) from all terms in the polynomial 4x2−4x−484x^2 - 4x - 48.
4(x2−x−12)4(x^2 - x - 12)
Factoring out the GCF simplifies the polynomial and makes the remaining quadratic expression easier to factor.
2
Find two integers that multiply to the constant term (-12) and add up to the coefficient of the middle term (-1).
The two integers are -4 and +3.
These integers provide the constants needed for the two binomial factors of the quadratic trinomial.
3
Write the final expression by combining the GCF with the factored binomials.
4(x−4)(x+3)4(x - 4)(x + 3)
This shows the polynomial broken down into its prime, indivisible factors.

Key Concept

Factoring out a Greatest Common Factor (GCF) before factoring a quadratic trinomial.
Rate this question

Topics

Factoring Polynomials

More questions from this topic