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Factor the greatest common factor: −4y2 + 12y − 16. −1(4y2 − 12y + 16) −4y(y2 − 3y + 4) −4(y2 − 3y + 4) −4(y2 + 3y − 4)

Question

Factor the greatest common factor:

-4y² + 12y - 16.

-1(4y² - 12y + 16)
-4y(y² - 3y + 4)
-4(y² - 3y + 4)
-4(y² + 3y - 4)

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Solution

To factor the greatest common factor of the expression 4y2+12y16-4y^2 + 12y - 16, let's go through the following steps:

1. Break Down the Problem

We need to factor the given quadratic expression 4y2+12y16-4y^2 + 12y - 16.

2. Relevant Concepts

The first step in factoring is to identify the greatest common factor (GCF) of the polynomial terms.

3. Analysis and Detail

  1. Identify the coefficients of each term:

    • For 4y2-4y^2, the coefficient is 4-4.
    • For 12y12y, the coefficient is 1212.
    • For 16-16, the coefficient is 16-16.
  2. Determine the GCF of 4-4, 1212, and 16-16:

    • The GCF is 44.
  3. Factor out the GCF from the expression: 4(y23y+4) -4(y^2 - 3y + 4) So, the expression can be rewritten as 4(y23y+4)-4(y^2 - 3y + 4).

4. Verify and Summarize

Now let's verify our factoring by distributing: 4(y23y+4)=4y2+12y16 -4(y^2 - 3y + 4) = -4y^2 + 12y - 16 This confirms that our factoring is correct.

Final Answer

The factored form with the greatest common factor is: 4(y23y+4) -4(y^2 - 3y + 4)

This problem has been solved

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