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Find the GCF of 18j+27

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To find the greatest common factor (GCF) of the expression \(18j + 27\), we first identify the coefficients of the terms:

  1. The coefficients are 18 and 27.
  2. We will find the GCF of these numbers.

The factors of 18 are:

  • 1, 2, 3, 6, 9, 18

The factors of 27 are:

  • 1, 3, 9, 27

The common factors of 18 and 27 are:

  • 1, 3, 9

The greatest of these is 9.

Now, we can also factor factored out of the original expression: \[ 18j + 27 = 9(2j + 3) \]

Thus, the GCF of \( 18j + 27 \) is 9.

Find the GCF of 42m−28n

To find the greatest common factor (GCF) of the expression \(42m - 28n\), we'll first identify the coefficients of the terms and then determine their GCF.

  1. The coefficients here are 42 and -28.
  2. We'll find the GCF of these numbers.

The factors of 42 are:

  • 1, 2, 3, 6, 7, 14, 21, 42

The factors of 28 are:

  • 1, 2, 4, 7, 14, 28

The common factors of 42 and 28 are:

  • 1, 2, 7, 14

The greatest of these is 14.

Now, we can factor out the GCF from the original expression: \[ 42m - 28n = 14(3m - 2n) \]

Thus, the GCF of \(42m - 28n\) is 14.

Use properties of operations to factor 8w + 16 using the GCF

To factor the expression \(8w + 16\) using the greatest common factor (GCF), we follow these steps:

  1. Identify the GCF of the coefficients.

    • The coefficients are 8 and 16.
    • The factors of 8 are \(1, 2, 4, 8\).
    • The factors of 16 are \(1, 2, 4, 8, 16\).
    • The GCF of 8 and 16 is \(8\).

  2. Factor out the GCF from the expression. \[ 8w + 16 = 8(w + 2) \]

So, the expression \(8w + 16\) factored using the GCF is: \[ 8(w + 2) \]

Factor −27h + 6 using the GCF

To factor the expression \(-27h + 6\) using the greatest common factor (GCF), follow these steps:

  1. Identify the GCF of the coefficients.

    • The coefficients are \(-27\) and \(6\).
    • The factors of \(27\) (ignoring the sign for now) are \(1, 3, 9, 27\).
    • The factors of \(6\) are \(1, 2, 3, 6\).
    • The common factors are \(1\) and \(3\).
    • The GCF is \(3\).

  2. Factor out the GCF from the expression.

    • Note that since one of the terms is negative, we can factor out \(-3\) to keep the leading coefficient positive. \[ -27h + 6 = -3(9h - 2) \]

So, the expression \(-27h + 6\) factored using the GCF is: \[ -3(9h - 2) \]

Factor −27h + 6 using the GCF. (1 point)
Responses

​​​​​​​3(9h − 2)
3 Left Parenthesis 9 h minus 2 Right Parenthesis

​​​​​​​3(−9h + 2)
3 Left Parenthesis negative 9 h plus 2 Right Parenthesis

​​​​​​​3(9h + 2)
3 Left Parenthesis 9 h plus 2 Right Parenthesis

​​​​​​​3(−9h − 2)

To factor \(-27h + 6\) using the greatest common factor (GCF), we previously determined that the GCF is \(3\).

When factoring out \(3\), we want to maintain the correct signs. Since the original expression is \(-27h + 6\), we can factor out \(-3\) instead, as that will help keep a positive leading coefficient in the parentheses:

\[ -27h + 6 = -3(9h - 2) \]

Now let's evaluate the given response options:

  1. 3(9h − 2) → This is incorrect because it doesn't account for the negative in front of the \(27h\).

  2. 3(−9h + 2) → This is incorrect since it has the wrong sign for \(h\).

  3. 3(9h + 2) → This is incorrect since it changes the sign of the \(2\).

  4. 3(−9h − 2) → This is also incorrect since it does not accurately represent the factored form.

The correct answer can be rewritten as:

\[ -3(9h - 2) \]

Since none of the options correctly represent the factored form, the closest to what we derived would have been "3(−9h + 2)" only if you were to factor out \(−3\) from \(-27h + 6\). However, given that no choice matches our finding directly, it appears there may be an issue with the provided options.

Thus, none of the provided options is the correct answer for the factoring of \(-27h + 6\). The correct factored form, as stated, is \(-3(9h - 2)\).

You have to choose one of the answers

Given the options provided:

  1. 3(9h − 2)
  2. 3(−9h + 2)
  3. 3(9h + 2)
  4. 3(−9h − 2)

The best option to choose, given the expression \(-27h + 6\), is 3(−9h + 2).

This selection reflects the correct sign for \(h\) and represents a valid relationship derived from factoring the expression with a GCF of \(3\) while adjusting the signs appropriately.

So, I choose: 3(−9h + 2).