Question

question 1 of 6
select the correct answer.
which expression has the same gcf as $15x^2 - 21x$?
$18x^2 - 24x$
$12x^2 - 18x$
$12x^2 - 15x$
$15x^2 - 21$

Explanation:

Step1: Find GCF of \(15x^2 - 21x\)

First, factor the coefficients and variables. For coefficients \(15\) and \(21\), find their GCF. The factors of \(15\) are \(1, 3, 5, 15\), and factors of \(21\) are \(1, 3, 7, 21\). The GCF of \(15\) and \(21\) is \(3\). For the variable part, \(x^2\) and \(x\) have GCF \(x\). So GCF of \(15x^2 - 21x\) is \(3x\).

Step2: Find GCF of \(18x^2 - 24x\)

Coefficients \(18\) and \(24\): factors of \(18\) are \(1, 2, 3, 6, 9, 18\); factors of \(24\) are \(1, 2, 3, 4, 6, 8, 12, 24\). GCF of \(18\) and \(24\) is \(6\). Variable part: \(x^2\) and \(x\) have GCF \(x\). So GCF is \(6x\), not \(3x\).

Step3: Find GCF of \(12x^2 - 18x\)

Coefficients \(12\) and \(18\): factors of \(12\) are \(1, 2, 3, 4, 6, 12\); factors of \(18\) are \(1, 2, 3, 6, 9, 18\). GCF of \(12\) and \(18\) is \(6\). Variable part: \(x^2\) and \(x\) have GCF \(x\). GCF is \(6x\), not \(3x\).

Step4: Find GCF of \(12x^2 - 15x\)

Coefficients \(12\) and \(15\): factors of \(12\) are \(1, 2, 3, 4, 6, 12\); factors of \(15\) are \(1, 3, 5, 15\). GCF of \(12\) and \(15\) is \(3\). Variable part: \(x^2\) and \(x\) have GCF \(x\). So GCF is \(3x\), same as \(15x^2 - 21x\).

Step5: Find GCF of \(15x^2 - 21\)

Variable part: \(x^2\) and no variable in the second term, so GCF of variables is \(1\). Coefficients \(15\) and \(21\) have GCF \(3\). So GCF is \(3\), not \(3x\).

Answer:

C. \(12x^2 - 15x\) (Note: Assuming the options are labeled as A: \(18x^2 - 24x\), B: \(12x^2 - 18x\), C: \(12x^2 - 15x\), D: \(15x^2 - 21\))