Respuesta :
[tex]8x^4 -12x^3 + 20x^2[/tex]
The greatest common factor is 4x². The coefficients are multiples of 4 (2 isn't the largest, and 8 is too large. The term that has the lowest degree has x to the 2nd power, so we know it can be pulled out of the expression. When 4x² is pulled out, the expression looks like this:
[tex]8x^4 -12x^3 + 20x^2 \\ \\ 4 x^{2} (2x^2-3x+5)[/tex]
Your answer should be B, 4x².
The greatest common factor is 4x². The coefficients are multiples of 4 (2 isn't the largest, and 8 is too large. The term that has the lowest degree has x to the 2nd power, so we know it can be pulled out of the expression. When 4x² is pulled out, the expression looks like this:
[tex]8x^4 -12x^3 + 20x^2 \\ \\ 4 x^{2} (2x^2-3x+5)[/tex]
Your answer should be B, 4x².
The greatest common factor of the terms of the polynomial is [tex]$4 x^{2}$[/tex].
How to estimate the greatest common factor?
Find the common factors for the numerical part: 8, -12, 20
The factors for 8 are 1, 2, 4, and 8.
The factors for 8 are all numbers between 1 and 8, which divide 8 evenly. Check numbers between 1 and 8.
Find the factor pairs of 8 where [tex]$x \cdot y=8$[/tex].
x 1 2
y 8 4
List the factors for 8.
1, 2, 4, 8
The factors for -12 are -12, -6, -4, -3, -2, -1, 1, 2, 3, 4, 6, 12.
The factors for -12 are all numbers between 1 and 12, which divide -12 evenly. Check numbers between 1 and 12
Find the factor pairs of -12 where [tex]$x \cdot y=-12$[/tex].
List the factors for -12.
-12, -6, -4, -3, -2, -1, 1, 2, 3, 4, 6, 12
The factors for 20 are 1, 2, 4, 5, 10, 20.
The factors for 20 are all numbers between 1 and 20, which divide 20 evenly. Check numbers between 1 and 20
Find the factor pairs of 20 where [tex]$x \cdot y=20$[/tex].
x 1 2 4
y 20 10 5
List the factors for 20.
1, 2, 4, 5, 10, 20
List all the factors for 8, -12, and 20 to find the common factors.
8: 1, 2, 4, 8
-12: 12, -6, -4, -3, -2, -1, 1, 2, 3, 4, 6, 12
20: 1, 2, 4, 5, 10, 20
The common factors for 8, -12, 20 are 1, 2, 4 .
The greatest common factor for the numerical part is 4 .
[tex]$\mathrm{GCF}_{\text {Numerical }}=4$[/tex]
Next, find the common factors for the variable part: [tex]$x^{4}, x^{3}, x^{2}$[/tex]
The factors for [tex]$x^{4}$[/tex] are [tex]$x \cdot x \cdot x \cdot x$[/tex].
[tex]$x \cdot x \cdot x \cdot x$[/tex]
The factors for [tex]$x^{3}$[/tex] are [tex]$x \cdot x \cdot x$[/tex].
[tex]$x \cdot x \cdot x$[/tex]
The factors for [tex]$x^{2}$[/tex] are [tex]$x \cdot x$[/tex].
[tex]$x \cdot x$[/tex]
List all the factors for [tex]$x^{4}, x^{3}, x^{2}$[/tex] to find the common factors.
[tex]${data-answer}amp;x^{4}=x \cdot x \cdot x \cdot x \\[/tex]
[tex]${data-answer}amp;x^{3}=x \cdot x \cdot x \\[/tex]
[tex]${data-answer}amp;x^{2}=x \cdot x[/tex]
The common factors for the variables [tex]$x^{4}, x^{3}, x^{2}$[/tex] are [tex]$x \cdot x$[/tex].
[tex]$x \cdot x$[/tex]
The greatest common factor for the variable part is [tex]$x^{2}$[/tex].
[tex]$\mathrm{GCF}_{\text {Variable }}=x^{2}$[/tex]
Multiply the greatest common factor of the numerical part 4 and the greatest common factor of the variable part [tex]$x^{2}$[/tex].
The greatest common factor of the terms of the polynomial is [tex]$4 x^{2}$[/tex].
Therefore, the correct answer is option B. [tex]$4 x^{2}$[/tex]
To learn more about the greatest common factor
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