Question

factor the expression completely. use the graph to determine the roots for synthetic division. all factors use only integer coefficients and constants.
factor common factor
90x⁴ + 384x³ + 432x² - 96
determine the greatest common factor and then rewrite the expression.
90x⁴ + 384x³ + 432x² - 96
common factor:
enter the result.

Explanation:

Step1: Find GCF of coefficients

Find GCF of 90, 384, 432, 96:
Prime factors:
$90=2\times3^2\times5$, $384=2^7\times3$, $432=2^4\times3^3$, $96=2^5\times3$
GCF = $2\times3=6$
No common variable factor (last term has no $x$).

Step2: Factor out GCF from expression

Divide each term by 6:
$90x^4\div6=15x^4$, $384x^3\div6=64x^3$, $432x^2\div6=72x^2$, $-96\div6=-16$

Answer:

Common Factor: $6$
Result: $6(15x^4 + 64x^3 + 72x^2 - 16)$