Mathematics, 26.09.2019 17:00 Sillydork6872

Factor completely: x^4-14x^2+32

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Quadratic formula:

x⁴ - 14x² + 32

x = - (-14) ± √(-14)² - 4(1)(32) /2(1)

x = 14 ± √196 - 128 / 2

x = 14 ± √68 / 2

x = 14 ± 2√17 / 2

Factor the numerator

x = 2(7 ± √17) / 2

Cancel out the two on both the numerator and denominator.

x = 7 ± √17

The two zeros for this problem are 7 ± √17.

So far, the zeros are irrational. These roots are real, unequal, irrational roots. The zeros are not perfect squares.

If you graph this polynomial function into a graphing calculator, you'll see that the parabola doesn't intersect the x-axis at rational values.

Furthermore, I have tried to factor this polynomial function by doing the AC method and grouping. However, the closest factorization I got was:

(x² - 12)(x² - 2.667) which is not even equivalent to the given function.

Although this function has real zeros, I believe that it is impossible to factor. Therefore, my answer is that this function is not factorable.

Factor completely: x^4-14x^2+32

Answer from: Quest

dunno

step-by-step explanation:

Answer from: Quest

the system of inequity is

$y\leq -x+4$

$3y> x$

step-by-step explanation:

from the given graph it is noticed that we have two related lines. one is solid and another is dashed.

if a line passing through two points, then the equation of line is

$y-y_1=\frac{y_2-y_1}{x_2-x_1}(x-x_1)$

the solid line passing through the points (0,4) and (4,0).

$y-4=\frac{0-4}{4-0}(x-0)$

$y=-x+4$

the related equation of solid line is $y=-x+4$ .

similarly, find the related equation of dashed line. the dashed liune passing through the points (0,0) and (3,1).

$y-0=\frac{0-1}{3-0}(x-0)$

$3y=x$

the related equation of dashed line is $3y=x$

from the given graph it is noticed that the point (0,1) lies on the shaded region, therefore the point (0,1) must be satisfied by the related equations.

check the related equations by the point (0,1).

$1=-0+4$

$1=4$

this statement is true if the sign of inequality is < instead of equality. since it is an solid line therefore the sign of inequality will be $\leq$ . the required inequality is

$y\leq -x+4$

similarly, check the second related equation.

$3(1)=0$

it is a dashed line, so this statement is true if the sign of inequality is > . the required inequality is

$3y> x$

15 points write a system of inequalities to represent the shaded portion of the graph

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