Mathematics, 06.10.2019 20:20 germaniranda619

I'm a bit flustered. can someone me ?
polynomial division and the remainder theorem

create a quadratic polynomial function f(x) and a linear binomial in the form (x − a).

part 1. show all work using long division to divide your polynomial by the binomial.

part 2. show all work to evaluate f(a) using the function you created.

part 3. use complete sentences to explain how the remainder theorem is used to determine whether your linear binomial is a factor of your polynomial function.

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You are told to divide a polynomial by a monomial, right? A monomial would be something like x + 3, and your polynomial could be something like x^2 + 7x + 12. The remainder theorem tells you that if you use long division to divide the polynomial by the monomial, if you have a remainder, the monomial is NOT a factor of the polynomial. You put the polynomial under the division sign and the monomial outside the division sign and do the dividing, just like you would if you had 80 under the division sign and 10 outside. When you divide the 80 by the 10, it comes out evenly with no remainder. Same thing with this: if you can divide x^2 + 7x + 12 by x + 3 and there is no remainder, then x + 3 is a factor of the polynomial. What's up on top above the division sign is the other factor. So when you multiply the x + 3 by what's on top, you get back your polyomial. It's really a very perfect and cool thing.

Answer from: Quest

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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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I'm a bit flustered. can someone me ?
polynomial division and the remainder theorem

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