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2 years ago

Find the remainder when f(x)=2x3-5x2+8x+4 is divided by 2x-1 and use it to determine if 2x-1 is a factor

Mathematics

1 answer:

ollegr [7]2 years ago

5 0

The remainder of f(x) = 7

Step-by-step explanation:

f(x) = $2x^{3} - 5x^{2} +8x + 4$

Here 2x - 1 is a factor.

We will apply Factor theorem ( states that if (x-a) is a factor of f(x) then f(a) is the remainder)

Putting x = 1/2 in f(x) we will get the remainder.

f(1/2) = 2(1/2)^3 -5(1/2)^2 +8(1/2) +4

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1 year ago

What is the equation of this line in standard form? 8x−7y=−25 8x−9y=23 8x−9y=−23 9x−8y=23 Number graph ranging from negative fiv

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Answer:

The equation of line is:

$8x-9y=-23$

Step-by-step explanation:

We are given that a graph is a that passes through two points:

$(-4,-1)$ and $(\dfrac{1}{2},3)$

We know that the equation of line passing through two points:

$(a,b)$ and $(c,d)$ is given by:

$y-b=\dfrac{d-b}{b-a}\times (x-a)$

Here we have:

$(a,b)=(-4,-1)$ and $(c,d)=(\dfrac{1}{2},3)$

Hence, the equation of line is:

$y-(-1)=\dfrac{3-(-1)}{\dfrac{1}{2}-(-4)}\times (x-(-4))\\\\y+1=\dfrac{3+1}{\dfrac{1}{2}+4}\times (x+4)\\\\y+1=\dfrac{4}{\dfrac{9}{2}}\times (x+4)\\\\y+1=\dfrac{4\times 2}{9}\times (x+4)\\\\y+1=\dfrac{8}{9}\times (x+4)\\\\9\times (y+1)=8\times (x+4)\\\\9y+9=8x+8\times 4\\\\9y+9=8x+32\\\\8x-9y=9-32\\\\8x-9y=-23$

Hence the equation of line is:

$8x-9y=-23$

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2 years ago