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3 years ago

When this polynomial is divided by (x+3) , the remainder is 0. What is the value of the polynomial’s constant term.

Mathematics

2 answers:

saveliy_v [14]3 years ago

5 0

Answer:

- 15

Step-by-step explanation:

Given f(x) divided by (x + h) then the remainder is the value of f(- h)

Here

f(x) = 3x³ - 5x² - 47x + k ← k is the constant term , then

f(- 3) = 3(- 3)³ - 5(- 3)² - 47(- 3) + k = 0 , that is

3(- 27) - 5(9) + 141 + k = 0

- 81 - 45 + 141 + k = 0

15 + k = 0 ( subtract 15 from both sides )

k = - 15

Marat540 [252]3 years ago

5 0

Answer: The missing value is -15 (negative 15)

Step-by-step explanation: Well start off with long division and see how far you get before you run into the constant term you're looking for. The answer entirely is 3x^2 -14x -5 when solved and ensuring there is no remainder that follows after

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Part 1: The equation of the line is $y=2x+1$

Part 2: The equation of the line in slope intercept form is $y=-3x-1$

Explanation:

Part 1: It is given that the point A is $(1,3)$ and the line B is $y=2 x-2$

To determine the line passing through the point A and parallel to line B, let us first determine the slope and y-intercept.

From the equation of line B, the slope is $m=2$

Substituting the point $(1,3)$ and $m=2$ in slope intercept form $y=mx+b$ , we have,

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$3=2+b$

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Thus, the y-intercept is $b=1$

Let us substitute the values $m=2$ and $b=1$ in the slope intercept form $y=mx+b$ , we get,

$y=2x+1$

Thus, the equation of the line passing though point A and parallel to line B is $y=2x+1$

Part 2: The given two coordinates are $(-1,2)$ and $(1,-4)$

To determine the equation of line in slope intercept form, first we shall find the slope and y-intercept.

From the graph, we can see that the line touches the y-axis at -1.

Hence, the y-intercept is $b=-1$

The formula for slope is $m=\frac{y_{2}-y_{1}}{x_{2}-x_{1}}$

Substituting the coordinates $(-1,2)$ and $(1,-4)$ , we have,

$m=\frac{-4-2}{1+1} =\frac{-6}{2} =-3$

Thus, the slope is $m=-3$

Substituting the values $b=-1$ and $m=-3$ in the slope intercept formula $y=mx+b$ , we get,

$y=-3x-1$

Thus, the equation of the line in slope intercept form is $y=-3x-1$

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