Given 5x3+8x2−7x−6. 1) the binomial (x+2) is a factor of the polynomial expression. describe how you know it is a factor. 2) the binomial (x+1) is not a factor of the polynomial expression. explain how you know it is not a factor.

ANSWER TO QUESTION 1

Given

We can use the factor theorem to determine if

is a factor of the polynomial or not.

According to this theorem, if is a factor of , then .

How did we get the ?

We set and then solve to obtain .

So now let us plug in in to the function to see if it will simplify to zero.

Since the result simplifies to zero, we conclude that

is a factor of

ANSWER TO QUESTION 2

We have the function,

We can use the remainder theorem to show that

is NOT a factor of the polynomial.

According to this theorem, if is not a factor of , then .

So now let us plug in in to the function to see if it will simplify to non-zero number.

Since the result simplifies to a non zero number, we conclude that

is NOT a factor of

5x + 3y = - 4

step-by-step explanation:

the equation of a line in standard form is

ax + by = c ( a is a positive integer and b, c are integers )

express the line first of all in slope- intercept form

y = mx + c ( m is the slope and c the y-intercept )

to calculate m use the gradient formula

m = ( y₂ - y₁ ) / ( x₂ - x₁ )

with (x₁, y₁ ) = (7, - 3) and (x₂, y₂ ) = (4, - 8)

m = = -

y = - x + c ← is the partial equation

to find c substitute either of the 2 points into the partial equation

using (4, - 8 ), then

- 8 = - + c ⇒ c = -

y = - x - ← in slope-intercept form

multiply all terms by 3 to eliminate the fractions

3y = - 5x - 4 ( add 5x to both sides )

5x + 3y = - 4 ← in standard form