Use synthetic division to solve (2x^3+4x^2-35x+15) divided by (x-3) what is the quotient?

The quotient of the division operation with 2x³ + 4x² - 35x + 15 being the dividend and x - 3 the divisor is 2x² + 10x - 5

___| 2x² + 10x - 5

___|

x-3 | 2x³ + 4x² - 35x + 15 - - - - - - - step 1

___ 2x³ - 6x²

- 10x²- 35x + 15 - - - - - - - - step 2

10x²- 30x + 15

- - 5x + 15 - - - - - - - - - step 3

-5x + 15

-0

Step 1 : Divide 2x³ by x, we obtain a quotient value of 2x² ; multiply the quotient value by the divisor and Subtract to obtain a dividend of 10x² - 35x + 15

Step 2 : Divide 10x² by x, we obtain a quotient value of 10x ; multiply the quotient value by the divisor and Subtract to obtain a dividend of - 5x + 15

Step 3 : Divide - 5x by x, we obtain a quotient value of - 5 ; multiply the quotient value by the divisor and add to obtain 0.

Therefore, the quotient of the division operation is 2x² + 10x - 5

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Step-by-step explanation:

The only thing you need to watch carefully is the divisor which in this case is   x - 3. The divisor, in synthetic division, is the number that will make the binomial go to 0.  

x - 3 =0

x = 3

So the divisor is 3.

3  ||  2    4    -35    15

             6     30    -15

       2   10    -5      0

So the quotient is

2x^2 + 10x - 5 with no remainder

b. an equilateral triangle inscribed in a circle

step-by-step explanation:

we are given the figure of two circles having a triangle inside.

now, we know that,

"when a figure is lying inside an another figure, then the outside figure is known as circumscribed figure and the figure lying inside is referred to as the inscribed figure".

as we see that, the circles are containing the triangle completely.

thus, the circles are the circumscribed figures and the triangle is the inscribed figure.

hence, we get, 'an equilateral triangle is inscribed in a circle'.

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