Mathematics, 23.08.2019 05:20 brianna8739

Divide: (10x²-3x+4)÷(2x-5)
this is a review homework for algebra ii the question is about algebra i. i would like an explanation .

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Answer from: jakeSanT5737

$\frac{10x^2-3x+4}{2x-5}=5x+11+\frac{59}{2x-5}$

Quotient: 5x+11

Remainder: 59

Step-by-step explanation:

I'm going to do long division.

The bottom goes on the outside and the top goes in the inside.

Setup:

---------------------------------

2x-5 | 10x^2 -3x +4

Starting the problem from the setup:

5x +11 (I put 5x on top because 5x(2x)=10x^2)

--------------------------------- (We are going to distribute 5x to the divisor)

2x-5 | 10x^2 -3x +4

-(10x^2 -25x) (We are now going to subtract to see what's left.)

-----------------------------------

22x +4 (I know 2x goes into 22x, 11 times.)

( I have put +11 on top as a result.)

-(22x -55) (I distribute 11 to the divisor.)

-----------------------

59 (We are done since the divisor is higher degree.)

The quotient is 5x+11.

The remainder is 59.

The result of the division is equal to:

$5x+11+\frac{59}{2x-5}$ .

We can actually use synthetic division as well since the denominator is linear.

Let's solve 2x-5=0 to find what to put on the outside of the synthetic division setup:

2x-5=0

Add 5 on both:

2x=5

Divide both sides by 2:

x=5/2

Or realize that 2x-5 is the same as 2(x-(5/2)) which you will have to do anyways if you choose this route:

So 5/2 will go on the outside:

5/2 | 10 -3 4

| 25 55

------------------------------

10 22 59

So we have:

$\frac{10x^2-3x+4}{2x-5}$

$=\frac{10x^2-3x+4}{2(x-\frac{5}{2})}=\frac{1}{2} \cdot \frac{10x^2-3x+4}{x-\frac{5}{2}}=\frac{1}{2}(10x+22+\frac{59}{x-\frac{5}{2}})$

Distribute the 1/2 back:

$\frac{10x^2-3x+4}{2x-5}=\frac{10x+22}{2}+\frac{59}{2(x-\frac{5}{2})}$

$\frac{10x^2-3x+4}{2x-5}=5x+11+\frac{59}{2x-5}$

Answer from: Quest

step-by-step explanation:

mean or average is 40.6

Answer from: Quest

answer is 8x+24

area of vanessa's patio = length × width

given, length = (3x² + 5x + 10)

width = (x² - 3x - 1)

area of vanessa's patio = (3x² + 5x + 10)(x² - 3x - 1)

= 3x²(x² - 3x - 1) + 5x(x² - 3x - 1) + 10(x² - 3x - 1)

= 3x⁴ - 9x³ - 3x² + 5x³ - 15x² - 5x + 10x² - 30x - 10

= 3x⁴ - 4x³ - 8x² - 35x - 10

hence, expression of vanessa's patio = (3x⁴ - 4x³ - 8x² - 35x - 10)

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Divide: (10x²-3x+4)÷(2x-5)
this is a review homework for algebra ii the question is about algeb...

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