Sorry, let me try that long division again?

Question

(-8x^4+10x^3-4x^2+9) divided by (4x+3)
Q(x)=quotient R(x)= remainder
Where the answer is in the form of Q(x)+R(x)/4x+3

Answer 1

WoW hi Dear Schnitzel ; we met again ;

First rewrite it like that;
-8x^4 +10x^3 - 4x^2 + 9 ÷ 4x+3

▪ Step1
( 4x+3 ) ( -2x^3 ) = -8x^4 - 6x^3 ; { let R1 = -2x^3 }
-8x^4 +10x^3 - 4x^2 + 9 - ( -8x^4 - 6x^3 ) =
-8x^4 +10x^3 - 4x^2 + 9 + 8x^4 + 6x^3= +16x^3 - 4x^2 + 9{remainder}

▪ Step 2
-16x^3 - 4x^2 + 9 ÷ 4x+3
(4x+3) (4x^2) = 16x^3 + 12 x^2 ; { let R2 = + 4x^2 }
+16x^3 - 4x^2 + 9 - ( 16x^3 + 12 x^2 ) =
+16x^3 - 4x^2 + 9 - 16x^3 - 12 x^2 = -16x^2 + 9 {remainder}

▪ Step 3
-16x^2 + 9 ÷ 4x+3
(4x+3) (-4x) = -16x^2 - 12x ; { let R3 = - 4x }
-16x^2 + 9 - ( -16x^2 - 12x ) =
-16x^2 + 9 +16x^2 + 12x =12x + 9 {remainder}

▪ Step 4
12x + 9 ÷ 4x+3
(4x+3) ( +3) = 12x + 9 ; { let R4 = +3 }
12x + 9 - ( 12x + 9) =
12x + 9 - 12x - 9 = 0 {remainder}

▪ Step 5
Sum R1 , R2 , R3 , R4
R1 + R2 + R3 +R4
-2x^3 + 4x^2 - 4x + 3
(-8x^4 + 10x^3 - 4x^2 + 9) ÷ (4x+3) = R1 + R2 + R3 +R4

So;
(-8x^4 + 10x^3 - 4x^2 + 9) ÷ (4x+3) = -2x^3 + 4x^2 - 4x + 3

Q(x) OR quotient = -2x^3 + 4x^2 - 4x + 3
R(x) OR Remainder is Zero

Good Luck dear.

Answer 2

4x+3)-8x^4+10x^3-4x^2+0x+9 (-2x^3+4x^2-4x+3=Q
-8x^4-6x^3
16x^3-4x^2
16x^3+12x^2
-16x^2+0x
-16x^2-12x
12x+9
12x+9
R=0
-2x^3+4x^2-4x+3=Q and R=0/(4x+3)

Answer 3

............- 2x^3 + 4x^2 - 4x + 3
...........-------------------------------------
4x + 3 ) -8x^4 +10x^3 - 4x^2 + 0x + 9
............-8x^4 -...6x^3
............------------------------
....................+ 16x^3 -.. 4x^2
....................+ 16x^3 + 12x^2
.......................-----------------------
................................- 16x^2 +..0x
................................- 16x^2 - 12x
................................-----------------------
..............................................12x + 9
..............................................12x + 9

I get no remainder - how about you?

Yahoo should really do something so math posters can control the horizontal formatting! The above looks OK until I post it.

Answer 4

.........-2x³....+ 4x² - 4x + 3
4x+3|-8x⁴+10x³ - 4x² ........ + 9
.........-8x⁴...-6x³
.........---------------
....................16x³ - 4x²
....................16x³ +12x²
................. ...--------------
................. ...........-16x²
................. ...........-16x² - 12x
................. ..........----------------
................. ............. ..........12x + 9
................. ............. ..........12x + 9
................. ............. ..........----------
................. ............. ....................0

Thus, (-8x⁴+10x³ - 4x²+ 9)/(4x+3) = -2x³ + 4x² - 4x + 3 with no remainder.