Question

Worth 30 points please give the whole answers.

1. (2r + 9)(2r-9) + (2r - 9)^2 ???

2. 12 - 5 [ ( a^3 + a^2 - a ) / a] + 5a

3. x^4 + 7 is divided by x - 3. Long division

Answer 1

1)
Remember:
(a+b)(a-b)=a²-b²²
(a+b)²=a²+2ab+b²

(2r+9)(2r-9)+(2r-9)²=4r²-81+4r²-36r+81=8r²-36r

Answer: (2r+9)(2r-9)=8r²-36r

2)
12-[(a³+a²-a)/a]+5a=12-(a²+a-1)+5a=12-a²-a+1+5a=-a²+4a+13

Answer: 12-[(a³+a²-a)/a]+5a=-a²+4a+13

3)
(x⁴+7) / (x-3)

x³+3x²+9x+27
x-3 x⁴+0x³+0x²+0x+7
-x⁴+3x³
--------------------------
3x³+0x²+0x+7
-3x³+9x²
---------------------------
9x²+0x+7
-9x²+27x
-----------------------------
27x+7
-27x+81
------------------------------
88

Quotient: Q(x)= x³+3x²+9x+27
Remainder R(x)=88

Therefore:(x⁴+7) / (x-3)= x³+3x²+9x+27 + 88/(x-3)

Answer 2

1. (2r + 9)(2r-9) = 4r^2 -81
+ (2r - 9)^2 = 4r^2 - 36r + 81
= 8r^2 - 36r

2. 12 - 5 [ a^2 + a - 1 ] + 5a
= 12 - 5a^2 - 5a + 5 +5a
= 17 - 5a^2

x^3 + 3x^2 + 6x + 18
______
3. x-3/ x^4 + 7
- ( x^4 - 3x^3)
----------------
3x^3 + 7
- (3x^3 - 6x^2)
-------------------
6x^2 + 7
- (6x^2 - 18x)
-------------------
18x + 7
- (18x - 54)
--------------
7 + 54 = R = 61

welp That's What I get