Help me please!!!!
Solve. (–18x3 + 17x + 6) ÷ (3x + 2) (1point)
–6x^2 + 4x + 3
6x^2 + 4x – 3
–6x^2 + 4x – 3
6x^2 – 4x + 3
The width, w, of a rectangular garden is x – 2. The area of the garden is x^3 — 2x – 4. What is an expression for the length of the garden? (1 point)
x^2 – 2x – 2
x^2 + 2x – 2
x^2 – 2x + 2
x^2 + 2x + 2
******** -6 x^2 + 4 x + 3
********____________________________
(3x+2) | -18 x^3 + 0 x^2 + 17 x + 6
*********-18 x^3 -12 x^2
*****************12 x^2 + 17 x + 6
*****************12 x^2 + 8 x
*************************9 x + 6
*************************9 x + 6
remainder = 0
================================
(x^3 - 2 x - 4) /(x-2)
do it long division as above
******________________________
(x-2) | x^3 + 0 x^2 - 2 x - 4
get x^2 + 2 x + 2
so #1 is A and #2 is D?
LOL - Yes, I suppose.
Thank you soo much what grade are you in
Ah, math problems! Let's give it a go!
For the first problem, let's perform the division. I like to call it the "divide and conquer" method! So, (-18x^3 + 17x + 6) ÷ (3x + 2) gives us -6x^2 + 4x - 3. Ta-da!
Now, onto the second problem. We're trying to find the expression for the length of a rectangular garden. We know that the width is x - 2 and the area is x^3 - 2x - 4. To find the length, we can divide the area by the width. So, the expression for the length is x^2 - 2x + 2.
Hope that helps! Let me know if you need anything else, and I'll be here clowning around!
To solve the first problem, you need to perform polynomial division. Here's how you can approach it:
Step 1: Divide the first term of the dividend by the first term of the divisor.
-18x^3 ÷ 3x equals -6x^2.
Step 2: Multiply the divisor (3x + 2) by the result from step 1 (-6x^2) and subtract it from the dividend (-18x^3 + 17x + 6).
(-6x^2)(3x + 2) equals -18x^3 - 12x^2.
Subtracting this from the dividend gives:
(-18x^3 + 17x + 6) - (-18x^3 - 12x^2) equals 17x + 12x^2 + 6.
Step 3: Repeat steps 1 and 2 with the new dividend (17x + 12x^2 + 6).
Dividing 17x by 3x gives 17/3, which is not divisible evenly.
Thus, the resulting expression is (–6x^2 + 4x + 3). So the answer is option A.
For the second problem:
Given that the width of the rectangular garden is x - 2 and the area is x^3 - 2x - 4, we can determine the length by dividing the area by the width.
So, the expression for the length of the garden is:
(x^3 - 2x - 4) ÷ (x - 2).
You can now perform polynomial division to simplify the expression and determine the length of the garden.