(-6v^2 - 4 + 9v +v^3)/ (v - 4)i am just a little lost can someone explain this to me. thanks.
Arrange the polonomial in descending order...
v^3-6v^2 +9v -4
Then divide.
v-4 !v^3-6v^2 +9v -4
The first term is v^2, so v^2*(v-4) is
v^3-4v^2
subtracting that from the polonomial gives
v-4 ! -2v^2+9v-4
so dividing one gets -2v, then multiplying by v-4 gives
-2v(v-4)=-2v^2+8v, and subtracting that frm -2v^2+9v-4 gives
v-4 ! v-4, and dividing gives 1.
so the answer is v^2 -2v +1
check my thinking.
Your thinking is correct! Let me explain the steps in detail:
1. Arrange the polynomial in descending order:
(-6v^2 - 4 + 9v + v^3) becomes v^3 - 6v^2 + 9v - 4.
2. Divide the polynomial by (v - 4):
Place the dividend (v^3 - 6v^2 + 9v - 4) and divisor (v - 4) in long division format.
3. Divide the first term:
Divide v^3 by v, which gives v^2. Write this answer on top.
4. Multiply the divisor by the quotient found in step 3:
Multiply (v - 4) by v^2, which gives v^3 - 4v^2. Write this below the dividend.
5. Subtract the product obtained in step 4 from the dividend:
Subtract (v^3 - 4v^2) from (v^3 - 6v^2 + 9v - 4). This gives -2v^2 + 9v - 4.
6. Repeat the division process with the new polynomial obtained in step 5:
Bring down the next term (-2v^2) and repeat steps 3-5.
7. Divide the next term:
Divide -2v^2 by v, which gives -2v. Write this on top.
8. Multiply the divisor by the quotient found in step 7:
Multiply (v - 4) by -2v, which gives -2v^2 + 8v. Write this below the polynomial obtained in step 5.
9. Subtract the product obtained in step 8 from the polynomial:
Subtract (-2v^2 + 8v) from (-2v^2 + 9v - 4). This gives v - 4.
10. Repeat the division process with the new polynomial obtained in step 9:
Bring down the next term (v) and repeat steps 3-5.
11. Divide the next term:
Divide v by v, which gives 1. Write this on top.
12. Multiply the divisor by the quotient found in step 11:
Multiply (v - 4) by 1, which gives v - 4. Write this below the polynomial obtained in step 9.
13. Subtract the product obtained in step 12 from the polynomial:
Subtract (v - 4) from (v - 4). This gives 0.
14. At this point, we have reached a remainder of 0, which means we have successfully divided the polynomial. The quotient we obtained during the division process is v^2 - 2v + 1.
So, the answer is v^2 - 2v + 1.
Great job on checking your work! It's always important to review your thinking and make sure you've followed the steps correctly.