Answer: <span><span>2x² + x - 2</span> (the first option)
Explanation:
1) Question: divide 8x⁴+2x³-7x²+3x-2 by 4x² - x + 1
2) First term of the quotient
</span><span> 8x⁴ + 2x³ - 7x² + 3x - 2 | 4x² - x + 1
---------------------
-8x⁴ + 2x³ - 2x² 2x²
----------------------------------
4x³ - 9x² + 3x - 2
3) Second term of the quotient:
</span>
<span> 8x⁴ + 2x³ - 7x² + 3x - 2 | 4x² - x + 1
---------------------
-8x⁴ + 2x³ - 2x² 2x² + x
----------------------------------
4x³ - 9x² + 3x - 2
-4x³ + x² - x
----------------------------
- 8x² + 2x - 2
4) third term of the quotient:
</span>
<span> 8x⁴ + 2x³ - 7x² + 3x - 2 | 4x² - x + 1
---------------------
-8x⁴ + 2x³ - 2x² 2x² + x - 2
----------------------------------
4x³ - 9x² + 3x - 2
-4x³ + x² - x
----------------------------
- 8x² + 2x - 2
8x² - 2x + 2
-------------------------
0
5) Conclusion: since the remainder is 0, the division is exact and the quotient is </span>2x² + x - 2
You can verify the answer by multiplying the quotient obtained by the divisor. The result has to be the dividend.
15x²+16x+4 =0 (ax² +bx +c=0)
Δ = b²-4ac =256 - 4×15×4 =16
x1 = (-b+√Δ) / 2a = (-16+√16) / 30 =( -16+4) / 30 = -12/30 = - 2/5
x2 = (-b -√Δ) / 2a = (-16 -√16) / 30 = (-16 -4) /30 = -20/30 = -2/3
Use a calculator and it would give you 1/20. Best of luck!
Answer:
900
Step-by-step explanation:
We assume that your 4-digit number must be in the range 1000 to 9999. Clearly, any number ending in zero will meet your requirement:
1000/100 = 10
3890/389 = 10
However, the requirement cannot be met when the 1s digit is other than zero.
__
For some 3-digit number N and some 1s digit x, the 4-digit number will be
4-digit number: 10N+x
Dividing this by N will give ...
(10N+x)/N = 10 remainder x
N will only be a factor of 10N+x when x=0.
So, there are 900 4-digit numbers that meet your requirement. They range from 1000 to 9990.
