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The quotient if the polynomial f(x) = 50x2 - 90x - 25 leaves a remainder of -5, when divided by 5x - 10, will be __________
- a)10x + 2
- b)10x - 2
- c)-10x + 2
- d)-10x - 2
Correct answer is option 'A'. Can you explain this answer?
Verified Answer
The quotient if the polynomial f(x) = 50x2- 90x - 25 leaves a remainde...
We know that,
f(x) = q(x) × g(x) + r(x)
Where, f(x) is the dividend, q(x) is the quotient, g(x) is the divisor and r(x) is the remainder.
∴ 50x2 - 90x - 25 = q(x) × 5x - 10 - 5
50x2 - 90x - 25 + 5 = q(x) × 5x - 10
f(x) = q(x) × g(x) + r(x)
Where, f(x) is the dividend, q(x) is the quotient, g(x) is the divisor and r(x) is the remainder.
∴ 50x2 - 90x - 25 = q(x) × 5x - 10 - 5
50x2 - 90x - 25 + 5 = q(x) × 5x - 10
We get, q(x) = 10x + 2
Most Upvoted Answer
The quotient if the polynomial f(x) = 50x2- 90x - 25 leaves a remainde...
To find the quotient when dividing a polynomial by another polynomial, we can use polynomial long division. This process is similar to long division with numbers.
Given polynomial:
f(x) = 50x^2 - 90x - 25
Divisor polynomial:
5x - 10
We want to find the quotient when f(x) is divided by 5x - 10.
Step 1: Set up the long division
Write the dividend (f(x)) and divisor (5x - 10) as shown below:
```
10x
______________________
5x - 10 | 50x^2 - 90x - 25
```
Step 2: Divide the first term
Divide the first term of the dividend (50x^2) by the first term of the divisor (5x), which gives us 10x. Write this as the first term of the quotient above the line:
```
10x
______________________
5x - 10 | 50x^2 - 90x - 25
- (50x^2 - 100x)
_________________
10x
```
Step 3: Multiply the divisor by the quotient term
Multiply the entire divisor (5x - 10) by the quotient term (10x) and write the result below the line. Then subtract this result from the dividend:
```
10x
______________________
5x - 10 | 50x^2 - 90x - 25
- (50x^2 - 100x)
_________________
10x - 25
```
Step 4: Repeat the process
Repeat steps 2 and 3 with the new dividend (10x - 25) until we can no longer divide.
```
10x - 2
______________________
5x - 10 | 50x^2 - 90x - 25
- (50x^2 - 100x)
_________________
10x - 25
- (10x - 20)
______________
- 5
```
Step 5: Write the final quotient
The final quotient is the sum of all the quotient terms:
```
10x - 2
```
Therefore, the quotient when f(x) is divided by 5x - 10 is 10x - 2, which corresponds to option 'A'.
Given polynomial:
f(x) = 50x^2 - 90x - 25
Divisor polynomial:
5x - 10
We want to find the quotient when f(x) is divided by 5x - 10.
Step 1: Set up the long division
Write the dividend (f(x)) and divisor (5x - 10) as shown below:
```
10x
______________________
5x - 10 | 50x^2 - 90x - 25
```
Step 2: Divide the first term
Divide the first term of the dividend (50x^2) by the first term of the divisor (5x), which gives us 10x. Write this as the first term of the quotient above the line:
```
10x
______________________
5x - 10 | 50x^2 - 90x - 25
- (50x^2 - 100x)
_________________
10x
```
Step 3: Multiply the divisor by the quotient term
Multiply the entire divisor (5x - 10) by the quotient term (10x) and write the result below the line. Then subtract this result from the dividend:
```
10x
______________________
5x - 10 | 50x^2 - 90x - 25
- (50x^2 - 100x)
_________________
10x - 25
```
Step 4: Repeat the process
Repeat steps 2 and 3 with the new dividend (10x - 25) until we can no longer divide.
```
10x - 2
______________________
5x - 10 | 50x^2 - 90x - 25
- (50x^2 - 100x)
_________________
10x - 25
- (10x - 20)
______________
- 5
```
Step 5: Write the final quotient
The final quotient is the sum of all the quotient terms:
```
10x - 2
```
Therefore, the quotient when f(x) is divided by 5x - 10 is 10x - 2, which corresponds to option 'A'.
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Community Answer
The quotient if the polynomial f(x) = 50x2- 90x - 25 leaves a remainde...
We know that,
f(x) = q(x) × g(x) + r(x)
Where, f(x) is the dividend, q(x) is the quotient, g(x) is the divisor and r(x) is the remainder.
∴ 50x2 - 90x - 25 = q(x) × 5x - 10 - 5
50x2 - 90x - 25 + 5 = q(x) × 5x - 10
f(x) = q(x) × g(x) + r(x)
Where, f(x) is the dividend, q(x) is the quotient, g(x) is the divisor and r(x) is the remainder.
∴ 50x2 - 90x - 25 = q(x) × 5x - 10 - 5
50x2 - 90x - 25 + 5 = q(x) × 5x - 10
We get, q(x) = 10x + 2
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