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When a polynomial f(x) = acx3 + bcx + d, is divided by g(x), it leaves quotient as cx, and remainder as d. The value of g(x)will be _____
- a)-ax2 + b
- b)ax2 - b
- c)ax2 + b
- d)x2 + b
Correct answer is option 'C'. Can you explain this answer?
Verified Answer
When a polynomial f(x) = acx3+ bcx + d, is divided by g(x), it leaves ...
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.
acx3 + bcx + d = cx × g(x) + d
acx3 + bcx + d – d = cx × g(x)
g(x) = ax2 + b
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.
acx3 + bcx + d = cx × g(x) + d
acx3 + bcx + d – d = cx × g(x)
g(x) = ax2 + b
Most Upvoted Answer
When a polynomial f(x) = acx3+ bcx + d, is divided by g(x), it leaves ...
To find the value of g(x), we need to perform polynomial division using the given information. Let's break down the steps:
1. Polynomial Division Setup:
We have a polynomial f(x) = acx^3 + bcx + d divided by g(x). The division leaves a quotient as cx and a remainder as d.
2. Polynomial Division Algorithm:
We need to divide f(x) by g(x) using the polynomial division algorithm. The algorithm involves dividing the terms of the dividend (f(x)) by the divisor (g(x)) and finding the quotient and remainder.
3. Dividing the Polynomial:
The first step is to divide the first term of f(x) (acx^3) by the first term of g(x) to obtain the leading term of the quotient. Since the leading term of the quotient is cx, the leading term of g(x) must be cx^2.
4. Multiplying the Divisor:
Next, we multiply the entire divisor g(x) by the leading term of the quotient, which is cx. This gives us cx * (cx^2), which simplifies to cx^3.
5. Subtracting the Result:
We then subtract the result from the original dividend f(x). Since the result is cx^3, we subtract acx^3 from acx^3, which cancels out the leading term in the dividend.
6. Continuing the Division:
We repeat the process by dividing the next term of the remaining dividend (bcx) by the new leading term of the divisor (cx^2). This gives us the next term of the quotient as b.
7. Multiplying the Divisor Again:
We multiply the entire divisor g(x) by the new term of the quotient, which is b. This gives us b * (cx^2), which simplifies to bcx^2.
8. Subtracting Again:
We subtract the result from the remaining dividend. Since the result is bcx^2, we subtract bcx^2 from bcx^2, canceling out the term in the dividend.
9. Final Steps:
After repeating the division process for the remaining term d, we find that the remainder is d. Therefore, the divisor g(x) is a polynomial that leaves a quotient as cx and a remainder as d.
10. Answer:
The correct answer is option 'C': g(x) = ax^2 + bd.
1. Polynomial Division Setup:
We have a polynomial f(x) = acx^3 + bcx + d divided by g(x). The division leaves a quotient as cx and a remainder as d.
2. Polynomial Division Algorithm:
We need to divide f(x) by g(x) using the polynomial division algorithm. The algorithm involves dividing the terms of the dividend (f(x)) by the divisor (g(x)) and finding the quotient and remainder.
3. Dividing the Polynomial:
The first step is to divide the first term of f(x) (acx^3) by the first term of g(x) to obtain the leading term of the quotient. Since the leading term of the quotient is cx, the leading term of g(x) must be cx^2.
4. Multiplying the Divisor:
Next, we multiply the entire divisor g(x) by the leading term of the quotient, which is cx. This gives us cx * (cx^2), which simplifies to cx^3.
5. Subtracting the Result:
We then subtract the result from the original dividend f(x). Since the result is cx^3, we subtract acx^3 from acx^3, which cancels out the leading term in the dividend.
6. Continuing the Division:
We repeat the process by dividing the next term of the remaining dividend (bcx) by the new leading term of the divisor (cx^2). This gives us the next term of the quotient as b.
7. Multiplying the Divisor Again:
We multiply the entire divisor g(x) by the new term of the quotient, which is b. This gives us b * (cx^2), which simplifies to bcx^2.
8. Subtracting Again:
We subtract the result from the remaining dividend. Since the result is bcx^2, we subtract bcx^2 from bcx^2, canceling out the term in the dividend.
9. Final Steps:
After repeating the division process for the remaining term d, we find that the remainder is d. Therefore, the divisor g(x) is a polynomial that leaves a quotient as cx and a remainder as d.
10. Answer:
The correct answer is option 'C': g(x) = ax^2 + bd.
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Community Answer
When a polynomial f(x) = acx3+ bcx + d, is divided by g(x), it leaves ...
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.
acx3 + bcx + d = cx × g(x) + d
acx3 + bcx + d – d = cx × g(x)
g(x) = ax2 + b
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.
acx3 + bcx + d = cx × g(x) + d
acx3 + bcx + d – d = cx × g(x)
g(x) = ax2 + b
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When a polynomial f(x) = acx3+ bcx + d, is divided by g(x), it leaves quotient as cx, and remainder as d. The value of g(x)will be _____a)-ax2+ bb)ax2- bc)ax2+ bd)x2+ bCorrect answer is option 'C'. Can you explain this answer?
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