does the equation 2x+6=(X+10)-(4-x) have any solution ?? . with step by step explaination how did you get your answer
Answers
19. Let f(x) = 4x3 + 7x2 – 13x – 3 and g(x) = x + 3. Find f(x)/g(x)
Solution:
f(x) = 4x3 + 7x2 – 13x – 3
g(x) = x + 3
f(x)/g(x) = (4x3 + 7x2 – 13x – 3)/(x + 3)
We solved the division in both the ways;
(4x3 + 7x2 – 13x – 3) ÷ (x + 3) by using synthetic division

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Answer:
Quotient = 4x2 – 5x + 2
Remainder = -9
OR
(4x3 + 7x2 – 13x – 3) ÷ (x + 3) by using long division

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Answer:
Quotient = 4x2 – 5x + 2
Remainder = -9
20. Let f(x) = 3x3 - 4x – 1 and g(x) = x + 1. Find f(x)/g(x)
Solution:
f(x) = 3x3 - 4x – 1
g(x) = x + 1
f(x)/g(x) = (3x3 - 4x – 1)/(x + 1)
We first need to rearrange all the terms of the dividend according to descending powers of x. The dividend then becomes 3x3 - 4x – 1, with 3 understood as the coefficient of the first term. No x2 term is there in the polynomial, but we take a zero as a place holder in the x2 position, so the dividend is written as 3x3 + 0x2 - 4x – 1.
We solved the division in both the ways;
(3x3 + 0x2 - 4x – 1) ÷ (x + 1) by using synthetic divisiON
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Quotient: 3x2 – 3x – 1
Remainder: 0
3x3 + 0x2 - 4x – 1.
(3x3 + 0x2 - 4x – 1) ÷ (x + 1) by using long division
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Quotient: 3x2 – 3x – 1
Remainder: 0
Answer: 3x2 – 3x – 1
21. Let f(x) = x4 – 8x3 + 16x2 – 19 and g(x) = x - 5. Find f(x)/g(x)
Solution:
f(x) = x4 – 8x3 + 16x2 – 19
g(x) = x – 5
f(x)/g(x) = (x4 – 8x3 + 16x2 – 19)/(x - 5)
We first need to rearrange all the terms of the dividend according to descending powers of x. The dividend then becomes x4 – 8x3 + 16x2 – 19, with 1 understood as the coefficient of the first term. No x term is there in the polynomial, but we take a zero as a place holder in the x position, so the dividend is written as x4 – 8x3 + 16x2 + 0x – 19.
We solved the division in both the ways;
(x4 – 8x3 + 16x2 + 0x – 19) ÷ (x - 5) by using synthetic division
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Quotient = x3 - 3x2 + x + 5
Remainder = 6
x4 – 8x3 + 16x2 + 0x – 19.
(x4 – 8x3 + 16x2 + 0x – 19) ÷ (x - 5) by using long division
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Quotient = x3 - 3x2 + x + 5
Remainder = 6
Answer:
Quotient = x3 - 3x2 + x + 5
Remainder = 6
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Answer:
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