Question

On dividing the polynomial 3x3+4x2+5x-13 by the polynomial g(x) , the quotient and the remainder were (3x+10) and (16x-43) respectively. Find g(x)

Answer 1

let g(x) = y
now
divisor * quotient + remainder  = dividend
y * (3x+10) + 16x-43 = 3x^3 + 4x² + 5x - 13
y * (3x+10) = 3x^3 + 4x² - 11x + 30

now we can calculate the value of y by dividing
3x^3 + 4x² - 11x +30 from  3x+10

so 
y = x² - 2x + 3

Answer 2

Answer:

x² - 2x + 3

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Step-by-step explanation:

Given That,

p(x) = 3x³ + 4x² + 5x - 13

q(x) = 3x + 10

r(x) = 16x - 43

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We know that,

p(x) = g(x) × q(x) + r(x)

p(x) - r(x) = g(x) × q(x)

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$\dashrightarrow \ \sf \dfrac{p(x) - r(x)}{q(x)} = g(x)$

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$\sf \dashrightarrow \ \dfrac{3x^{3} + 4x^{2} + 5x - 13 - (16x - 43)}{3x + 10} = g(x)$

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$\sf \dashrightarrow \ \dfrac{3x^{3} + 4x^{2} + 5x - 13 - 16x + 43}{3x + 10} = g(x)$

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$\sf \dashrightarrow \ \dfrac{3x^{3} + 4x^{2} - 11x + 30}{3x + 10} = g(x)$

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[Division Provided in the attachment]

∴ x² - 2x + 3 is the g(x)

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