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Chapter 9: Problem 133

What polynomial has quotient \(3 x-4\) when divided by \(4 x+5 ?\)

Short Answer

Expert verified
The polynomial that has a quotient of \(3x-4\) when divided by \(4x+5\) is \(12x^2 - x - 20\).

Step by step solution

01

Understand the Relationship

Let's assume that the polynomial we're trying to find is called 'P'. We know that when we divide P by \(4x+5\), we get a quotient of \(3x-4\) and since the remainder isn't mentioned, we can safely assume that there's no remainder.
02

Formulate the Equation

According to the Polynomial Division Algorithm, the formula should be 'Divident = Divisor * Quotient + Remainder'. Substituting the given terms, we get 'P = (4x+5) * (3x-4)'.
03

Simplify the Equation

Expand the equation to get the polynomial P. 'P = 12x^2 - 16x + 15x - 20'.
04

Further Simplification

Combine like terms using simple arithmetic to get: 'P = 12x^2 - x - 20'

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