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If 3x + 4 is a factor of the expression, what is the value of 'a'?

a) 4/3
b) -4/3
c) 3/4
d) -3/4

User Peti
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1 Answer

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Final answer:

The original question about the value of 'a' cannot be answered due to missing information. The examples and explanation provided illustrate how one would typically find 'a' when a factor of a polynomial is known and the procedure for solving a quadratic equation using the quadratic formula.

Step-by-step explanation:

The question is incomplete as it does not provide the full expression in which 3x + 4 is a factor, nor does it mention how 'a' is related to this expression. Typically, if you know that 3x + 4 is a factor of some polynomial expression, we would set it to zero to find the roots of the expression, implying 3x + 4 = 0. If we were solving for x, we would get x = -4/3. However, without the complete polynomial, we cannot solve for 'a'.

Let's look at a different example to demonstrate how we would find 'a' if we had a complete polynomial. Suppose we had the polynomial P(x) = 3x² + ax + 12 and we knew that 3x + 4 was a factor. We would set the factor equal to zero and solve for x, which yields x = -4/3. We then substitute x back into the polynomial to solve for 'a': P(-4/3) = 3(-4/3)² + a(-4/3) + 12 = 0. Simplifying and solving for a would give us the value we're looking for.

Exercise 2.4.2 asks for answers in scientific notation with appropriate significant figures. For instance, part a, which is 217 ÷ 903, would be calculated and then written in scientific notation considering significant figures.

The expression from another part of the question, 3.59, seems to refer to a quadratic equation of the form at² + bt + c = 0. To solve for the roots, you would use the quadratic formula, which requires the values of a, b, and c. These values must be provided to complete the problem.

User Jim Fell
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