Question

When the function f(x) is divided by x + 5, the quotient is 2x² + 7x – 6, and the remainder is – 7. Find the function f(x) and write the result in standard form.

a) f(x) = 2x³ + 7x² - 6x - 7
b) f(x) = 2x³ + 7x² - 6x + 7
c) f(x) = 2x³ + 7x² - 6x - 5
d) f(x) = 2x³ + 7x² - 6x - 4

Answer 1

To find the function f(x), one multiplies the quotient by the divisor and then adds the remainder. After doing so and combining like terms, we find that f(x) does not match any of the provided options, suggesting there may be a typo in the question.

Step-by-step explanation:

Given that the function f(x) when divided by x + 5 provides a quotient of 2x2 + 7x - 6 and a remainder of -7, we can write f(x) in the form:

f(x) = (2x2 + 7x - 6)(x + 5) - 7

In order to find f(x), we simply need to distribute (or multiply out) the terms in the brackets and then subtract 7:

• First step: Multiply 2x2 by (x + 5)
• Second Step: Multiply 7x by (x + 5)
• Third Step: Multiply -6 by (x + 5)
• Fourth Step: Combine all the products and subtract 7

So, f(x) = (2x3 + 10x2 + 7x2 + 35x - 6x - 30) - 7

Combining like terms, we get:

f(x) = 2x3 + 17x2 + 29x - 37

Therefore, f(x) is none of the options given. There might be a typo in the question options.