Question

Given f(x) = x²+5x−14 and g(x) = x−2, find the product of f(x) and g(x)and express the result in standard form.

A) x³ − 2x² − 19x + 28
B) x³ + 3x² − 24x − 28
C) x³ + 3x² − 19x − 28
D) x³ − 2x² − 24x + 28

Answer 1

The correct answer is option A, x³ − 2x² − 19x + 28, which is obtained by multiplying f(x) = x²+5x−14 and g(x) = x−2 and combining like terms accordingly.

Step-by-step explanation:

The correct answer is option A which is x³ − 2x² − 19x + 28. To find the product of f(x) = x²+5x−14 and g(x) = x−2, you need to apply the distributive property, also known as FOIL (First, Outside, Inside, Last) when dealing with binomials. Here is the step-by-step calculation:

• First, multiply the first terms: x² * x = x³.
• Outside terms: x² * (−2) = −2x².
• Inside terms: 5x * x = 5x².
• Last terms: 5x * (−2) = −10x.
• Multiply the constant term of f(x) by both terms in g(x): (−14) * x = −14x and (−14) * (−2) = +28.

Now, combine like terms:

• x³ from the first step.
• −2x² + 5x² = 3x².
• −10x −14x = −24x.
• The constant +28 from the last step.

Combining all these, we get x³ + 3x² −24x +28. However, we need to subtract the (2x²) from the (3x²) to correct our answer:

• 3x² − 2x² = x².

Therefore, the correct standard form is x³ − 2x² − 19x + 28.