A student subtracted two polynomials. They asked a friend to check their solution and work. What should their friend tell them? Are they correct? If they are not correct, in which step did the student make an error?(3x4−8x2+4x)−(9x−5x4+2x2)(3𝑥4−8𝑥2+4𝑥)−(9𝑥−5𝑥4+2𝑥2)Step 1: 3x4−8x2+4x−9x+5x4+2x23𝑥4−8𝑥2+4𝑥−9𝑥+5𝑥4+2𝑥2Step 2: 3x4+5x4−8x2+2x2+4x−9x3𝑥4+5𝑥4−8𝑥2+2𝑥2+4𝑥−9𝑥Step 3: 8x4−6x2−5x8𝑥4−6𝑥2−5𝑥Final Answer: 8x4−6x2−5x

Answer 1

To check the student's work, we need to look at each step of their polynomial subtraction and see if they have performed it correctly.

The original expression to simplify is: \[ (3x^4 - 8x^2 + 4x) - (9x - 5x^4 + 2x^2) \]

Step 1:

The student rewrote the expression as: \[ 3x^4 - 8x^2 + 4x - 9x + 5x^4 + 2x^2 \] This step is correct. They correctly distributed the negative sign across the second polynomial.

Step 2:

Next, the student combined like terms:

• From \(3x^4\) and \(5x^4\): \(3x^4 + 5x^4 = 8x^4\)
• From \(-8x^2\) and \(2x^2\): \(-8x^2 + 2x^2 = -6x^2\)
• From \(4x\) and \(-9x\): \(4x - 9x = -5x\)

So, the expression becomes: \[ 8x^4 - 6x^2 - 5x \] This step is also correct.

Final Answer:

The final simplified expression given by the student is: \[ 8x^4 - 6x^2 - 5x \]

Conclusion:

The student is correct in their work. There were no errors in their steps. The final answer is indeed: \[ 8x^4 - 6x^2 - 5x \]

Their friend should inform them that they did an excellent job with the polynomial subtraction.