How do you subtract 2k³ + k² + 9 from 5k³ + 3k + 7?

To perform the subtraction of the polynomials 2k³ + k² + 9 from 5k³ + 3k + 7, we follow a straightforward process.

First, we write down the two expressions:

• 5k³ + 3k + 7
• – (2k³ + k² + 9)

Next, we distribute the negative sign across the second polynomial:

• 5k³ + 3k + 7 – 2k³ – k² – 9

Now, we combine like terms:

• Combine the k³ terms: 5k³ – 2k³ = 3k³
• No k² term in the first polynomial, so we just take -k².
• Combine the k terms: 3k (there are no k terms in the second polynomial).
• Combine the constant terms: 7 – 9 = -2.

Putting it all together, we get:

3k³ – k² + 3k – 2

So the result of subtracting 2k³ + k² + 9 from 5k³ + 3k + 7 is: 3k³ – k² + 3k – 2.