To find the coefficient of 𝑥4 in the polynomial (𝑥 − 1)3(𝑥 − 2)3, we can expand the polynomial using the binomial theorem.

First, let's expand (𝑥 − 1)3. Using the binomial theorem, we have:

(𝑥 − 1)3 = 𝑥3 - 3𝑥2 + 3𝑥 - 1

Next, let's expand (𝑥 − 2)3. Again, using the binomial theorem, we have:

(𝑥 − 2)3 = 𝑥3 - 3𝑥2 + 3𝑥 - 8

Now, to find the coefficient of 𝑥4, we need to multiply the terms that have 𝑥4 in them. In this case, we have 𝑥3 from (𝑥 − 1)3 and 𝑥 from (𝑥 − 2)3.

Multiplying 𝑥3 and 𝑥, we get 𝑥4.

Therefore, the coefficient of 𝑥4 in the polynomial (𝑥 − 1)3(𝑥 − 2)3 is 1.

Question

To find the coefficient of 𝑥4 in the polynomial (𝑥 − 1)3(𝑥 − 2)3, we can expand the polynomial using the binomial theorem.

First, let's expand (𝑥 − 1)3. Using the binomial theorem, we have:

(𝑥 − 1)3 = 𝑥3 - 3𝑥2 + 3𝑥 - 1

Next, let's expand (𝑥 − 2)3. Again, using the binomial theorem, we have:

(𝑥 − 2)3 = 𝑥3 - 3𝑥2 + 3𝑥 - 8

Now, to find the coefficient of 𝑥4, we need to multiply the terms that have 𝑥4 in them. In this case, we have 𝑥3 from (𝑥 − 1)3 and 𝑥 from (𝑥 − 2)3.

Multiplying 𝑥3 and 𝑥, we get 𝑥4.

Therefore, the coefficient of 𝑥4 in the polynomial (𝑥 − 1)3(𝑥 − 2)3 is 1.

Knowee AI · Accepted Answer