Find the product of the polynomials (9x2−6x+1)(3x−1) .(1 point) Responses 27x3−27x4+9x−1 27 x cubed minus 27 x to the 4th power plus 9 x minus 1 - no response given 27x3−27x2+9x−1 27 x cubed minus 27 x squared plus 9 x minus 1 - no response given 27x3−9x2+27x−1 27 x cubed minus 9 x squared plus 27 x minus 1 - no response given 27x3+27x2+9x+1

Answer 1

To find the product of the polynomials \((9x^2 - 6x + 1)(3x - 1)\), we can use the distributive property (also known as the FOIL method for binomials).

Let's multiply each term in the first polynomial by each term in the second polynomial:

1. Multiply \(9x^2\) by \(3x\): \[ 9x^2 \cdot 3x = 27x^3 \]

2. Multiply \(9x^2\) by \(-1\): \[ 9x^2 \cdot -1 = -9x^2 \]

3. Multiply \(-6x\) by \(3x\): \[ -6x \cdot 3x = -18x^2 \]

4. Multiply \(-6x\) by \(-1\): \[ -6x \cdot -1 = 6x \]

5. Multiply \(1\) by \(3x\): \[ 1 \cdot 3x = 3x \]

6. Multiply \(1\) by \(-1\): \[ 1 \cdot -1 = -1 \]

Now, combine all these results: \[ 27x^3 + (-9x^2 - 18x^2) + (6x + 3x) - 1 \] This simplifies to: \[ 27x^3 + (-27x^2) + 9x - 1 \]

So the combined polynomial is: \[ 27x^3 - 27x^2 + 9x - 1 \]

Looking at the response options, the correct answer is: 27x³ - 27x² + 9x - 1