Answer:
1. (x+6)(2x - 3)(x - 1)²
2.(x-2)²(-2x - 1)²(-x + 1)
3. (-x + 1)³(x + 2)²(x - 3)
4. (-2x + 1)²(x - 3)²(x + 1)
Step-by-step explanation:
1. Degree 4, leading coefficient positive
(x+6)(2x - 3)(x - 1)²
That's the only equation with a degree of 4 (meaning x^4).
If you square the last parenthesis, you'll get an x^2, multiplied by the 2nd parenthesis you'll get an x^3 and multiply with the first parenthesis you'll get an x^4.
2. Degree is 5, leading coefficient is negative
(x-2)²(-2x - 1)²(-x + 1)
If you do the square of each of the first two parenthesis, you'll get something like (x²...)(4x²...)(-x + 1)
Multiply the first two parenthesis, to get (4x^4....)(-x + 1)
So, at the end you'll get -4x^5....
3. Degree 6, leading coefficient negative
(-x + 1)³(x + 2)²(x - 3)
That's the only equation of degree 6 given... so the choice is easy. Let's verify it's degree 6 and with negative leading coefficient.
Cube the first term and square the second one, you'll get something like...
(-x³...)(x²....)(x - 3)
If you combine all that you'll get something like -x^6....
4. Degree is 5, leading coefficient is positive
(-2x + 1)²(x - 3)²(x + 1)
If you do the square of each of the first two parenthesis, you'll get something like (4x²...)(x²...)(x + 1)
Multiply the first two parenthesis, to get (4x^4....)(x + 1)
So, at the end you'll get 4x^5....
