Question

7x³ - 21x² + 5x - 15

7x²(x - 3) + 5(x -3)
Which is the completely factored form of her polynomial?

Answer 1

To find the completely factored form of the polynomial 7x³ - 21x² + 5x - 157x²(x - 3) + 5(x -3), we need to simplify it by distributing and combining like terms.

Step-by-step explanation:

The student's question is about finding the completely factored form of the given polynomial: 7x³ - 21x² + 5x - 157x²(x - 3) + 5(x -3). To factor this polynomial, we need to first simplify it by distributing and combining like terms. Let's first distribute the -157x² across (x - 3):

-157x²(x) + (-157x²)(-3) = -157x³ + 471x²

Now, distribute 5 across (x - 3):

5(x) + 5(-3) = 5x - 15

Now, combine all like terms:

7x³ - 157x³ - 21x² + 471x² + 5x + 5x - 15

-150x³ + 450x² + 10x - 15

Then, we can factor out the greatest common factor:

-5(30x³ - 90x² - 2x + 3)

However, without the polynomial being completely expanded, we cannot fully factor it, and additional context or information might be required to further factor the expression.