Question

Write the function in factored form. Check by multiplication.

y = - 4x³ - 16x² +84x
y= (Factor completely.)

Answer 1

Explanation:

We can factor out a common factor of -4x from the equation:

y = -4x(x² + 4x - 21)

To factor the quadratic expression in the parentheses, we need to find two numbers that multiply to -21 and add to 4. These numbers are 7 and -3:

y = -4x(x + 7)(x - 3)

To check our work, we can multiply the three factors:

y = -4x(x + 7)(x - 3) = -4x(x² + 4x - 21) = -4x³ - 16x² + 84x

So the factored form is y = -4x(x + 7)(x - 3), and the check shows that we have factored the equation correctly.