Download katesmathlessons.com You can use educated to factor a quadratic

katesmathlessons.com
You can use educated ________________________ to factor a quadratic and use
_________ to see if you’ve factored correctly.
You can also use the Quadratic Formula to find the __________ of a quadratic. Roots (also
called zeros) are the values that make the expression equal to ____. If -2 is a root, that
means ___________ is a factor. If -4 is a root, then ___________ is a factor.
Can you use the Quadratic Formula with degree 3 or higher polynomials? _____
Why isn’t guess-and-check a good idea for higher degree polynomials?
_________________________________________________________________
The Rational Roots Theorem says that if a polynomial has a _____________ root, it can be
written in the form p/q, where p is a factor of the _______________ term and q is a factor
of the ______________ ___________________.
This theorem helps you _______________ down options to try.
Step 1: Identify possible rational roots.
The possible rational roots of x3 + 2x2 – 11x – 12 are
factors of factors of This means IF the polynomial has a rational root, it’s going to be 1, -1, 2, -2, 3, -3, 4, -4,
____________________________.
Does the Rational Root Theorem guarantee that one of the above numbers will work? Why
or why not? __________________________________________________
Step 2: Use synthetic division to test possible roots.
If the remainder is ____, that means it’s a root. If the remainder is not zero, move on to
the next possible root.
1 1 2 11 12
1 1 2 11 12
Step 3: Write two factors.
-1 is a root, so ___________ is a factor. Use the coefficients from the quotient to write the
second factor.
x3 + 2x2 – 11x – 12 = (
)(
)
Step 4: Factor the remaining quadratic.
Next, use the Quadratic formula or educated guess-and-check to factor the quadratic.
x2 + x – 12 = (
)(
)
Step 5: Write the final factored answer.
the degree of the polynomial.
x3 + 2x2 – 11x – 12 = (
The number of factors should always __________
)(
)(
)
Factor x3 + 3x2 + 25x + 75
Step 1: Identify possible rational roots. _________________________________________
Step 2: Use synthetic division to test possible roots.
Step 3: Write two factors (use the root that worked and the coefficients of the quotient).
x3 + 3x2 + 25x + 75 = (
)(
)
Step 4: Use the Quadratic Formula or guess-and-check to factor the remaining quadratic.
Step 5: Write the final factored answer: ___________________________________
1. You can use the Quadratic Formula to factor a 3rd degree or higher polynomial. _______
2. The possible rational roots of x3 + 4x2 + 9x + 14 are _______________________________
3. The possible rational roots of x5 - 3x3 + 8x – 10 are _______________________________
4. After you’ve determined possible rational roots, the next step should be to
_______________________________________________________________
5. Which number is a root of the polynomial x3 + 9x2 + 18x – 8
____
6. Synthetic division was used to test a possible root. What can you tell from the
information given?
____________________________________
7. Synthetic division was used to find a root. Which option is best
for the next step?
________________________________________________________
8. Synthetic division was used to find a rational root.
Next, the Quadratic Formula was used. What is the
final factorization of the polynomial?
________________________
9. Factor completely. x3 – 3x2 – 10x + 24
10. Factor completely. x3 + 8x2 – 11x – 18
Want the answer key? Teachers can use their school email to submit a request at
http://www.katesmathlessons.com/contact.html
Please include the name of your school and the specific answer key you are requesting.