Factor or Nah Bruh
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The factor theorem says that if a polynomial is divided by x-c and the remainder is ______, then x-c is a factor.
What is 0
When would you factor by GROUPING?
When you have 4 terms
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The Fundamental Theorem of Algebra says that a polynomial of degree n has exactly ___________________.
n roots
Where are the zeros of a function if you are looking at the graph?
the x-intercepts
Write the polynomial in standard form given the zeros. Remember to find any missing zeros first!
0, -3, 2
f(x)=x3 + 5x2 +6x
Is (x-2) a factor of the polynomial f(x)=x4-2x3-8x+16?
Yes
Same, Opposite, Always Positive
Sum/Difference of Perfect Cubes
How many roots/zeros does the polynomial function have.
f(x)=4x7+3x15-1
15
What are some other words for "zeros" of a function? (give at least 2)
Roots, solutions, x-intercepts, what x=
Write the polynomial in standard form given the zeros. Remember to find any missing zeros first!
1, 2, 3
f(x)=x3 - 6x2 + 11x - 6
Is (x+3) a factor of f(x)=x4-4x3+2x2+4x-3. EXPLAIN WHY OR WHY NOT
No, the remainder is not 0.
Factor 32x3 - 4x2 - 8x + 1
(8x-1)(2x+1)(2x-1)
If x=5+4i is a root, what else is a root?
5-4i
Given the polynomial in factored form, find the zeros:
f(x)=x(3x+4)(x+2)
x=0, x=-4/3, x=-2
Write the polynomial in standard form given the zeros. Remember to find any missing zeros first!
-5, 2i
f(x)=x3 + 5x2 +4x +20
Is (x+3) a factor of x4 + x3 - 9x2 - 3x + 18?
Yes
Factor 125x3 - 216
(5x-6)(25x2+30x+36)
How many roots does the polynomial have?
f(x)=-2x2 + 4x12 -2x6
12
f(x)=(x+2)(3x+5)(x+4)(3x-1)
x=2, x=-5/3, x=-4, x=1/3
Write the polynomial in standard form given the zeros. Remember to find any missing zeros first!
-2i, 3i
f(x)=x4 + 13x2 + 36
Is (x-4) a factor of x4 + 5x3 - 27x - 135 ?
yes.
Factor 81x5 + 24x2
Given the degree and some of the roots, find any remaining roots of the polynomial:
Degree: 5
Roots: 3, 2-7i, -5+3i
2+7i and -5-3i
Use your calculator to find the zeros (aka SOLVE) the polynomial
f(x)=x3 - 4x2 +3x
x=0, x=1, x=3
Write the polynomial in standard form given the zeros. Remember to find any missing zeros first!
x=2, x=0, x=5i
f(x)=x4 - 2x3 + 25x2 - 50x