Download Worksheet 6

Worksheet 5.4 & 5.5
Algebra 2
Factoring: Look for a greatest common
Synthetic Division: Divide using coefficients.
factor and then look at the number of terms of Ex.: Simplify (x3 – 7x – 6) ÷ (x – 2)
the problem for a clue on how to start the
factoring. See the notes on factoring (before
Ch. 5) for more examples.
The numbers at the bottom stand for the coefficients of the answer,
Remainder Theorem: The remainder from
synthetic division is the value of the function
at that point.
Ex: Use synthetic division to find the value
of P(5) if P(x) = 3x4 – 5x2 + x – 9.
The value for x is 5 because of the function
notation. Put 5 outside the box and put the
coefficients of the polynomial inside the box.
Remember to use all descending powers, so
there’s a 0x3.
which is
.
Factor Theorem: If a remainder is zero, the number outside the
box in synthetic division is a zero of the function; therefore, the
related factor is a factor of the polynomial.
Ex: Factor f(x) = 2x3 + 11x2 + 18x + 9, given that f(-3) = 0.
The value for x is -3 because of the f(x) notation. Put -3 outside the
box, and the coefficients of the polynomial inside the box.
The remainder is 0, so x = -3 is a zero of the function. The
remainder of the problem is 2x2 + 5x + 3, which factors as (2x + 3)(x
+ 1). x = -3 becomes the factor (x + 3) when you move the -3 over.
The remainder is 1746, so P(5)=1746.
The factors of 2x3 + 11x2 + 18x + 9 are (2x + 3),(x + 1), and
(x + 3).
Factor.
1. 216x3 + 1
2. 3x2 + 11x + 6
3. x3 – 4x2 + 4x – 16
4. x4 + 3x2 + 2
5. 2x7 – 32x3
6. 4x4 – 5x2 – 9
Solve by factoring. (Find real and/or imaginary answers.)
7. x3 + 2x2 – x = 2
8. x3 + 8 = 0
9. 3x4 + 15x2 – 72 = 0
Divide using synthetic division.
10. ( x3 – 14x + 8) ÷ (x + 4)
11. (x4 – 6x3 – 40x + 33) ÷ (x – 7) 12. (3x2 – 10x) ÷ (x – 6)
Factor the polynomial.
13. f(x) = x3 – 3x2 – 16x – 12, and f(6) = 0.
14. f(x) = x3 – 11x2 + 14x + 80, and f(8) = 0.
15. f(x) = 2x3 + 7x2 – 33x – 18, and f(-6) = 0.
16. f(x) = x3 – x2 – 21x + 45, and f(-5) = 0.
Find the zeros of the function given that one of the zeros is ___.
17. f(x) = 2x3 + 3x2 – 39x – 20, and 4 is a zero.
18. f(x) = x3 + 11x2 – 150x – 1512, & -14 is a zero.
19. f(x) = x3 + x2 +2x + 24, and -3 is a zero.
20. f(x) = 4x3 + 9x2 – 52x + 15, and -5 is a zero.