Remainder and factor theorem. Project in Math.

1. REMAINDER
THEOREM

2. REMAINDER THEOREM
Overview:
 As the Remainder Theorem points
out, if you divide a polynomial
p(x) by a factor x – a of that
polynomial, then you will get a zero
remainder.

3. REMAINDER THEOREM
 p(x) = (x – a)q(x) + r(x)
If x – a is indeed a factor of p(x), then
the remainder after division by x –
a will be zero. That is:
p(x) = (x – a)q(x)
Overview:

4. REMAINDER THEOREM
Overview:
 In terms of the Remainder Theorem, this
means that, if x – a is a factor of p(x),
then the remainder, when we
do synthetic division by
x = a, will be zero.

5. FACTOR
THEOREM

6. FACTOR THEOREM
Overview:
 The point of the Factor Theorem is the
reverse of the Remainder Theorem: If you
synthetic-divide a polynomial
by x = a and get a zero remainder, then,
not only is x = a a zero of the polynomial,
but x – a is also a factor of the
polynomial.

7. FACTOR THEOREM
Overview:
 Just as with the Remainder Theorem, the
point here is not to do the long division of
a given polynomial by a given factor. This
Theorem isn't repeating what you already
know, but is instead trying to make your
life simpler.

8. REMINDER

9. Reminders:
F(x)= D(x) ● Q(x) + R
Dividend Divisor Quotient Remainder
DIVISION ALORITHIM

10. EXAMPLE:

11. 1. 5x2 – 2x +1 ÷ x +2
-2 5 -2 1
-10 24
5 -12 25
USING SYNTHETIC DIVISION:
ANSWER:5x – 12 + 25
X + 2

12. TRY IT YOURSELF:
1. x2 – 2x +1 ÷ x +2
2. x4 – 16𝑥3
+ 18𝑥2
-128 ÷ x +2
3. 𝑥3- 𝑥2-8x- 4 ÷ 3x+2

13. PREPARED BY:
HANNAH MARIE
ESPAÑOLA
MAYLENE DADIVAS
BRENT VALELO
RICK LASTRADO
YENIZA CLARE
SANTIAGO
10-NEWTON
THANK
YOU!!!!!!!