Name: ________________________________________Grade & Section: _________________
Subject: MATH 10 Teacher: DENNIS V. SABORNIDO
Score: ______________
Lesson
Activity Title
Learning Target
Reference(s)
LAS Writer
: Quarter 1 Week 7 LAS 1
: Factoring
: Factors Polynomials
: SLM Mathematics 10
: Dennis V. Sabornido, TII
The Remainder Theorem. It is another method in finding the remainder. Simply change the sign of
“r” in (x – r) and substitute into the given polynomial P(x). To check the remainder, use the
synthetic division.
Example 1. Find the remainder when P(x) = (x3 − 2x2 − 5x − 8) divided by (x – 2)
Solution: Therefore, the remainder when P(x) = (x3 − 2x2 − 5x − 8 is divided by x – 2
is -18.
Example 2. Find the remainder when P(x) = P(x) = 2x2 − 4x + 6 is divided by (x + 1).
Therefore, the remainder when P(x) = 2x2 − 4x + 6 is divided by (x + 1) is 12.
Activity.
A. Find the remainder using Remainder Theorem.
1. p(x) = x3 + 2x2 − 15x − 36 at x = −3
2. p(x) = x4 + 3x3 − 16x2 + 2x − 7 at x = 3
3. p(a) = a3 + 5a2 + 10a + 22 at a = −2
Name: ________________________________________Grade & Section: _________________
Subject: MATH 10 Teacher: DENNIS V. SABORNIDO
Score: ______________
Lesson
Activity Title
Learning Target
Reference(s)
LAS Writer
: Quarter 1 Week 7 LAS 2
: Factoring
: Factors Polynomials
: SLM Mathematics 10
: Dennis V. Sabornido, TII
The Factor Theorem is a special case of the Remainder Theorem where the
remainder P(r) = 0. P(x) has a factor (x - r) if and only P(r) = 0.
Example 1. Show that (x – 2) is a factor of P(x) = x3 − 5x2 + 6x
The Rational Root Theorem provides a complete list of possible rational roots of
the polynomial equation anxn + an–1xn–1 + ··· + a2x2 + a1x + a0 = 0 where
all coefficients are integers
.
Example 2. Find all the roots of y = x4 + 5x3 + 5x2 − 5x − 6. Using Rational Root Test the possible
roots: ±1,±2, ±3, ±6. Let's factor using synthetic division:
Activity.
A. Using Factor Theorem, determine if the given binomial is a factor of the
Polynomial.
1. (x4 − x3 − 24) ÷ (x + 2)
2. (x5 + x4 − 2x3 + 2x + 4) ÷ (x + 2)
3. (5x4 − 23x3 + 20x2 − 32) ÷ (x − 4)
B. Find possible rational root, rational root of polynomials
1. x3 + x2 − 5x + 3 = 0
3. x3 + 4x2 + 5x + 2 =
2. x3 − 7x2 + 11x − 5 = 0