36117364-strategic-intervention-material.doc

T

itle Card

16x2 + 4xy 4xy - y2 16x2 + 0xy – y2 Arrange the terms in descending form

Operations on Polynomials: Multiplicatio n

(4x - y)(4x + y) = 16x2 – y2

Special Product Patterns Sum and Difference (a+b)(a-b)=a²-b² Example

G

uide Card

In dealing with Polynomials, we must be knowledgeable on how operations are made with them. In multiplying polynomials, the properties of real numbers, laws of exponents and law of signs must be rendered the most. Ex. (4x – y)(4x + y)

(x+3)(x-3) = x²-9

Square of a Binomial (a+b)²=a²+2ab+b² (a-b)²=a²-2ab+b² Example (y+4)²=y²+8y+16 (3t²-2)²=9t4-12t²+4 Cube of a Binomial (a+b)³=a³+3a²b+3ab²+b³ (a-b)³=a³-3a²b+3ab²-b³ 1

B. Multiply the following

Example

applying the special product patterns:

(x+1)³=x³+3x²+3x+1 (p-2)³=p³-6p²+12p-8

1. (x+4)² 2. (x+9)(x-2)(x+7) 3. (x+6)(x+5) 4. (x²-6x+5) + (x²+x-2) 5. (16-13x) – (10x-11) 6. (7y-x)² 7. (x+3)(x-4)(x+7) 8. 5x²(x-3) 9. 3x + (7x+2-6x²+2x³) 10. (7x³-1) – (10x³+4x²2x+4)

Sharpen your Skills Multiply the following: 1. (x)(x)= _____________________ 2. 2x (1+3x)= ___________________ 3. x • x • x • y= _____________

A

ctivity Card

A

ssessment Card Multiply the following

A. Use the laws of

1. 2. 3. 4. 5.

exponent to find the product of the following: 1. (6xy)(7x2y) 2. (-8x2y)(-4x2y) 3. -2/3xy(6x2y – 9xy2 + 12 xy) 4. (x + 5y)(x+3y) 5. 5x2y3z3(5xy – 7x2y) E

5x(3x²-x+3) 10x²(x-5) (x+1)(5x³-x²+x-4) (x-5)(x+5) (2x+5)(3x³-x²+x)

nrichment Card 2

1. Simplify (4x2 – 4x – 7)(x + 3) 2. Simplify (x + 2)(x3 + 3x2 + 4x – 17) 3. Simplify (3x2 – 9x + 5)(2x2 + 4x – 7) 4. Simplify (x3 + 2x2 + 4)(2x3 + x + 1)

R

eference Card

www.WebMath.com Making Connections in Mathematics IV by Generoso Obaña and Edna Mangaldan

Answer Key

Student’s Notes

Sharpen your Skills 1. x2 2. 2x + 6x2 3. x3y

__________________________ __________________________

Activity Card

__________________________ __________________________

A.

__________________________ __________________________ __________________________ __________________________ __________________________ __________________________ __________________________ __________________________ __________________________ __________________________ __________________________ __________________________

1. 2. 3. 4. 5.

42 x3y2 32x4y2 4x3y2 – 6x2y3 + 8 x2y2 x2 + 15y2 + 8xy 25 x3y4z3 – 35 x4y4z3

1. 2. 3. 4. 5. 6.

x²+8x+16 x³+14x²+31x-126 x²+11x+30 2x²-5x+3 -23x+27 49y²-14xy+x

B.

3

7. x³+6x²-19x-84 8. 5x³-15x² 9. 2x³-6x²+10x+2 10. 3x³+4x²-2x-5

Assessment Card 1. 2. 3. 4. 5.

15x³-5x²+15x 10x³-50x² 5x4+4x³-3x-4 X²-25 6x4+13x³-3x²+5x

Enrichment Card 1. 2. 3. 4.

4x3 + 8x2 – 19x – 21 x4 + 5x3 + 10x2 – 9x – 34 6x4 – 6x3 – 47x2 + 83x – 35 2x6 + 4x5 + x4 + 11x3 + 2x2 + 4x + 4

This humble SIM is brought to you by Gonzales , April Jane C.,

4