Question

ACTIVITY - 03
- Illustrate the factorization of a quadratic polynomial ax+ bx + x using graph papers​

Answer 1

Answer:

Math Labs with Activity – Interpret Geometrically the Factors of a Quadratic Expression

February 1, 2018 by Prasanna

Math Labs with Activity – Interpret Geometrically the Factors of a Quadratic Expression

OBJECTIVE

To interpret geometrically the factors of a quadratic expression of the form x2 + bx + c

Materials Required

Two sheets of graph paper

A geometry box

Theory

The polynomials (x + p) and (x + q) are the factors of a

quadratic expression x2+bx + c if p + q=b and pq = c.

Procedure

For convenience, we take x = 10.

Case I – Let us first consider the expression x2 +7x+ 12. Then, b =7 and c = 12

Step 1: Find two numbers such that their sum is 7 and their product is 12. Two such numbers are 3 and 4.

Step 2: Construct a square ABCD having each side = x (= 10 cm) on a graph paper as shown in Figure 12.1.

Step 3: Construct a rectangle BEFC having sides BE=CF = 3 cm and BC =EF = x (= 10 cm) as shown in Figure 12.1. Shade the rectangle BEFC.

Step 4: Construct a rectangle DCGH having sides DC =GH = x (= 10 cm) and DH =CG =4 cm as shown in Figure 12.1. Shade the rectangle DCGH.

Step 5: Construct a rectangle CFIG having sides CF =GI = 3 cm and CG = FI = 4 cm as shown in Figure

Step 6: Record your observations (see Observations and Calculations, Case I).

Math Labs with Activity - Interpret Geometrically the Factors of a Quadratic Expression 1

Case II – Let us now consider the expression x2 -x -12 Then, b = -1 and c = -12

Step 1: Find two numbers such that their sum is -1 and