Exercise 40 Page 50

Table:

Product of Two Binomials	ax^2+mx+px+c	ax^2+bx+c	m* p	a* c
(2x+3)(x+4)	2x^2+8x+3x+12	2x^2+11x+12	24	24
(x+1)(3x+5)	3x^2+5x+3x+5	3x^2+8x+5	15	15
(2x-1)(4x+1)	8x^2+2x-4x-1	8x^2-2x-1	- 8	- 8
(3x+5)(4x-2)	12x^2-6x+20x-10	12x^2+14x-10	- 120	- 120

Practice makes perfect

We need to use the Distributive Property to complete the table.

Product of Two Binomials	ax^2+mx+px+c	ax^2+bx+c	m* p	a* c
(2x+3)(x+4)	2x^2+8x+3x+12	2x^2+11x+12	24	24
(x+1)(3x+5)	3x^2+5x+3x+5	3x^2+8x+5	15	15
(2x-1)(4x+1)	8x^2+2x-4x-1	8x^2-2x-1	- 8	- 8
(3x+5)(4x-2)	12x^2-6x+20x-10	12x^2+14x-10	- 120	- 120

From the table in Part A, we see that the product of m and p is equal to the product of a and c.

m * p = a * c

The second and third column in the table shows us that the sum of m and p is equal to b.

m + p = b

To factor trinomials in the form ax^2+bx+c, we first need to find two numbers, m and p, with a product of a* c and a sum of b.

ax^2+bx+c ⇕ ax^2+mx+px+c This expression can be factored by grouping.

Exercises p.49-51

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