# Algebra!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!

1.16x^2-100

2. 4x^2-36x

3. x^2-19x+48

4. x^2-5x-24

5. x^2+6x-72

1). 16x2- 100

This expression it can be written as

=(4x)2-(102) .....................(1)

Compare equation(1)with  mathematical index property a2- b2= (a-b)(a+b)

a = 4x and b = 10

(4x)2-102) = (4x -10)(4x +10)

Therefore above 16x2 -100 factors are (4x -10)and(4x +10)

2.  4x2-36x

Take out common factor 4x

4x2-36x

= 4x(x-9)

therefore above  4x2-36x factors are 4x and x-9

3. x2-19x+48

now solve the equation using factor method.

Look at the product of the first and last coefficients: (1)(48) = 48.

We want two factors of 48 whose sum middle coefficient of -19, and they are -16 and -3.

=  x2- 3x -16x + 48

Take out common terms x and 16

x(x-3)-16(x-3)

Take out common factor (x-3)

(x-3)(x-16)

therefore above x2-19x+48 factors are(x-3) and (x-16)

4.  x2-5x-24

now solve the equation using factor method.

Look at the product of the first and last coefficients: (1)(-24) = -24.

We want two factors of -24 whose sum middle coefficient of -5, and they are -8 and +3.

=  x2- 8x+3x- 24

Take out common terms x and 3

x(x-8)+3(x-8)

Take out common factor (x-8)

(x+3)(x-8)

Therefore above x2-5x-24 factors are(x+3) and (x-8)

+1 vote

5. x2+ 6x-72

now solve the equation using factor method.

Look at the product of the first and last coefficients: (1)(-72) = -72.

We want two factors of -72 whose sum middle coefficient of 6, and they are 12 and -6.

=  x2- 6x+12x- 72

Take out common terms x and  +12

x(x-6)+12(x-6)

Take out common factor (x-6)

(x-6)(x+12)

Therefore above x2+6x-72 factors are(x-6) and (x+12)