Algebra!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!

Question

1.16x^2-100

 

2. 4x^2-36x

 

3. x^2-19x+48

 

4. x^2-5x-24

 

5. x^2+6x-72

Answer 1

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)

Answer 2

2.  4x²-36x

Take out common factor 4x

4x²-36x

= 4x(x-9)

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

Answer 3

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)

Answer 4

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)

Answer 5

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)