Question

Select the factored form of each expression.

16x2-8x+1 =
x2-x- 30 =
9x2 - 49 =
3x2 + 17x - 6 =

Answer 1

16,2,-8,1,x,x

x,2,-x,-30

9,x,2,-49

3,x,2,17,x,-6

Answer 2

Answer:

$16 {x}^{2} - 8x + 1= (4x - 1)(4x - 1)$

${x}^{2} - x - 30 = (x - 6)(x + 5)$

$9 {x}^{2} - 49 = (3x - 7)(3x + 7)$

$3 {x}^{2} + 17x - 6 = (x + 6)(3x - 1)$

Step-by-step explanation:

For first equation -

$16 {x}^{2} - 8x + 1 \\= 16 {x}^{2} - (4 + 4)x + 1 \\ = 16 {x}^{2} - 4x - 4x + 1 \\ =4x(4x - 1) - (4x - 1) \\ = (4x - 1)(4x - 1)$

Factor of the equation is (4x-1)

For second equation -

${x}^{2} - x - 30 \\ = {x}^{2} - 6x + 5x - 30 \\= x(x - 6) + 5(x - 6) \\ =(x - 6)(x + 5)$

Factors of the above equation are (x-6) and (x+5)

For third equation -

$9 {x}^{2} - 49 \\= {(3x)}^{2} - {7}^{2} \\ =(3x - 7)(3x + 7)$

Factors of the above equation are (3x-7) (3x+7)

For fourth equation -

$3 {x}^{2} + 17x - 6 \\ = 3 {x}^{2} + 18x - x - 6 \\ = 3x(x + 6) - (x + 6) \\ = (x + 6)(3x - 1)$

Factors of the above equation are (x+6)(3x-1)

Here applied formulas are

(i)  middle term method

(ii)   ${x}^{2} - {y}^{2} = (x + y)(x - y)$