Question

Is 16x^2 - 56x + 49 a perfect square trinomial? How do you know? If it is, factor the expression. Please show your work.

Answer 1

Answer:

Step-by-step explanation:

16x^2-56x+49

(4x)^2-2.4x.7+(7)^2

This is in the form of (a-b)^2, where a= 4x and b= 7

Thus it is a perfect square

Factorized form=(4x-7)^2

Mark brainliest..................

Answer 2

Answer:

(4x-7)²

Step-by-step explanation:

16x^2 - 56x + 49

To be a perfect Square means equal roots

and equal roots mean

D = b² - 4ac = 0

so

56² - 4×16×49 = 0

=>  3136 - 3136 = 0

=> 0 = 0

=> LHS = RHS

equation holds true

so polynomial is perfect square

16x² - 56x + 49

= 16x² - 28x - 28x + 49

= 4x(4x - 7) - 7(4x -7)

= (4x-7)(4x-7)

= (4x-7)²

x = 7/4