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factor (16x^2-8x+1)
Please show your work lol

Sagot :

Answer:

(4x - 1)^2.

Step-by-step explanation:

16x^2 - 8x + 1

Multiplying the first and last coefficients:

16 * 1 = 16

We need 2 numbers whose product is 16 and whose sum is -8.

These are - 4 and -4.

So we now write:

16x^2 - 4x - 4x + 1

Now factor by grouping :

= 4x(4x - 1) - 1(4x - 1)

= (4x - 1)(4x - 1)

= (4x - 1)^2

This method of factoring quadratics is called the 'ac' method - you split the middle term ( in this case the -8x) into 2 parts.

semsee45

Answer:

[tex](4x-1)^2[/tex]

Step-by-step explanation:

Given quadratic expression:

[tex]16x^2-8x+1[/tex]

To factor a quadratic in the form [tex]ax^2+bx+c[/tex], find two numbers that multiply to ac and sum to b:

  • [tex]ac = 16 \times 1 = 16[/tex]
  • [tex]b = -8[/tex]

Therefore, two numbers are: -4 and -4

Rewrite the middle term as the sum of these two numbers:

[tex]\implies 16x^2-4x-4x+1[/tex]

Factorize the first two terms and the last two terms separately:

[tex]\implies 4x(4x-1)-1(4x-1)[/tex]

Factor out the common term (4x - 1):

[tex]\implies (4x-1)(4x-1)[/tex]

Apply the exponent rule:  aa = a²

[tex]\implies (4x-1)^2[/tex]

Learn more about factoring quadratics here:

https://brainly.com/question/27956741

https://brainly.com/question/27947331

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