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How do you factor #4x^2+4x+1#?

Answer 1

Kennedy Adams

#(2x+1)^2#

#"'split 4x into " 2x+2x#

#rArr4x^2+2x+2x+1#

#"factorise each 'pair'""#

#color(red)(2x)(2x+1)color(red)(+1)(2x+1)#

#"take out the common factor " (2x+1)#

#(2x+1)(color(red)(2x+1))#

#rArr4x^2+4x+1#

#=(2x+1)(2x+1)=(2x+1)^2#

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Answer 2

Eva Abramson

To factor the quadratic expression 4x^2 + 4x + 1, you can use the technique known as "factoring by grouping."

First, multiply the coefficient of the x^2 term (4) by the constant term (1). You get 4 * 1 = 4.

Now, find two numbers that multiply to give you 4 and add to give you the coefficient of the x term (4). In this case, the numbers are 2 and 2.

Now, rewrite the middle term (4x) as the sum of these two numbers: 4x = 2x + 2x

Now, group the terms: 4x^2 + 2x + 2x + 1

Factor by grouping: (4x^2 + 2x) + (2x + 1)

Factor out the greatest common factor from each group: 2x(2x + 1) + 1(2x + 1)

Now, you can see that both terms have a common factor of (2x + 1): (2x + 1)(2x + 1)

So, the factored form of 4x^2 + 4x + 1 is (2x + 1)(2x + 1), or (2x + 1)^2.

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Answer from HIX Tutor

When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.