Question

I have no idea what im doing someone help pls! due soon

Answer 1

ok so we know that 49 stays the same.

_(x + _)^2+ 49

So 4 and 28 both have a factor of 4 right? If we take out the 4 we get....

4(x^2 + 7x) + 49

Hmm.... Oh wait we can take out an x!!

4x(x + 7) + 49

That's your answer!

Answer 2

4x2-28x+49

Final result :

(2x - 7)2

Step by step solution :

Step 1 :

Equation at the end of step 1 :

(22x2 - 28x) + 49

Step 2 :

Trying to factor by splitting the middle term

2.1 Factoring 4x2-28x+49

The first term is, 4x2 its coefficient is 4 .

The middle term is, -28x its coefficient is -28 .

The last term, "the constant", is +49

Step-1 : Multiply the coefficient of the first term by the constant 4 • 49 = 196

Step-2 : Find two factors of 196 whose sum equals the coefficient of the middle term, which is -28 .

-196 + -1 = -197

-98 + -2 = -100

-49 + -4 = -53

-28 + -7 = -35

-14 + -14 = -28 That's it

Step-3 : Rewrite the polynomial splitting the middle term using the two factors found in step 2 above, -14 and -14

4x2 - 14x - 14x - 49

Step-4 : Add up the first 2 terms, pulling out like factors :

2x • (2x-7)

Add up the last 2 terms, pulling out common factors :

7 • (2x-7)

Step-5 : Add up the four terms of step 4 :

(2x-7) • (2x-7)

Which is the desired factorization

Multiplying Exponential Expressions :

2.2 Multiply (2x-7) by (2x-7)

The rule says : To multiply exponential expressions which have the same base, add up their exponents.

In our case, the common base is (2x-7) and the exponents are :

1 , as (2x-7) is the same number as (2x-7)1

and 1 , as (2x-7) is the same number as (2x-7)1

The product is therefore, (2x-7)(1+1) = (2x-7)2

Final result :

(2x - 7)2