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
are the values of x for which 2x + 1 < 0