Factor. 4k^2-140k+672=0
Answers
Answer:
Two solutions were found :
k =(-6-√52)/8=(-3-√ 13 )/4= -1.651
k =(-6+√52)/8=(-3+√ 13 )/4= 0.151
Step-by-step explanation:
Step 1 :
Equation at the end of step 1 :
(22k2 - 104k) + 672 = 0
Step 2 :
Step 3 :
Pulling out like terms :
3.1 Pull out like factors :
4k2 - 104k + 672 = 4 • (k2 - 26k + 168)
Trying to factor by splitting the middle term
3.2 Factoring k2 - 26k + 168
The first term is, k2 its coefficient is 1 .
The middle term is, -26k its coefficient is -26 .
The last term, "the constant", is +168
Step-1 : Multiply the coefficient of the first term by the constant 1 • 168 = 168
Step-2 : Find two factors of 168 whose sum equals the coefficient of the middle term, which is -26 .
-168 + -1 = -169
-84 + -2 = -86
-56 + -3 = -59
-42 + -4 = -46
-28 + -6 = -34
-24 + -7 = -31
-21 + -8 = -29
-14 + -12 = -26 That's it
Step-3 : Rewrite the polynomial splitting the middle term using the two factors found in step 2 above, -14 and -12
k2 - 14k - 12k - 168
Step-4 : Add up the first 2 terms, pulling out like factors :
k • (k-14)
Add up the last 2 terms, pulling out common factors :
12 • (k-14)
Step-5 : Add up the four terms of step 4 :
(k-12) • (k-14)
Which is the desired factorization
Equation at the end of step 3 :
4 • (k - 12) • (k - 14) = 0