Answer: (2t-9)*(2t-7)
Step-by-step explanation:
Factoring 4t2-32t+63
The first term is, 4t2 its coefficient is 4 .
The middle term is, -32t its coefficient is -32 .
The last term, "the constant", is +63
Step-1 : Multiply the coefficient of the first term by the constant 4 • 63 = 252
Step-2 : Find two factors of 252 whose sum equals the coefficient of the middle term, which is -32 .
-252 + -1 = -253
-126 + -2 = -128
-84 + -3 = -87
-63 + -4 = -67
-42 + -6 = -48
-36 + -7 = -43
-28 + -9 = -37
-21 + -12 = -33
-18 + -14 = -32 That's it
Step-3 : Rewrite the polynomial splitting the middle term using the two factors found in step 2 above, -18 and -14
4t2 - 18t - 14t - 63
Step-4 : Add up the first 2 terms, pulling out like factors :
2t • (2t-9)
Add up the last 2 terms, pulling out common factors :
7 • (2t-9)
Step-5 : Add up the four terms of step 4 :
(2t-7) • (2t-9)
Which is the desired factorization
Final result :
(2t - 9) • (2t - 7)
