The quadratic equation x2−6x−16=0x2−6x−16=0 has sum of roots equal to 6 and product of roots equal to ______
Answers
1.1 Factoring x2-6x-16
The first term is, x2 its coefficient is 1 .
The middle term is, -6x its coefficient is -6 .
The last term, "the constant", is -16
Step-1 : Multiply the coefficient of the first term by the constant 1 • -16 = -16
Step-2 : Find two factors of -16 whose sum equals the coefficient of the middle term, which is -6 .
-16 + 1 = -15
-8 + 2 = -6 That's it
Step-3 : Rewrite the polynomial splitting the middle term using the two factors found in step 2 above, -8 and 2
x2 - 8x + 2x - 16
Step-4 : Add up the first 2 terms, pulling out like factors :
x • (x-8)
Add up the last 2 terms, pulling out common factors :
2 • (x-8)
Step-5 : Add up the four terms of step 4 :
(x+2) • (x-8)
Which is the desired factorization