find the zero of the polynomial p(x) = x²-2x-8 by factorisation
Answers
Answer:
Step-by-step explanation:
Factoring x^2-2x-8
The first term is, x^2 its coefficient is 1 .
The middle term is, -2x its coefficient is -2 .
The last term, "the constant", is -8
Step-1 : Multiply the coefficient of the first term by the constant 1 • -8 = -8
Step-2 : Find two factors of -8 whose sum equals the coefficient of the middle term, which is -2 .
-8 + 1 = -7
-4 + 2 = -2 That's it
Step-3 : Rewrite the polynomial splitting the middle term using the two factors found in step 2 above, -4 and 2
x^2 - 4x + 2x - 8
Step-4 : Add up the first 2 terms, pulling out like factors :
x • (x-4)
Add up the last 2 terms, pulling out common factors :
2 • (x-4)
Step-5 : Add up the four terms of step 4 :
(x+2) • (x-4)
Which is the desired factorization
(x + 2) • (x - 4) = 0
the zeroes are 4 & -2