x^4-13x-42/(x^2-x-6)
Answers
Answer:
x⁴ - 13x - 42
Simplify ————————
x² - x - 6
Step-by-step explanation:
Factoring x⁴ - 13x² + 42
The first term is, x⁴ its coefficient is 1 .
The middle term is, -13x² its coefficient is -13 .
The last term, "the constant", is +42
Step-2 : Find two factors of 42 whose sum equals the coefficient of the middle term, which is -13 .
-42 + -1 = -43
-21 + -2 = -23
-14 + -3 = -17
-7 + -6 = -13 That's it
Step-3 : Rewrite the polynomial splitting the middle term using the two factors found in step 2 above, -7 and -6
x⁴ - 7x² - 6x² - 42
Step-4 : Add up the first 2 terms, pulling out like factors :
x² • (x²-7)
Add up the last 2 terms, pulling out common factors :
6 • (x²-7)
Step-5 : Add up the four terms of step 4 :
(x²-6) • (x²-7)
Which is the desired factorization.
2.4 Factoring x²-x-6
The first term is, x² its coefficient is 1 .
The middle term is, -x its coefficient is -1 .
The last term, "the constant", is -6
Step-1 : Multiply the coefficient of the first term by the constant 1 • -6 = -6
Step-2 : Find two factors of -6 whose sum equals the coefficient of the middle term, which is -1 .
-6 + 1 = -5
-3 + 2 = -1 That's it
Step-3 : Rewrite the polynomial splitting the middle term using the two factors found in step 2 above, -3 and 2
x² - 3x + 2x - 6
Step-4 : Add up the first 2 terms, pulling out like factors :
x • (x-3)
Add up the last 2 terms, pulling out common factors :
2 • (x-3)
Step-5 : Add up the four terms of step 4 :
(x+2) • (x-3)
Which is the desired factorization.