simplify (X square+23x-210)÷(x-7)
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Answers
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The first term is, x2 its coefficient is 1 .
The middle term is, +23x its coefficient is 23 .
The last term, "the constant", is -210
Step-1 : Multiply the coefficient of the first term by the constant 1 • -210 = -210
Step-2 : Find two factors of -210 whose sum equals the coefficient of the middle term, which is 23 .
-210 + 1 = -209
-105 + 2 = -103
-70 + 3 = -67
-42 + 5 = -37
-35 + 6 = -29
-30 + 7 = -23
-21 + 10 = -11
-15 + 14 = -1
-14 + 15 = 1
-10 + 21 = 11
-7 + 30 = 23 That's it
Step-3 : Rewrite the polynomial splitting the middle term using the two factors found in step 2 above, -7 and 30
x2 - 7x + 30x - 210
Step-4 : Add up the first 2 terms, pulling out like factors :
x • (x-7)
Add up the last 2 terms, pulling out common factors :
30 • (x-7)
Step-5 : Add up the four terms of step 4 :
(x+30) • (x-7)
Which is the desired factorization
Final result :
(x + 30) • (x - 7)