In order to use the remainder theorem, you need to have some idea what to divide by. The rational root theorem tells you rational roots will be from the list derived from the factors of the constant term, {±1, ±5}. When we compare coefficients of odd power terms to those of even power terms, we find their sums are equal, which means -1 is a root and (x +1) is a factor.
Dividing that from the cubic, we get a quotient of x² +6x +5 (and a remainder of zero). We recognize that 6 is the sum of the factors 1 and 5 of the constant term 5, so the factorization is
... = (x +1)(x +1)(x +5)
... = (x +1)²(x +5)
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The product of factors (x +a)(x +b) will be x² + (a+b)x + ab. That is, the factorization can be found by looking for factors of the constant term (ab) that add to give the coefficient of the linear term (a+b). The numbers found can be put directly into the binomial factors to make (x+a)(x+b).
When we have 1·5 = 5 and 1+5 = 6, we know the factorization of x²+6x+5 is (x+1)(x+5).
Answer:
the number of miles is 14,722
Step-by-step explanation:
The computation of the number of miles drive last year is shown below:
= Total cost ÷ cost per mile
= $1,560 + $3,740 ÷ $0.36 per mile
= $5,300 ÷ $0.36 per mile
= 14,722 miles
Hence, the number of miles is 14,722
Answer:6
Step-by-step explanation:
since it is A half circle it is the hhalf Value of the area of the full circle
(48a^3 + 32a^2 + 16a) / 4a = ?
48a^3 / 4a = 12a^2
32a^2 / 4a = 8a
16a / 4a = 4
so
(48a^3 + 32a^2 + 16a) / 4a = 12a^2 + 8a + 4
Answer is D. 12a^2 + 8a + 4
