If x - 3 is a factor of p(x)=x^3-7x^2+15-9, which of the following represents the complete factorization for p(x) a.(x-3)(x+3)(x+1) b.(x-3)(x+4)(x+1) c.(x-3)(x+3)(x-1) d.(x-3)(x-3)(x-1)

Option D.

Step-by-step explanation:

Given that (x-3) is a factor of  P(x)=x^3-7x^2+15x-9. If we divide the P(x) by (x-3) we will get a second grade polynomial, which is easier to factorize.

Dividing x^3-7x^2+15x-9 by (x-3), the answer is: x^2 - 4x + 3 with a remainder of zero.

Now, to factorize x^2-4x+3 we just need to find two numbers that equal -4 when added and 3 when multiplied. These two numbers are -1 and -3.

So the complete factorization of P(x) is: (x-3)(x-1)(x-3)

Which is option D.

b.) 160 miles on a 5 gallons car

step-by-step explanation:

240/10=24 miles/gallon

160/5=32 miles/gallon

30/1=30 miles/gallon

168/6= 28 miles/gallon

32 miles/gallon is the most amount, so this is the best.