5d2

-145d +600

5 * (d - 5) * (d - 24)

Step-by-step explanation:

Reformatting the input:

Changes made your input should not affect the solution:

(1): "d2" was replace by "d^2".

Step by step solution:

Step 1:

Equation at the end of step 1:

(5d2 - 145d) + 600

Step 2:

Step 3:

Pulling out like terms:

3.1 Pull out like factors:

5d2 - 145d + 600 = 5 * (d2 - 29d + 120)

Trying to factor by splitting the middle term

3.2   Factoring d2 - 29d + 120

The first term is, d2 its coefficient is 1.

The middle term is, -29d its coefficient is -29.

The last term, "the constant", is + 120

Step-1: Multiply the coefficient of the first term by the constant 1 * 120 = 120

Step-2: Find two factors of 120 whose sum equal to coefficient of the middle term, which is  - 29.

-120 + -1 = -121

-60 + -2 = -62

-40 + -3 = -43

-30 + -4 = -34

-24 + -5 = -29

(That's it)

Step-3: Rewrite the polynomial splitting the middle term using the two factors found in the step 2 above, -24 and -5

d2 - 24d - 5d - 120

Step 4: Add up the first 2 terms,  pulling out like factors:

Add up the last 2 terms, pulling out like factors.

5 * (d - 24)

Step-5: Add up the four terms of step 4:

(d - 5) * (d- 24)

Final result:

5 * (d - 5) * (d - 24)

5(d - 5)(d - 24).

Step-by-step explanation:

5d^2 - 145d + 600     Take out the GCF which is 5:

= 5(d^2 - 29d + 120)

Now we want 2 numbers whose product is  120 and whose sum is -29.

These are  - 5 and - 24 so the factors are:

5(d - 5)(d - 24).

1) 2/5

2) zero=0/1

3) zero=0/2

4) -4/5

5) undefined=3/0

about 168 miles

step-by-step explanation: