F(x) = x4 + x3 + 2x2 + ax + b,
where a and b are constants.
When f(x) is divided by (x - 1), the remainder is 7
(a) Show that a + b = 3
When f(x) is divided by (x + 2), the remainder is -8
(b) Find the value of a and the value of b

see explanation

Step-by-step explanation:

The remainder theorem states that if f(x) is divided by (x - h)

The the remainder is f(h)

(a)

Given f(x) is divided by (x - 1) then remainder is f(1), thus

f(1) = + 1³ + 2(1)² + a + b = 7, that is

1 + 1 + 2 + a + b = 7

4 + a + b = 7 ( subtract 4 from both sides )

a + b = 3 ← as required → (1)

(b

Given f(x) is divided by (x + 2) then the remainder is f(- 2), thus

f(- 2) = + (- 2)³ + 2(- 2)² + 2a + b = - 8, that is

16 - 8 + 8 + 2a + b = - 8

16 + 2a + b = - 8 ( subtract 16 from both sides )

2a + b = - 24 → (2)

Multiply (1) by 2

2a + 2b = 6 → (3)

Add (2) and (3) term by term to eliminate the term in a

3b = - 18 ( divide both sides by 3 )

b = - 6

Substitute b = - 6 into (1)

a - 6 = 3 ( add 6 to both sides )

a = 9

Thus a = 9 and b = - 6

the camry sales+accord sale=828,000. to make it so the two numbers are 18 thousand apart and still equal 828,000, you first need to find out what half of 828,000 is. 828,000/2=414,000. for the two numbers to equal 828,000, you have to add the same amount as you subtract from the middle. in this case, the number is 9,000 because it's half of 18,000. to equal 828,000, you have to add 9,000 to 414,000 for the camry and subtract 9,000 from 414,000 for the accord. 414,000+9,000=423,000.

414,000-9,000=405,000.

423,000+405,000=828,000.

423,000-405,000=18,

hope it