Question

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Divide -3x^2-4x^2+4x+3 by x-2

Answer 1

(x-2)(-3x^2-10x-16) - 29

Explanation:

test -3x^3-4x^2+4x+3 for root at x=2

-3(2)^3-4(2)^2+4(2)+3

=-3*8-4*4+8+3

=-29

so x=2 is not a root n dividing -3x^3-4x^2+4x+3 by x-2 will have a quotient

solving by long division

-3x^3-4x^2+4x+3 x-2

-3x^2

-3x^3+6x^2

-10x^2+4x+3

-10x

-10x^2+20x

-16x+3

-16

-16x+32

-29

so divide -3x^3-4x^2+4x+3 by x-2

= (x-2)(-3x^2-10x-16) - 29

Answer 2

-3x^2 -10x -16 -29/(x-2)

Explanation:

-3x^3-4x^2+4x+3

We can do synthetic division

-3 -4 4 3

2

----------------------------

Bring the first term down

-3 -4 4 3

2

----------------------------

-3

Multiply -3 times 2

-3 -4 4 3

2 -6

----------------------------

-3

Add -4 and -6

-3 -4 4 3

2 -6

----------------------------

-3 -10

Multiply 2 *-10

-3 -4 4 3

2 -6 -20

----------------------------

-3 -10

Add 4 and -20

-3 -4 4 3

2 -6 -20

----------------------------

-3 -10 -16

Multiply the 2 by -16

-3 -4 4 3

2 -6 -20 -32

----------------------------

-3 -10 -16 -29

The result is -3x^2 -10x -16 -29/(x-2)