Divide and check:
(3x^2-2x-13)divided by (x-2)
(3x^2 - 2x - 13) / (x-2) = (3x + 4),
-5 Remainder.
Long division was used, but it is difficult to show here.
Check:
(x-2)(3x+4) =
3x^2 + 4x -6x - 8 =
(3x^2 - 2x -8) -5 = 3x^2 - 2x - 13.
To divide the polynomial (3x^2 - 2x - 13) by the linear binomial (x - 2), we can use a method called polynomial long division. Here's how to do it:
Step 1: Rewrite the dividend and divisor in descending order of their exponents.
Dividend: 3x^2 - 2x - 13
Divisor: x - 2
Step 2: Look at the term with the highest exponent in the dividend (in this case, 3x^2), and divide it by the term with the highest exponent in the divisor (which is x). Write the result above a horizontal line.
Quotient: 3x
Step 3: Multiply the divisor by the quotient and write the result below the dividend, aligning the coefficients of like terms.
Multiply: 3x * (x - 2) = 3x^2 - 6x
3x
_______
x - 2 | 3x^2 - 2x - 13
-(3x^2 - 6x)
_______________
4x - 13
Step 4: Subtract the result obtained in the previous step from the original dividend.
Subtract: (3x^2 - 2x - 13) - (3x^2 - 6x) = 4x - 13
Step 5: Repeat steps 2 to 4 with the new dividend obtained (4x - 13) until there are no more terms left to divide.
In this case, we have no more terms to divide, so the division is completed.
Therefore, the quotient is 3x + 4, and the remainder is 4x - 13.