Divide the polynomial 12x2+2x−9 by 4x−2 . Then express the polynomial as the product of the divisor and the quotient plus the remainder. (1 point)
Responses
12x2+2x−9=(4x−2)(3x+2)−13
12 x squared plus 2 x minus 9 is equal to open paren 4 x minus 2 close paren times open paren 3 x plus 2 close paren minus 13
12x2+2x−9=(4x−2)(3x+2)−5
12 x squared plus 2 x minus 9 is equal to open paren 4 x minus 2 close paren times open paren 3 x plus 2 close paren minus 5
12x2+2x−9=(4x−2)(3x−1)−11
12 x squared plus 2 x minus 9 is equal to open paren 4 x minus 2 close paren times open paren 3 x minus 1 close paren minus 11
12x2+2x−9=(4x−2)(3x+2)+5
12 x squared plus 2 x minus 9 is equal to open paren 4 x minus 2 close paren times open paren 3 x plus 2 close paren plus 5
12x^2 + 2x - 9 = (4x - 2)(3x + 2) + 5
12x squared plus 2x minus 9 is equal to open parenthesis 4x minus 2 close parenthesis times open parenthesis 3x plus 2 close parenthesis plus 5
To divide the polynomial 12x^2 + 2x - 9 by 4x - 2, we can use the long division method. Here's how you can do it:
Step 1: Set up the long division expression by dividing the first term of the dividend (12x^2) by the first term of the divisor (4x). Write the result (3x) above a division line.
_________
4x - 2 | 12x^2 + 2x - 9
3x
Step 2: Multiply the entire divisor (4x - 2) by the quotient from Step 1 (3x). Write the result (12x^2 - 6x) beneath the dividend, aligned by degrees of the variable.
_________
4x - 2 | 12x^2 + 2x - 9
- (12x^2 - 6x)
8x - 9
Step 3: Subtract the entire result (12x^2 - 6x) from the dividend (12x^2 + 2x - 9). Write the difference (8x - 9) beneath the line.
_________
4x - 2 | 12x^2 + 2x - 9
- (12x^2 - 6x)
_______________
8x - 9
Step 4: Now we have a new expression (8x - 9) to divide. Repeat steps 1-3 until you cannot divide anymore.
Since we cannot divide further, the remainder is 8x - 9.
Therefore, the expression 12x^2 + 2x - 9 divided by 4x - 2 is:
Dividend = Divisor * Quotient + Remainder
12x^2 + 2x - 9 = (4x - 2)(3x) + (8x - 9)
So the correct answer would be:
12x^2 + 2x - 9 = (4x - 2)(3x) + (8x - 9)