the polynomial $6x^{2}+x - 15$ has a factor of $2x - 3$. what is the other factor?\n3x - 5\n3x + 5\n4x…

Explanation:

Step1: Use polynomial long - division

Divide (6x^{2}+x - 15) by (2x - 3). First, divide the leading term of the dividend (6x^{2}) by the leading term of the divisor (2x). (\frac{6x^{2}}{2x}=3x).

Step2: Multiply and subtract

Multiply (2x - 3) by (3x) to get (6x^{2}-9x). Subtract this from (6x^{2}+x - 15): ((6x^{2}+x - 15)-(6x^{2}-9x)=10x - 15).

Step3: Divide the new leading term

Divide the leading term of (10x - 15) (which is (10x)) by the leading term of (2x - 3) (which is (2x)). (\frac{10x}{2x}=5).

Step4: Multiply and check

Multiply (2x - 3) by (5) to get (10x-15). Subtracting (10x - 15) from (10x - 15) gives a remainder of (0). So the quotient is (3x + 5).

Answer:

B. (3x + 5)