Final answer:
To find the divisor given the remainder, quotient, and dividend, use the division equation: dividend = (divisor × quotient) + remainder. For this problem with dividend 2x² +7x+7, quotient 2x +3, and remainder 1, the divisor is (b) x+2.
Step-by-step explanation:
The student is asking how to find the divisor when given the remainder, quotient, and dividend of a division problem in algebra. To solve this, we need to use the relationship that links these elements in division: dividend = (divisor × quotient) + remainder. Here, the dividend is 2x² +7x+7, the quotient is 2x +3, and the remainder is 1. Substituting the quotient and remainder back into the equation gives us:
2x² +7x+7 = (divisor × (2x +3)) + 1
We can then distribute the divisor within the parentheses and subtract '1' from both sides of the equation to solve for the divisor:
- 2x² +7x+7 - 1 = divisor × (2x +3)
- 2x² +7x+6 = divisor × (2x +3)
Since the left side of the equation is a quadratic expression, and we are multiplying the divisor by a linear expression to get that quadratic, the divisor must be a linear expression as well. By matching coefficients of x² and x, we can deduce that the correct divisor is option (b) x+2.