SAT Mathematics Practice Test 2

Since 2x(3x+5)+3(3x+5)=ax2+bx+c for all values of x, the two sides of the equation are equal, and the value of b can be determined by simplifying the left-hand side of the equation and writing it in the same form as the right-hand side. Using the distributive property, the equation becomes (6x2+10x)+(9x+15)=ax2+bx+c. Combining like terms gives 6x2+19x+15=ax2+bx+c The value of b is the coefficient of x, which is 19.