(a) Expand and simplify (x − 3)(x + 5), ..2 marks.. (b) Solve x^2 + 8x − 9 = 0 ..3 marks..
(a) Remember: Multiply each term in the left bracket by every term in the right bracket.(x-3)(x+5) = x2+ 5x - 3x -15.Collecting all of the like terms:= x2+ 2x -15.
(b) Solve x2 + 8x − 9 = 0Remember to put equation in the form ax2 + bx + c = 0. Here, the equation is already in that form.We need to find two numbers to go into the brackets that add to make 8 (b) and also multiply to make -9 (a x c).We find these numbers are 9 and -1. (9 + -1 = 8 and -1 x 9 = -9)So (x+9)(x-1) = 0.Setting each bracket to = 0, we get:x + 9 = 0, or, x -1 = 0So, x = -9 or x = 1.
