Question

1. What is the quotient x^2-16/2x^2-9x+4 divide by 2x^2+14x+24/4x+4
2What is the simplified form for the product x+1/x^2-25 time x+5/x^2+8x+7
3.What are the coordinates of the x-intercepts of the graph of y = 2x^2 + 6x – 20?
4.What is the simplified form of the product x^2+8x+15/x-4 times x^2-16/2x+6

Answer 1

factorise the quadratics where possible

look at the numerator 1st

\[\frac{(x-4)(x+4)}{(2x-1)(x -4)} = \frac{(x +4)}{(2x-1)}\]

now for the denominator

\[\frac{2(x^2 + 7x + 12)}{4(x +1)} = \frac{(x +3)(x+4)}{2(x +1)}\]

dividing by a fraction requires the denominator to be flipped and then multiplied

\[\frac{(x +4)}{(2x -1)} \times \frac{2(x+1)}{(x+3)(x+4)}\]

cancel the common factor (x +4)

leaves

\[\frac{2(x +1)}{(2x-1)(x+3)}\]

all you need to do is expand and collect like terms

\[\frac{2x + 2}{2x^2 + 5x - 3}\]

Answer 2

1) C 2) C 3) A 4) B
these are correct!