Saw this in a "could you pass a Year 12 Maths exam?" article. Clearly the answer is "no". I want to understand the answer to the question and how it is arrived at.
http://www.smh.com.au/cqstatic/12z7v7/HSCQ8729px.png
Thanks!
Posted Oct 24, 2017, 12:01 PM UTC
You can either factor the given expression:
3x^2 - x - 2
= 3x^2 - 3x + 2x - 2
= 3x(x - 1) + 2(x - 1)
= (3x + 2)(x - 1) .... option D
Or expand each of the given options using distribution:
(A)
(3x - 1)(x + 2)
= 3x(x) + 3x(2) - 1(x) - 1(2)
= 3x^2 + 6x - x - 2
= 3x^2 + 5x - 2 ..... not the same.
(B)
(3x + 1)(x - 2)
= 3x(x) + 3x(-2) + 1(x) + 1(-2)
= 3x^2 - 6x + 1 - 2
= 3x^2 - 5x - 2 ..... not the same
etc.
Just remember to FOIL! Multiply the First, Outer, Inner, and last of each equation to expand it. So, First: 3x Times x = 3x^2, Outer: 3x Times -1 = -3x, Inner: 2 times x = 2x and finally, Last: 2 times -1 = -2. So then you have 3x^2 -3x + 2x - 2. Combine like terms and you have 3x^2 - x - 2. The answer is D
It would be D, because multiplying paranthesis together goes like this:
(a + b)(c + d) = a * c + b * c + a * d + b * d
So:
(3x+2)(x-1)
3x * x = x^2
3x * (-1) = -3x
2 * x = 2x
2 * (-1) = -2
x^2 - 3x + 2x - 2 = x^2 - 1x - 2