Explanation for Question 10 From the Math (No Calc) Section on the 2017 October Sat
Question 10 says the equation above is true for all X where a and 2 B are constants. What is the value of a B? 3 So we're just going to start by distributing and adding and subtracting link terms. 4 So a X times five X squared is five, 5 a X cutie plus, 6 that's what I do right there. Plus I X times negative BX is negative 7 a B X squared plus four X 8 right there. Plus three times five X squared is 15 9 X squared. Plus three times negative VX is 10 negative three, the X plus three 11 times four is 12 and that's equal to 20 12 X cubed plus negative nine X squared plus negative two 13 X plus 12. 14 Now we can add and subtract like terms on the left side. 15 So there's only 1, 5, 8 X cubed. 16 So five, a X cubed. 17 Um, and that's the only execute term plus negative 18 a B ax squared plus 15 X squared. 19 I'm just grouping together the similar terms plus, 20 uh, for a X plus negative three BX plus 12. 21 So since this equation is true for all values of X, 22 that means that the left side of the equation is exactly the same as 23 the right side of the equation, which means that for example, 24 the constants are both equal to 12. 25 So that means that we can take any terms that are similar and just 26 set them equal to each other. So five X cubed is equal 27 to 20 X cube. For example, you can divide both sides by X cubed 28 to get five a is equal to 20 and divide both sides by five. 29 And that gives you a is equal to four. 30 So now that we know that a is equal to four, we can s...