2017年GRE考试数学考点讲解5

　　Finding Real Roots

　　If (x-c) is a factor of the polynomial p(x), then c is a root of p(x).

　　We can find the real roots of polynomial p(x) by finding all the factors of p(x).

　　Example:

　　p(x)=x2+3x+2=(x+1)(x+2). Two real roots of p(x) are -1 and -2.

　　Remember:

　　To find if c is a root of p(x), evaluate p(c) and check if p(c)=0.

　　If x is a common factor of p(x), then zero is a root of p(x).

　　GRE数学考点介绍：Multiple Times

　　If probability of an event happening is p, then the probability that the event happens n times in a row is p∧n.

　　Example:

　　The probability that a coin toss results in head is 0.5. Then the probability that when the coin is tossed twice, both of them are head is 0.5∧2=0.25.

　　Probability that a roll of a six-sided die land with face 1 is 1/6. Then the probability that 1 will turn up three times in a row is (1/6)∧3.

　　Remember:

　　Note that probability of the event happening does not change from trial to trial.