Question

2b²-3b-2=0
Solve by factoring

Answer 1

b = 2, b = -1/2

Explanation:

1.) To factor, you multiply the leading coefficient by the constant then see which numbers multiply to that number, but add up to the middle coefficient.

2.) 2 * -2 = -4, and the factors of -4 that add up to -3 are -4 and 1.

3.) Split up the middle term to make the equation 2b^2-4b+b-2=0

4.) Factor. You would get 2b(b-2)+(b-2)=0

5.) Factor again. You would get (2b+1)(b-2)=0

6.) By the Zero-Product Property, you know that 2b+1 could equal 0 or b-2 could equal 0. By solving these two equations, we get that b = 2, and b = -1/2.

Answer 2

The solutions to the equation 2b²-3b-2=0 are b = 2 or b = -1/2

Explanation:

To solve 2b²-3b-2=0 by factoring, we need to find two numbers that multiply to -4 and add up to -3, which are -4 and +1. We can then use these two numbers to split the middle term of the quadratic equation and rewrite it as: 2b² - 4b + b - 2 = 0

Next, we factor out the GCF of the first two terms and the GCF of the last two terms: 2b(b - 2) + 1(b - 2) = 0

Now, we can see that (b - 2) is a common factor of both terms, so we can factor it out: (b - 2)(2b + 1) = 0

Using the zero product property, we know that the product of two factors is equal to zero only if at least one of the factors is zero. Therefore, we can set each factor equal to zero and solve for b:

b - 2 = 0 or 2b + 1 = 0

b = 2 or b = -1/2