How do you factor #5y^2-3y-2#?

Question

Avery Alexander · Accepted Answer

#= color(blue)((5y+2)(y-1) #

#5y^2−3y-2#

We can Split the Middle Term of this expression to factorise it.

In this technique, if we have to factorise an expression like #ay^2 + by + c#, we need to think of 2 numbers such that:

#N_1*N_2 = a*c = 5*-2 = -10# and, #N_1 +N_2 = b = -3#

After trying out a few numbers we get #N_1 = -5# and #N_2 =2# #-5*2 = -10#, and #2+(-5)=-3#

#5y^2−color(blue)(3y)-2 = 5y^2−color(blue)(5y+2y)-2#

#= 5y(y-1) +2(y-1)#

#= color(blue)((5y+2)(y-1) #

Hazel Anglin · Answer

undefined To factor the expression $5y^2 - 3y - 2$, you can use the factoring method. First, multiply the leading coefficient (5) by the constant term (-2), which equals -10. Then, find two numbers that multiply to -10 and add up to the middle coefficient (-3). The numbers are -5 and 2. Now, rewrite the middle term (-3y) as the sum of these two numbers: -5y + 2y.

Now, split the expression $5y^2 - 3y - 2$ into two parts using the terms found above:
$5y^2 - 5y + 2y - 2$

Factor by grouping:
$y(5y - 5) + 2(5y - 1)$

Factor out the common factors:
$y(5(y - 1)) + 2(5(y - 1))$

Now, notice that both terms have a common factor of $5y - 1$. Factor it out:
$(5y - 1)(y + 2)$

So, the factored form of $5y^2 - 3y - 2$ is $(5y - 1)(y + 2)$.