How do you factor 8m² -34m -9 ?

Question

Abigail Allen · Accepted Answer

#8m^2- 34m - 9# In order to factorize this expression, we can split its middle term: In this technique, if we have to factorise an expression like #am^2 + bm + c#, we need to think of 2 numbers such that: #N_1*N_2 = axxc = 8xx(-9)= -72# And,  #N_1 +N_2 = b = -34# After trying out a few numbers we get #N_1 = -36# and #N_2 =2#
#(-36) xx 2 = -72#, and # -36 +2 = -34#  #8m^2- 34m - 9 = 8m^2- 36m + 2m - 9# # = 4m(2m - 9) + 1(2m - 9)# # = (4m + 1) (2m - 9) #
#color(green)((4m + 1) (2m - 9) )# is the Factorised form of #8m^2- 34m - 9#

Eli Assouline · Answer

undefined To factor the expression 8m² - 34m - 9, you can use the quadratic formula:

x = [-b ± √(b² - 4ac)] / (2a)

For the given expression, a = 8, b = -34, and c = -9. Plug these values into the quadratic formula:

x = [-(34) ± √((-34)² - 4(8)(-9))] / (2 * 8)

Calculate the discriminant:

b² - 4ac = (-34)² - 4(8)(-9) = 1156 + 288 = 1444

Now, plug the discriminant back into the quadratic formula:

x = [-(34) ± √(1444)] / 16

x = [-(34) ± 38] / 16

Now, find the roots:

x₁ = (-(34) + 38) / 16 = 4 / 16 = 1/4

x₂ = (-(34) - 38) / 16 = -72 / 16 = -9/2

So, the factored form of the expression is:

8m² - 34m - 9 = 8(m - 1/4)(m + 9/2)