Me : (
sari is teaching her best friend factor trinomials with a leading coefficient greater than 1. she starts with the trinomial 2x^2 + 5x + 3.
show/describe all of the steps for finding the factorization of the trinomial. be sure to include the final factorization in your description.

2x² + 5x + 3 = (2x + 3)(x + 1)

Step-by-step explanation:

* Lets explain how to factor a trinomial in the form ax² ± bx ± c:

- Look at the last term c  

# If the c term is a positive number, then its factors r , s  will both

 be positive or both be negative  

# a has two factors h and k  

# The brackets are (hx ± r)(kx ± s) where a = hk , c = rs and b = rk + hs

# If the c term is a negative number, then either r or s will be negative,  

  but not both.

# a has two factors h and k  

# The brackets are (hx + r)(kx - s) or (hx - r)(kx + s)where a = hk ,

   c = rs and b = rk - hs

* Lets solve the problem

∵ The equation is 2x² + 5x + 3 = 0

∵ The general form of the equation is ax² + bx + c = 0

∴ a = 2 , b = 5 , c = 3

∵ c is positive

∴ Its factors r and s have same sign

∵ c = 3

∵ 3 = 3 × 1

∴ r = 3 and s = 1  

∵ a = 2  

∵ The factors of a are h , k

∵ 2 = 2 × 1

∴ h = 2 and k = 1  

∵ The brackets are (hx + r)(kx + s)

∴ 2x² + 5x + 3 = (2x + 3)(x + 1)

37/3

step-by-step explanation:

step 1: simplify both sides of the equation.

7x+8(x+

1

4

)=3(6x−9)−8

7x+(8)(x)+(8)(

1

4

)=(3)(6x)+(3)(−9)+−8(distribute)

7x+8x+2=18x+−27+−8

(7x+8x)+(2)=(18x)+(−27+−8)(combine like terms)

15x+2=18x+−35

15x+2=18x−35

tep 2: subtract 18x from both sides.

15x+2−18x=18x−35−18x

−3x+2=−35

step 3: subtract 2 from both sides.

−3x+2−2=−35−2

−3x=−37

step 4: divide both sides by -3.

−3x

−3

=

−37

−3

x=

37

3