How do you divide #(15x^2 + 22x + 8)/( 5x + 4)#?

Question

Isaiah Anthony · Accepted Answer

#3x+2#

There is a slight problem with this. Look at the footnote in the explanation.

Method 1: Try to factor the numerator so that a portion of the denominator is eliminated. Method 2: Division by length. '~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~ #color(blue)("Trying method 1 first")# 15 factors -> {1,15} ; {3,5} 8 factors -> {1,8} ; {2,4} Attempt No 1: For this to work we need #(5x+4)# #=> (5x+4)(?_1 x+?_2) =15x^2+22x+8# With our list of variables, this would provide us with: #(5x+4)(3x+2) = 15x^2+10x+12x+8# '~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~ This works so we have: #((5x+4)(3x+2))/((5x+4))# #(5x+4)/(5x+4) xx (3x+2)# But #(5x+4)/(5x+4)=1# giving #3x+2 # as the answer. '~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~ However, you have to be mindful of the fact that division by 0 is 'not allowed' in mathematics (Undefined). Thus there is a value of x where #(5x+4)=0# so division by #(5x+4)# at that point gives you a bit of a problem!

Abigail Allen · Answer

undefined To divide (15x^2 + 22x + 8) by (5x + 4), you can use long division or synthetic division. Here is the step-by-step process using long division:

1. Divide the first term of the numerator (15x^2) by the first term of the denominator (5x). The result is 3x.

2. Multiply the entire denominator (5x + 4) by the result from step 1 (3x), and subtract it from the numerator (15x^2 + 22x + 8).

3. Bring down the next term from the numerator, which is 22x.

4. Divide the new expression (22x) by the first term of the denominator (5x). The result is 4.

5. Multiply the entire denominator (5x + 4) by the result from step 4 (4), and subtract it from the previous result.

6. Bring down the last term from the numerator, which is 8.

7. Divide the new expression (8) by the first term of the denominator (5x). The result is 1.6.

8. Multiply the entire denominator (5x + 4) by the result from step 7 (1.6), and subtract it from the previous result.

9. At this point, there are no more terms left in the numerator. The final result is the quotient: 3x + 4 + 1.6/(5x + 4).

Therefore, the division of (15x^2 + 22x + 8) by (5x + 4) is equal to 3x + 4 + 1.6/(5x + 4).