Answer:
1st option
Step-by-step explanation:
6x² - x - 15 = 0
Consider the factors of the product of the x² term and the constant term which sum to give the coefficient of the x- term.
product = 6 × - 15 = - 90 and sum = - 1
The factors are - 10 and + 9
Use these factors to split the x- term
6x² + 9x - 10x - 15 = 0 ( factor first/second and third/fourth terms )
3x(2x + 3) - 5(2x + 3) = 0 ← factor out (2x + 3) from each term
(2x + 3)(3x - 5) = 0
Equate each factor to zero and solve for x
2x + 3 = 0 ⇒ 2x = - 3 ⇒ x = - [tex]\frac{3}{2}[/tex]
3x - 5 = 0 ⇒ 3x = 5 ⇒ x = [tex]\frac{5}{3}[/tex]
Answer:
-10x and 9x
Step-by-step explanation:
Because this is the way you'll factor:
Factoring 6x2-x-15
The first term is, 6x2 its coefficient is 6 .
The middle term is, -x its coefficient is -1 .
The last term, "the constant", is -15
Step-1 : Multiply the coefficient of the first term by the constant 6 • -15 = -90
Step-2: Find two factors of -90 whose sum equals the coefficient of the middle term, which is -1 .
Step-3 : Rewrite the polynomial splitting the middle term using the two factors found in step 2 above, -10 and 9
6x2 - 10x + 9x - 15
Step-4 : Add up the first 2 terms, pulling out like factors :
2x • (3x-5)
Add up the last 2 terms, pulling out common factors :
3 • (3x-5)
Step-5 : Add up the four terms of step 4 :
(2x+3) • (3x-5)
Which is the desired factorization
