2 Points
Which of the following best describes the relationship between (x - 5) and the
polynomial 2x2 - 7x- 15?
O
A. It is impossible to tell whether (x - 5) is a factor.
O
B. (x-5) is a factor
O
C. (x - 5) is not a factor.
SUBMIT

B. (x-5) is a factor.

Step-by-step explanation:

To find out the relationship among the factor and an expression, we have to factorise it as,

2x² - 7x - 15

Here, sum = coeff. of x = -7

Product = constant × coeff of x² = -15 × 2 = -30

Now we have to find 2 numbers, which satisfies the above 2 conditions are -10 and 3.

-10 +3 = -7

-10× 3 = -30

2x² - 7x - 15

= 2x²- 10x + 3x - 15

Taking common terms as,

= 2x(x-5) +3(x - 5)

= (2x+3) (x-5)

So the expression is factorized and (x-5) is one of the factors of the expression.

step-by-step explanation:

equation

you are asked to write the equation

  expression = 0

using the given expression. when you do that, you have

  2x^2-2x-12 = 0

factoring

you can see that each of the coefficients is even, so a factor of 2 can be removed immediately.

  2(x^2 -x -6) = 0

if you multiply the binomials (x+a)(x+b), you get

  (x +a)(x +b) = x^2 +(a+b)x +ab

this tells you the coefficient of x is the sum of two factors of the constant term. here, that means -1 is the sum of two factors of -6. we want to know those factors so we can factor the trinomial.

  -6 = -1×6 = -2×3 = -3×2 = -6×1

the factor pair that sums to -1 is {-3, 2}, so our factorization is

  2(x -3)(x +2) = 0

solutions

the solutions to this equation are the values of x that make the product zero. a product is zero only when only of the factors of the product is zero. here, that means

  x - 3 = 0

  x = 3 . . . add 3 to both sides of the equation

or

  x +2 = 0

  x = -2 . . . add -2 to both sides of the equation

the solutions to the equation are x=3 or x=-2. both of these values of x satisfy the equation—they make it be true.

the third picture

step-by-step explanation: