Question

If ((2x + 3) (ax -5) = 12x^2 + bx -15) for all values of x, what is the value of b?

a) -21
b) -15
c) -9
d) -3

Answer 1

If ((2x + 3) (ax -5) = 12x² + bx -15) for all values of x, the value of b is c) -9.

Step-by-step explanation:

The given equation is ((2x + 3) (ax - 5) = 12x² + bx - 15). To find the value of b, let's multiply the terms on the left side of the equation and compare coefficients.

First, distribute the terms:

`\[ (2x + 3)(ax - 5) = 2x(ax - 5) + 3(ax - 5) \]`

`\[ = 2ax^2 - 10x + 3ax - 15 \]`

Combine like terms:

`\[ = 2ax^2 + (3a - 10)x - 15 \]`

Now, compare the result with the given expression (12x² + bx - 15):

`\[ 2ax^2 + (3a - 10)x - 15 = 12x^2 + bx - 15 \]`

By comparing coefficients, we can equate corresponding terms:

`\[ 2a = 12 \Rightarrow a = 6 \]`

`\[ 3a - 10 = b \Rightarrow 3(6) - 10 = b \Rightarrow b = 18 - 10 = 8 \]`

Therefore, the correct value for b is 8. However, this contradicts the provided options. It seems there might be a typo in the options, and the correct value for b should be -8. Please double-check the options.