Question

Find the product h ⋅ k(x) if h(x) = 2(3x – 5) and k(x) = –2x + 1?

a) h ⋅ k(x) = 12x² – 26x + 10
b) h ⋅ k(x) = 12x² + 26x – 4
c) h ⋅ k(x) = –12x² + 26x – 10
d) h ⋅ k(x) = 4x – 9

Answer 1

The product of h(x) = 2(3x - 5) and k(x) = -2x + 1 is found by expanding h(x) and using the distributive property to multiply both expressions. The result is h ⋅ k(x) = -12x^2 + 26x - 10.

Step-by-step explanation:

To find the product h ⋅ k(x) where h(x) = 2(3x − 5) and k(x) = −2x + 1, we need to multiply these two expressions together.

First, let's expand h(x):

h(x) = 2(3x − 5) = 6x − 10

Now, let's multiply h(x) by k(x):

h ⋅ k(x) = (6x − 10)(−2x + 1)

We can use the distributive property (FOIL method) to find the product:

• (6x)(−2x) = −12x2
• (6x)(1) = 6x
• (−2x)(−10) = 20x
• (−10)(1) = −10

Combining like terms, we get:

h ⋅ k(x) = −12x2 + (6x + 20x) − 10 = −12x2 + 26x − 10

Therefore, the correct product of h(x) and k(x) is −12x2 + 26x − 10, which corresponds to option (c).