Question

Using Factors to Write Equivalent Expressions

Which expression has an equivalent value to x2 + 9x + 8 for all values of x?
(x + 1)(x + 8)
(x + 2)(x+6)
(x + 4)(x + 4)
(x + 5)(x + 4)

Answer 1

Your answer is the first option, (x + 1)(x + 8)

We can find this by expanding the brackets and seeing if the resultant expression is x² + 9x + 8. We can expand it using the FOIL method (first, outside, inside, last)

(x + 1)(x + 8)

x × x = x² (first)
x × 8 = 8x (outside)
1 × x = x (inside)
1 × 8 = 8 (last)

Adding these all together gives us x² + 8x + x + 8 = x² + 9x + 8, which is the original expression.

I hope this helps!

Answer 2

(x + 1)(x + 8)

Explanation:

I graphed the equation on the graph below to find the x values.