Question

Given that f(x) = 2x + 12x + 23, Express f(x) in the form p(x +q) +r where p. q and r are integers to be found.

Answer 1

To express f(x) in the form p(x + q) + r, the given expression needs to be simplified by combining like terms and then factor out the coefficient of x. The final expression is 14(x + 0) + 23.

Step-by-step explanation:

To express f(x) in the form p(x +q) +r, we need to simplify the given expression. Combining like terms, we have f(x) = 14x + 23. Now, we need to factor out the coefficient of x to get p(x +q) +r form.

Step 1: Factor out the coefficient of x: 14(x) + 23 = 14x + 23.

Step 2: Identify p as the coefficient of x: p = 14.

Step 3: Identify q as 0, since there is no constant term in p(x + q) + r.

Step 4: Identify r as the constant term in the expression: r = 23.

Therefore, f(x) in the form p(x +q) +r is 14(x + 0) + 23.