what is k(p)= (p+3)(p-7)
FOIL
First: p^2
Outer: -7p
Inner:3p
last: -21
add them: k(p)=p^2-4p-21
(p+3)*(p-7)=p*p+p*3-7*p-7*3
=p^2+3p-7p-21
=p^2-4p-21
k(p)=p^2-4p-21
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The expression k(p) = (p + 3)(p - 7) represents a polynomial function. To understand what this expression means, let's break it down step by step:
Step 1: Distribute
Use the distributive property to expand the expression.
k(p) = p(p - 7) + 3(p - 7)
Step 2: Multiply
Multiply each term inside the parentheses.
k(p) = p^2 - 7p + 3p - 21
Step 3: Combine like terms
Combine the terms with the same exponent.
k(p) = p^2 - 4p - 21
So, the polynomial function k(p) = (p + 3)(p - 7) simplifies to k(p) = p^2 - 4p - 21. This function represents a quadratic function, where p is the independent variable and k(p) is the dependent variable.