can u do test 1 section 3 #15?

Sure! This one is all about corresponding coefficients of equivalent polynomials. When you expand what you’re given…

    \begin{align*}(ax+2)(bx+7)&=15x^2+cx+14\\abx^2+7ax+2bx+14&=15x^2+cx+14\\abx^2+(7a+2b)x+14&=15x^2+cx+14\end{align*}

…you can conclude that the corresponding coefficients of x^2 and x are equal. In other words, you know that ab=15 and 7a+2b=c. Since the question also tells you that a+b=8, you know that either a=3 and b=5 or a=5 and b=3. (Otherwise, ab won’t equal 15!)

The two possible values for c, then, are:

    \begin{align*}7(3)+2(5)&=31\\7(5)+2(3)&=41\end{align*}

That’s answer choice D.

Leave a Reply