91Ó°ÊÓ

In Exercises 57 and 58 , find all integers \(b\) such that the trinomial can be factored. $$ x^{2}+b x+18 $$

In Exercises \(51-62\), factor the polynomial by grouping. $$ 4 x^{2}-14 x+14 x-49 $$

A formula for the sum of the first \(n\) natural numbers is \(1+2+3+\cdots+n=\frac{1}{2} n(n+1)\). (a) Use the formula to find the sum of the first 15 natural numbers \((1+2+3+\cdots+15)\). (b) Use the formula to find \(n\) when the sum of the first \(n\) natural numbers is 210 .

In Exercises 57 and 58 , find all integers \(b\) such that the trinomial can be factored. $$ x^{2}+b x+10 $$

A formula for the sum of the first \(n\) natural numbers is \(1+2+3+\cdots+n=\frac{1}{2} n(n+1)\). (a) Use the formula to find the sum of the first 15 natural numbers \((1+2+3+\cdots+15)\). $$ \begin{array}{|l|l|l|l|l|} \hline X & 1 & 2 & 3 & 4 \\ \hline 5 & & & & \\ \hline \end{array} $$ (b) Use the formula to find \(n\) when the sum of the first \(n\) natural numbers is 210 .

Find two integers \(c\) such that the trinomial can be factored. (There are many correct answers.) $$ 8 x^{2}-3 x+c $$

What is the first thing you should do when you factor a polynomial?

In Exercises \(51-62\), factor the polynomial by grouping. $$ 4 x^{2}-6 x+6 x-9 $$

In Exercises \(51-62\), factor the polynomial by grouping. $$ 6 x^{2}+3 x-2 x-1 $$

In Exercises 59-62, determine whether the statement is true or false. Justify your answer. The only solution of \(x^{2}=4 x\) is \(x=4\).