Exam 11: Polynomials: Factoring

Write the word or phrase that best completes each statement or answers the question. Provide an appropriate response. -A student was trying to solve the problem $9 x(2 x-9)=0$ . The student knew that he or she should set $2 x-9=0$ but was confused about whether or not he or she should set $9 x=0$ , or $9=0$ and $x=0$ . How would you advise this student?

Factor. - $t^{2}+1.2 t+0.35$

Factor completely. - $6 x^{3}-9 x^{2}+4 x-6$

Factor completely. - $12 x^{4}+17 x^{2}+6$

Factor completely. - $64 x^{2}-16 x+1$

Find the GCF. - $-x^{2},-3 x,-24 x^{4}$

Factor completely. - $8 x^{2}-28 x-16$

Factor. - $5 x^{2}+25 x$

Factor by grouping. - $t^{2}+8 t+4 t+32$

Factor. - $x^{3}-x^{2}-30 x$

Solve the problem. -The product of two consecutive integers is 2 less than 2 times their sum. Find the integers.

Find the GCF. - $x^{5} y^{5}, x^{4} y^{3}, x^{4} y^{4},-x y$

Factor by grouping. - $6 x^{4}-4 x^{2}-15 x^{2}+10$

Write the word or phrase that best completes each statement or answers the question. Provide an appropriate response. -Why is the answer $\left(x^{2}-9\right)\left(x^{2}+9\right)$ not the correct answer to the instruction "Factor $\left(x^{4}\right.$ - 81) completely"?

Factor completely. - $4 m^{2}-\frac{25}{9}$

Factor by grouping. - $x^{3}-2 x^{2}-5 x+10$

Solve by factoring and using the principle of zero products. - $x(x-2)=48$

Solve using the principle of zero products. - $x(4 x+8)=0$

Factor using the ac-method. - $9 z^{2}+6 z-8$

Factor completely. - $36 x-49 x^{3}$