Determine whether the statement is true or false. If the statement is false, make the necessary change(s) to produce a true statement.

The polynomial $16 x^2+20 x+25$ is a perfect square trinomial.

Factor completely.

$$y^7+y$$

Determine whether the statement is true or false. If the statement is false, make the necessary change(s) to produce a true statement.

Any polynomial that is the sum of two squares is prime.

Multiply: $(x+7)(x+10)$.

Determine whether the statement is true or false. If the statement is false, make the necessary change(s) to produce a true statement.

All perfect square trinomials are squares of binomials.

Factor completely.

$$x^2+14 x+49-16 a^2$$

Use a graphing utility to graph each side of the equation in the same viewing rectangle. Do the graphs coincide? If so, this means that the polynomial on the left side has been factored correctly. If not, factor the polynomial correctly and then use your graphing utility to verify the factorization.

$$x^2+2 x+x+2=x(x+2)+1$$

Factor completely, or state that the polynomial is prime.

$$6 y^3+9 y^2+3 y$$

Use the method of your choice to factor each trinomial, or state that the trinomial is prime. Check each factorization using FOIL multiplication.

$$3 x^2+14 x-5$$

Factor completely, or state that the polynomial is prime.

$$3 x^2+10 x y+7 y^2$$

Fill in each blank so that the resulting statement is true.

True or false: $x^2+8 x+16$ is a perfect square trinomial. _____.

Factor completely, or state that the trinomial is prime.

$$x^2+19 x+48$$

Use factoring to solve the quadratic equation. Check by substitution or by using a graphing utility and identifying $x$-intercepts.

$$x^2+x-42=0$$

Factor the polynomial.

$$x^2-4 x+4$$