Chapter 6

Factor each trinomial completely. If a polynomial can't be factored, write "prime." $$ 13+14 m+m^{2} $$

Factor each trinomial completely. See Examples 1 through 5 . \(x+3 x^{2}-2\)

Solve each equation. $$ (x+0.2)(x+1.5)=0 $$

Factor each trinomial completely. $$ 2 n^{2}-28 n+98 $$

The equation \(D=\frac{1}{2} n(n-3)\) gives the number of diagonals \(D\) for a polygon with \(n\) sides. For example, a polygon with 6 sides has \(D=\frac{1}{2} \cdot 6(6-3)\) or \(D=9\) diagonals. (See if you can count all 9 diagonals. Some are shown in the figure.) Use this equation, \(D=\frac{1}{2} n(n-3),\) Find the number of diagonals for a polygon that has 15 sides.

Factor each trinomial by grouping. Exercises 9 through 12 are broken into parts to help you get started. $$ 10 x^{2}-9 x+2 $$

Find the \(G C F\) for each list. $$ -21 x^{3}, 14 x $$

Factor each trinomial completely. If a polynomial can't be factored, write "prime." $$ 17+18 n+n^{2} $$

Solve each equation. $$ (x+1.7)(x+2.3)=0 $$

Factor each trinomial completely. $$ x^{2} y^{2}-10 x y+25 $$

Find the number of diagonals for a polygon that has 15 sides.Find the number of sides \(n\) for a polygon that has 35 diagonals.

Factor each trinomial by grouping. Exercises 9 through 12 are broken into parts to help you get started. $$ 2 x^{2}-7 x+5 $$

Find the \(G C F\) for each list. $$ 12 x^{3},-6 x^{4}, 3 x^{5} $$

Factor each trinomial completely. If a polynomial can't be factored, write "prime." $$ 10 t-24+t^{2} $$

Factor each trinomial completely. See Examples 1 through 5 . \(6 x^{2}-13 x y+5 y^{2}\)

Solve. $$ x^{2}-13 x+36=0 $$

Factor each trinomial completely. $$ 4 x^{2} y^{2}-28 x y+49 $$

The equation \(D=\frac{1}{2} n(n-3)\) gives the number of diagonals \(D\) for a polygon with \(n\) sides. For example, a polygon with 6 sides has \(D=\frac{1}{2} \cdot 6(6-3)\) or \(D=9\) diagonals. (See if you can count all 9 diagonals. Some are shown in the figure.) Use this equation, \(D=\frac{1}{2} n(n-3),\) Find the number of sides \(n\) for a polygon that has 14 diagonals.

Factor each trinomial by grouping. Exercises 9 through 12 are broken into parts to help you get started. $$ 2 x^{2}-7 x+3 $$

Find the \(G C F\) for each list. $$ 15 y^{2}, 5 y^{7},-20 y^{3} $$

Factor each trinomial completely. If a polynomial can't be factored, write "prime." $$ 6 q-27+q^{2} $$

Factor each trinomial completely. See Examples 1 through 5 . \(8 x^{2}-14 x y+3 y^{2}\)

Solve. $$ x^{2}+2 x-63=0 $$

Factor each trinomial completely. $$ m^{3}+18 m^{2}+81 m $$

Find the \(G C F\) for each list. $$ -18 x^{2} y, 9 x^{3} y^{3}, 36 x^{3} y $$

Factor each trinomial completely. If a polynomial can't be factored, write "prime." $$ a^{2}-10 a b+16 b^{2} $$

Solve. $$ x^{2}+2 x-8=0 $$

Factor each trinomial completely. $$ y^{3}+12 y^{2}+36 y $$

The product of two consecutive page numbers is 420. Find the page numbers.

Find the \(G C F\) for each list. $$ 7 x^{3} y^{3},-21 x^{2} y^{2}, 14 x y^{4} $$

Factor each trinomial completely. If a polynomial can't be factored, write "prime." $$ a^{2}-9 a b+18 b^{2} $$

Factor each trinomial completely. See Examples 1 through 5 . \(25 n^{2}-5 n-6\)

Solve. $$ x^{2}-5 x+6=0 $$

Factor each trinomial completely. $$ 1+6 x^{2}+x^{4} $$

The product of two consecutive room numbers is 210. Find the room numbers.

Factor each trinomial by grouping. Exercises 9 through 12 are broken into parts to help you get started. $$ 4 x^{2}-8 x-21 $$

Find the \(G C F\) for each list. $$ 20 a^{6} b^{2} c^{8}, 50 a^{7} b $$

Factor each trinomial completely. Some of these trinomials contain a greatest common factor (other than 1). Don't forget to factor out the GCF first. $$ 2 z^{2}+20 z+32 $$

Factor each trinomial completely. See Examples 1 through 5 . \(-9 x+20+x^{2}\)

Solve. $$ x^{2}-7 x=0 $$

Factor each trinomial completely. $$ 1+16 x^{2}+x^{4} $$

The product of two consecutive room numbers is 210. Find the room numbers

Factor each trinomial by grouping. Exercises 9 through 12 are broken into parts to help you get started. $$ 6 x^{2}-11 x-10 $$

Find the \(G C F\) for each list. $$ 40 x^{7} y^{2} z, 64 x^{9} y $$

Factor each trinomial completely. Some of these trinomials contain a greatest common factor (other than 1). Don't forget to factor out the GCF first. $$ 3 x^{2}+30 x+63 $$

Factor each trinomial completely. See Examples 1 through 5 . \(-7 x+12+x^{2}\)

Solve. $$ x^{2}-3 x=0 $$

Factor each trinomial completely. $$ 9 x^{2}-24 x y+16 y^{2} $$

A ladder is leaning against a building so that the distance from the ground to the top of the ladder is one foot less than the length of the ladder. Find the length of the ladder if the distance from the bottom of the ladder to the building is 5 feet.

Factor each trinomial by grouping. Exercises 9 through 12 are broken into parts to help you get started. $$ 10 x^{2}-23 x+12 $$