Chapter 8.5, Problem 63PFA

a.

To determine

To find: Factor the given expression.

Answer to Problem 63PFA

  $6y^3+21y^2+4y+14=\left(3y^2+2\right)\left(2y+7\right)$

Explanation of Solution

Given information:

  $6y^3+21y^2+4y+14$

Given

  $6y^3+21y^2+4y+14$

On simplifying

We get

  $\begin{array}{l}6y^3+21y^2+4y+14=6y^3+4y+21y^2+14\\ \Rightarrow 6y^3+21y^2+4y+14=2y\left(3y^2+2\right)+7\left(3y^2+2\right)\\ \Rightarrow 6y^3+21y^2+4y+14=\left(3y^2+2\right)\left(2y+7\right)\end{array}$

Therefore,

On factoring

We get

  $6y^3+21y^2+4y+14=\left(3y^2+2\right)\left(2y+7\right)$

b.

To determine

To find: Factor the given expression.

Answer to Problem 63PFA

  $12a^2-20ab+9ay-15by=\left(4a+3y\right)\left(3a-5b\right)$

Explanation of Solution

Given information:

  $12a^2-20ab+9ay-15by$

Given

  $12a^2-20ab+9ay-15by$

On simplifying

We get

  $\begin{array}{l}12a^2-20ab+9ay-15by=12a^2+9ay-20ab-15by\\ \Rightarrow 12a^2-20ab+9ay-15by=3a\left(4a+3y\right)-5b\left(4a+3y\right)\\ \Rightarrow 12a^2-20ab+9ay-15by=\left(4a+3y\right)\left(3a-5b\right)\end{array}$

Therefore,

On factoring

We get

  $12a^2-20ab+9ay-15by=\left(4a+3y\right)\left(3a-5b\right)$

c.

To determine

To find: Factor the given expression.

Answer to Problem 63PFA

  $4w^3+3wz-8w^2-6z=\left(w-2\right)\left(4w^2+3z\right)$

Explanation of Solution

Given information:

  $4w^3+3wz-8w^2-6z$

Given

  $4w^3+3wz-8w^2-6z$

On simplifying

We get

  $\begin{array}{l}4w^3+3wz-8w^2-6z=4w^3-8w^2+3wz-6z\\ \Rightarrow 4w^3+3wz-8w^2-6z=4w^2\left(w-2\right)+3z\left(w-2\right)\\ \Rightarrow 4w^3+3wz-8w^2-6z=\left(w-2\right)\left(4w^2+3z\right)\end{array}$

Therefore,

On factoring

We get

  $4w^3+3wz-8w^2-6z=\left(w-2\right)\left(4w^2+3z\right)$

d.

To determine

To find: Factor the given expression.

Answer to Problem 63PFA

  $15m^{2}n+27m{n}^2=3mn\left(5m+9n\right)$

Explanation of Solution

Given information:

  $15m^{2}n+27m{n}^2$

Given

  $15m^{2}n+27m{n}^2$

On simplifying

We get

  $15m^{2}n+27m{n}^2=3mn\left(5m+9n\right)$

Therefore,

On factoring

We get

  $15m^{2}n+27m{n}^2=3mn\left(5m+9n\right)$

e.

To determine

To find: Factor the given expression.

Answer to Problem 63PFA

  $8wy+12xy+10wz+15xz=\left(4y+5z\right)\left(2w+3x\right)$

Explanation of Solution

Given information:

  $8wy+12xy+10wz+15xz$

Given

  $8wy+12xy+10wz+15xz$

On simplifying

We get

  $\begin{array}{l}8wy+12xy+10wz+15xz=8wy+10wz+12xy+15xz\\ \Rightarrow 8wy+12xy+10wz+15xz=2w\left(4y+5z\right)+3x\left(4y+5z\right)\\ \Rightarrow 8wy+12xy+10wz+15xz=\left(4y+5z\right)\left(2w+3x\right)\end{array}$

Therefore,

On factoring

We get

  $8wy+12xy+10wz+15xz=\left(4y+5z\right)\left(2w+3x\right)$