# Ex.14.3 Q1 Factorization - NCERT Maths Class 8

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## Question

Carry out the following divisions.

(i)\begin{align}\quad 28{x^4} \div 56x\end{align}

(ii)\begin{align}\quad - 36{y^3} \div 9{y^2}\end{align}

(iii)\begin{align}\quad 66p{q^2}{r^3} \div 11q{r^2}\end{align}

(iv)\begin{align}\quad 34{x^3}{y^3}{z^3} \div 51x{y^2}{z^3}\end{align}

(v)\begin{align}\quad 12{a^8}{b^8} \div ( { - 6{a^6}{b^4}} )\end{align}

## Text Solution

(i)$$\,28{x^4} \div 56x$$

What is known?

Algebraic expression.

What is unknown?

Division of the algebraic expression.

Reasoning:

Find out factor of $$28{x}^4$$ and $$56{x}$$ then cancel out common factor of$$28{x}^4$$ and $$56{x}$$.

Steps:

($$28{x^4}$$can be written as$$2 \times 2 \times 7 \times x \times x \times x \times x$$) and ($$56x$$ can be written as$$2 \times 2 \times 2 \times 7 \times x$$)

Then,

\begin{align}28{x^4} \div 56x &= \frac{{2 \times 2 \times 7 \times x \times x \times x \times x}}{{2 \times 2 \times 2 \times 7 \times x}}\\ &= \frac{{{x^3}}}{2}\\ &= \frac{1}{2}{x^3}\end{align}

(ii)$$\,- 36{y^3} \div 9{y^2}$$

What is known?

Algebraic expression.

What is unknown?

Division of the algebraic expression.

Reasoning:

Find out factor of $$-36{y^3}$$ and $$9{y^2}$$ then cancel out common factor of $$-36{y^3}$$ and $$9{y^2}$$

($$- 36{y^3}$$can be written as$$- 2 \times 2 \times 3 \times 3 \times y \times y \times y$$) and ($$9{y^2}$$can be written as$$3 \times 3 \times y \times y$$)

Then,

\begin{align}- 36{y^3} \div 9{y^2} &= \frac{{ - 2 \times 2 \times 3 \times 3 \times y \times y \times y}}{{3 \times 3 \times y \times y}}\\ &= - 4y\end{align}

(iii)$$\;66p{q^2}{r^3} \div 11q{r^2}$$

What is known?

Algebraic expression.

What is unknown?

Division of the algebraic expression.

Reasoning:

Find out factor of $$66p{q^2}$$ and $$11p{r^2}$$ then cancel out common factor of $$66p{q^2}$$ and $$11q{r^2}$$

($$66p{q^2}{r^3}$$ can be written as $$2 \times 3 \times 11 \times p \times q \times q \times r \times r \times r$$) and ($$11q{r^2}$$can be written as $$11 \times q \times r \times r$$)

Then,

\begin{align} 66p{q^2}{r^3} \div 11q{r^2} &= \frac{{2 \times 3 \times 11 \times p \times q \times q \times r \times r \times r}}{{11 \times q \times r \times r}}\\&= 6pqr\end{align}

(iv)$$\,34{x^3}{y^3}{z^3} \div 51x{y^2}{z^3}$$

What is known?

Algebraic expression.

What is unknown?

Division of the algebraic expression.

Reasoning:

Find out factor of $$34{x^3}{y^3}{z^3}$$ and $$51x{y^2}{z^3}$$ then cancel out common factor of $$34{x^3}{y^3}{z^3}$$ and $$51x{y^2}{z^3}$$

($$34{x^3}{y^3}{z^3}$$ can be written as$$2 \times 17 \times x \times x \times x \times y \times y \times y \times z \times z \times z$$) and ($$51x{y^2}{z^3}$$ can be written as $$3 \times 17 \times x \times y \times y \times z \times z \times z$$)

Then,

\begin{align}34{x^3}{y^3}{z^3} \div 51x{y^2}{z^3} &= \frac{{2 \times 17 \times x \times x \times x \times y \times y \times y \times z \times z \times z}}{{3 \times 17 \times x \times y \times y \times z \times z \times z}}\\&= \frac{2}{3}{x^2}y\end{align}

(v)$$\;12{a^8}{b^8} \div \left( { - 6{a^6}{b^4}} \right)$$

What is known?

Algebraic expression.

What is unknown?

Division of the algebraic expression.

Reasoning:

Find out factor of $$12{a^8}{b^8}$$ and $$- 6{a^6}{b^4}$$ then cancel out common factor of $$- 6{a^6}{b^4}$$ and $$51x{y^2}{z^3}$$

($$12{a^8}{b^8}$$can be written as$$2 \times 2 \times 3 \times {a^8} \times {b^8}$$) and ($$- 6{a^6}{b^4}$$can be written as$$- 2 \times 3 \times {a^6} \times {b^4}$$)

Then,

\begin{align}12{a^8}{b^8} \div \left( { - 6{a^6}{b^4}} \right) &= \frac{{2 \times 2 \times 3 \times {a^8} \times {b^8}}}{{ - 2 \times 3 \times {a^6} \times {b^4}}}\\&= - 2{a^2}{b^4}\end{align}