Gujarat BoardEnglish MediumSTD 8MATHSFactorization1 Mark
MCQ
Divide $44(a^2 - 5a^3 - 50a^2)$ by $11a(a - 10)$
A
$4a(a - 10)$
✓
$4a(a + 5)$
C
$4a$
D
$(a + 5) (a - 10)$
✓
Answer
Correct option: B.
$4a(a + 5)$
B. $4a(a + 5)$ Solution:
Write the division as a fraction
$\Rightarrow\frac{44(\text{a}^4-5\text{a}^3-50\text{a}^2)}{11\text{a}(\text{a}-10)}$
Find the factors of the numerator,
$\Rightarrow\frac{11\times4\text{a}^2(\text{a}^2-5\text{a}-50)}{11\text{a}(\text{a}-10)}$
$\Rightarrow\frac{11\times4\text{a}^2(\text{a}^2-10\text{a}+5\text{a}-50)}{11\text{a}(\text{a}-10)}$
$\Rightarrow\frac{11\times4\text{a}^2(\text{a}(\text{a}-10)+5(\text{a}-10))}{11\text{a}(\text{a}-10)}$
$\Rightarrow\frac{11\times4\text{a}^2(\text{a}+5)(\text{a}-10)}{11\text{a}(\text{a}-10)}$
Cancel the common factors from the numerator and denominator.
$\Rightarrow4(\text{a}+5)$
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