Factorize- x2 - 5 -5 x - 30

X^2 + 5 √(5) x + 30 = x^2 + 3 √(5)x + 2 √(5)x +30 ∵ 5 √(5) = 3 √(5)+ 2 √(5) 30 = 3 √(5)× 2 √(5) = x(x + 3 √(5))+ 2 √(5) (x + 3 √(5)) = (x + 3 √(5)) (x ...

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Byju's Answer

Standard IX

Mathematics

Factorisation of Quadratic Polynomials- Middle Term Splitting

Factorize: x2...

Question

Factorize:

$x^{2} + 5 \sqrt{5} x + 30$

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Solution

$x^{2} + 5 \sqrt{5} x + 30 = x^{2} + 3 \sqrt{5} x + 2 \sqrt{5} x + 30 {\begin{matrix} ∵ 5 \sqrt{5} = 3 \sqrt{5} + 2 \sqrt{5} 30 = 3 \sqrt{5} \times 2 \sqrt{5} \end{matrix}} = x (x + 3 \sqrt{5}) + 2 \sqrt{5} (x + 3 \sqrt{5}) = (x + 3 \sqrt{5}) (x + 2 \sqrt{5})$

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Factorize: x2+5√5x+30

x2+5√5x+30=x2+3√5x+2√5x+30{∵5√5=3√5+2√530=3√5×2√5}=x(x+3√5)+2√5(x+3√5)=(x+3√5)(x+2√5)

Factorize:

$x^{2} + 5 \sqrt{5} x + 30$

$x^{2} + 5 \sqrt{5} x + 30 = x^{2} + 3 \sqrt{5} x + 2 \sqrt{5} x + 30 {\begin{matrix} ∵ 5 \sqrt{5} = 3 \sqrt{5} + 2 \sqrt{5} 30 = 3 \sqrt{5} \times 2 \sqrt{5} \end{matrix}} = x (x + 3 \sqrt{5}) + 2 \sqrt{5} (x + 3 \sqrt{5}) = (x + 3 \sqrt{5}) (x + 2 \sqrt{5})$