Question

x²+1250x-375000
solve by middle spilliting​

Answer 1

Answer:

(x + 1500) (x - 250)

Step-by-step explanation:

Solving by splitting

$\: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \implies \sf \: {x}^{2} + 1250x - 375000$

• We need a number which will add together to 1250.

&

• Give a product as -375000

we get,

=> -250 + 1500 = 1250

=> -250 × 1500 = -375000

Let's Put it here,

$\: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \implies \sf \: \: {x}^{2} + 1500x - 250x - 375000$

$\: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: {\boxed { \implies \sf{(x + 1500)(x - 250)}}}$

What is needed -

• To factorize a quadratic equation splitting the middle term is much preferred.

• We search for a set of number which will add together to middle term. And also the same set of number should give a product as the last term.

• If p(a) = 0, p(b) = 0, then 'a,' and 'b' are factors. Now, you need to find what all possible values'a' and 'b' could take where constant term = a.b (375000 in this question.)

Answer 2

Solution :-

Given that, x² + 1250x - 375000.

[ By splitting middle term, We get : ]

↪ x² + 1500x - 250x - 375000

↪ x (x + 1500) - 250(x + 1500)

↪ ${\boxed{\red{\tt{(x + 1500) (x - 250)}}}}$

Some algebraic identities :-

• a² – b² = (a – b)(a + b)

• (a + b)² = a² + 2ab + b²

• a² + b² = (a + b)² – 2ab

• (a – b)² = a² – 2ab + b²

• (a+b+c)² =a²+b²+c²+2ab+ 2bc+2ca

• (a-b-c)² = a²+b²+ c²-2ab+2bc- 2ca

• (a + b)³ = a³ + 3a²b + 3ab²+ b³

• (a – b)³ = a³ – 3a²b + 3ab² – b³

• a³– b³ = (a – b)(a²+ ab + b²)

• a³ + b³ = (a + b)(a²– ab + b²)