Question

middle term splitting of x^2+32x-273

Answer 1

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Answer 2

Given:

A polynomial x^2 + 32x - 273.

To find:

The middle term splitting of the given polynomial.

Solution:

As we know that, the middle term splitting of the polynomial ax^2 + bx + c is the splitting of the middle term bx into the sum or difference of two terms px and qx such that p + q = b and pq = c.

So, as given,

We have a polynomial

${x}^{2} + 32x - 273$

This can be written as

${x}^{2} + 39x - 7x - 273$

[as 39 × (-7 ) = -273 and 39 - 7 = 32]

Now,

after grouping the terms and making factors, we have,

$x(x + 39) - 7(x + 39) = 0$

$(x + 39)(x - 7) = 0$

$x = - 39 \: and \: x = 7$

Hence, the factors obtained after splitting the middle term of the given expression is (x + 39) and (x - 7).