Question

Split the middle term of x²-2x-35

Answer 1

Step-by-step explanation:

x²-2x-35

x²-(7+5)x-35

x²-7x+5x-35

x(x-7)+5(x-7)

(x-7)(x+5)

therefore,(x-7) or (x+5)=0

(x-7)=0 or (x+5)=0

x=7 x=-5

therefore, x= 7, -5

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Answer 2

The polynomial given is as follows :-

x² - 2x - 35

To split the middle term of any Quadratic polynomial we have to see the a and c of the quadratic polynomial.

Thus :-

A*C of this quadratic polynomial is (-35)

This means we have to break 35 into two such numbers that their differences is equal to 2.

So,

7*5 = 35

7-5 = 2

7(-5)=(-35)

Hence,It satisfies all the requirements.

So,

We can write:-

${x}^{2} - 7x + 5x - 35 \\ \\ \\ = x(x - 7) + 5(x - 7) \\ \\ \\ = (x - 7)(x + 5)$

Equating the two factors with zero we can get the values of x.

Hence,

x = 7 or x =(-5)

Answer!