Question

find the factor of
x²+15x-100
​

Answer 1

(x-5)(+20) factor of x²+15x-100

Answer 2

Answer:

(x-5) (x+20)

Step-by-step explanation:

Step 1: Multiply last term and first term of this expression (-100x^2)

Step 2: Write the above term as a product of two factors

So, the factors can be said as,

1 x 100

2 x 50

4 x 25

5 x 20

10 x 10

Step 3: Observe the sign before the above term. If the sign is positive (+), then both factors will bear the same sign and if we add both factors, the sum should be equal to the coefficient of the middle term.

But if the sign is negative (-), then both factors will bear different signs and if we subtract both factors, the answer should be equal to the coefficient of the middle term.

In this case, before 100 there is a - sign. So we have to see, which two terms can be subtracted from one another to obtain 15.

From the above factors, only 20 and 5 fits this category.

Since the sign is - , then both will have different signs.

Theory: The larger factor will bear the same sign as the middle term. So, by considering these, you can write +ve value for 20 and -ve value for 5.

$x^{2} +$20x -5x - 100

=x(x+20)-5(x+20)

(x-5) (x+20)

Hope this was helpful and understandable:)