Factorizing 40 + 3x - x²
To factorize the given expression 40 + 3x - x², we need to follow a systematic approach to identify common factors and simplify the expression.

Step 1: Rearrange the terms
Rearrange the terms in descending order of powers of x:
-x² + 3x + 40

Step 2: Find the factors of the quadratic expression
To factorize a quadratic expression, we need to find two numbers that multiply to -40 (coefficient of the constant term) and add up to 3 (coefficient of the linear term). These numbers are 8 and -5.

Step 3: Rewrite the middle term
Rewrite the middle term using the two numbers found in the previous step:
-x² + 8x - 5x + 40

Step 4: Group the terms
Group the terms in pairs:
x(x - 8) - 5(x - 8)

Step 5: Factor out the common binomial
Factor out the common binomial (x - 8):
(x - 8)(x - 5)
Therefore, the factorized form of the expression 40 + 3x - x² is (x - 8)(x - 5).

40+3x-x^2=40+8x-5x-x^2=8(5+x)-x(5+x)(8-x)(5+x)(Ans).