Question

(X^2+ x– 12) (x^2+ 10x + 25)

When you multiply the two quadratic trinomials together, the coefficient for x is:

Answer 1

`\qquad \qquad\huge \underline{\boxed{\sf Answer}}`

let's evaluate ~

`\qquad \sf  \dashrightarrow \: ( {x}^(2) + x - 12)( {x}^(2) + 10x + 25)`

`\qquad \sf  \dashrightarrow \: {x}^(4) + 10 {x}^(3) + 25 {x}^(2) + {x}^(3) + 10 {x}^(2) + 25x - 12 {x}^(2) - 120x - 300`

`\qquad \sf  \dashrightarrow \: {x}^(4) + 11 {x}^(3) + 23 {x}^(2) - 95x - 300`

In the given expression we can clearly observe that the Coefficient of x is " -95 "

Answer 2

• (x² + x – 12)(x² + 10x + 25)
• => (x⁴ + 10x³ + 25x²) + (x³ + 10x² + 25x) + (-12x² - 120x - 300)
• => x⁴ + 10x³ + 25x² + x³ + 10x² + 25x - 12x² - 120x - 300
• => x⁴ + (10x³ + x³) + (25x² + 10x² - 12x²) + (25x - 120x) - 300
• => x⁴ + (11x³) + (23x²) + (-95x) - 300
• => x⁴ + 11x³ + 23x² - 95x - 300

The only term that has a x-variable is "-95x".

The coefficient of x is -95.