Question

write the co efficient of x^3,x^2 and x in the product (2x-5) (x+2) (x-3)

Answer 1

Given:

$\sf p(x)=(2x-5)(x+2)(x-3)$

To find:

coefficeint of x³,x²,x

Explanation:

$\longrightarrow \: \sf p(x) = (2x - 5)(x + 2)(x -3 ) \\ \\ \longrightarrow \: \sf p(x) =( 2 {x}^{2} + 4x - 5x - 10)(x - 3) \\ \\ \longrightarrow \: \sf p(x) =( 2x ^{2} - x - 10)(x - 3) \\ \\ \longrightarrow \: \sf p(x) = 2{x}^{3} - 6 {x}^{2} - {x}^{2} + 3x - 10x + 30 \\ \\ \longrightarrow \: \sf p(x) = 2 {x}^{3} - 7 {x}^{2} - 7x + 30$

Now

↔Coefficeint of x³=2

↔Coefficient of x²=(-7)

↔Coefficient of x=-7

More information:

For a cubic polynomial,

↔α+β+δ=-b/a (sum of roots)

↔αβ+βδ+βα=c/a

↔αβδ=-d/a(product of roots)

What is a Coefficeint?

↔Coefficient is a constant that is before a variable for a polynomial

for example

f(x)=x²-3

Here, Coefficeint of x²=1