What is the coefficient of x in (x^3 + x^2 + x + 1)(x^4 + 3x^3 + 4x^2 + 8x + 7)?
Expanding the product, we get \(x^7 + 4x^6 + 4x^5 + 19x^4 + 19x^3 + 16x^2 + 16x + 1\). We see that the coefficient of x is 16.
What is the coefficient of x in (x^3 + x^2 + x + 1)(x^4 + 3x^3 + 4x^2 + 8x + 7)?
(x3 + x2 + x + 1)(x4 + 3x3 + 4x2 + 8x + 7) x • 7 = 7x
(x3 + x2 + x + 1)(x4 + 3x3 + 4x2 + 8x + 7) 1 • 8x = 8x
add them up
15x
.
The 'x' coefficient will be the result of
1 * 8x + x * 7 = 8x + 7x = 15 x the coefficient of 'x' will be 15