+0

# coefficient

0
3
1
+794

plz help me

What is the coefficient of x^2 in (x^3 + x^2 + x + 1)(x^4 + 3x^3 + 8x + 7x + 1)?

Dec 26, 2023

#1
+676
+1

What is the coefficient of x^2 in (x^3 + x^2 + x + 1)(x^4 + 3x^3 + 8x + 7x + 1)?

Is that 8x a typo that should have been 8x2 ?

To get the product, you have to multiply every term inside the

first parentheses times every term in the second parentheses.

You could write it like this

x3 • (x4 + 3x3 + 15x + 1)       (1)

plus                                            x2 • (x4 + 3x3 + 15x + 1)       (2)

plus                                              x • (x4 + 3x3 + 15x + 1)       (3)

plus                                              1 • (x4 + 3x3 + 15x + 1)       (4)

Let's count up everything that results in an x to the second power.

From (1) there is no x2

From (2)                                     1 x2

From (3)                                   15 x2

From (4) there is no x2

Totalling up the x2 we have 16x2 so the coefficient of the x2 term is 16.

.

Dec 26, 2023