Question 1209342: What is the coefficient of x^2 in (x^3 + x^2 + x + 1)(5x^7 - 3x^4 + 10x^2 - 15)? Found 3 solutions by mccravyedwin, math_tutor2020, greenestamps:Answer by mccravyedwin(407) (Show Source):
(x3 + x2 + x + 1)(5x7 - 3x4 + 10x2 - 15)
We'll get a term in x2 when we
A. multiply the term x2 in the expression on the left by the term
-15 in the expression on the right, getting -15x2.
and when we
B. multiply the term 1 in the expression on the left by the 10x2 in
the expression on the right, getting 10x2
That's -15x2 + 10x2 = -5x2,
And the coefficient is ---
tada! ---
-5
Edwin
Place the terms of f(x) along the top.
Place the terms of g(x) along the left side.
x^3
x^2
x
1
5x^7
-3x^4
10x^2
-15
To fill out this table, we multiply the headers.
For instance 5x^10 would go in the top left corner (because x^3 times 5x^7 = 5x^10).
But since 5x^10 isn't an x^2 term, we'll leave this cell blank.
We only fill the cells that have x^2 in them
x^3
x^2
x
1
5x^7
-3x^4
10x^2
10x^2
-15
-15x^2
That would be -15x^2 and 10x^2
They combine to -5x^2
The partial products that contribute to the x^2 term in the product come from multiplying....
(1) the x^2 term in the first polynomial and the constant term in the second: (x^2)(-15) = -15x^2
(2) the x term in the first polynomial and the x term in the second: (x)(0x) = 0x^2
(1) the constant term in the first polynomial and the x^2 term in the second: (1)(10x^2) = 10x^2
(-15x^2) + (0x^2) + (10x^2) = -5x^2
ANSWER: the coefficient of x^2 in the product is -5
(