+0

+1
199
3

What is the coefficient of x^3 when

24x^4+6x^3+4x^2-7x-5

is multiplied by

6x^3+3x^2+3x+4

and the like terms are combined?

Dec 28, 2018

#1
+4322
+2

As you can see, just distribute as these range by increasing power. The answer should be -15. $$144x^7+108x^6+114x^5+84x^4\boxed{-15}x^3-20x^2-43x-20$$

.
Dec 28, 2018
#3
+800
-1

CoolStuffYT  Dec 28, 2018
#2
+800
-1

We want the $$x^3$$ coefficient of:

($$24x^4+6x^3+4x^2-7x-5)(6x^3+3x^2+3x+4)$$

We see that the only ways of this is $$x^3*x^0, x^2*x^1$$ .

Therefore, knock out the $$24x^4$$ .

Now pair some numbers: $$6x^3\times 4, 4x^2\times 3x, -7x \times 3x^2, -5 \times 6x^3$$

Expanding, we get $$24x^3+12x^3-21x^3-30x^3=3x^3-18x^3=-15x^3$$

Therefore, the coefficient of $$x^3$$ is -15.

You are very welcome!

:P

Dec 28, 2018