154k views
0 votes
Is X +10 a factor of F(x)= 5X^3 +60X^2+109X+90?

User Tmont
by
8.9k points

1 Answer

1 vote

Answer: Yes.

Explanation:

To see if it is a factor, we can check a few ways. I will show two here. First, we can graph. If the line intercepts the x-axis at x = -10, it is a factor. I have attached a picture of this graph, it does indeed intercept at this point.

A second way is to factor the given function. To do this, we will factor by grouping. This involves "breaking" the terms apart and factoring with different groups. Then, we are left with the same factor being multiplied by two different numbers. This becomes our other factor.

F(x) = 5x³ + 60x² + 109x + 90

F(x) = 5x³ + 10x² + 50x² + 100x + 9x + 90

F(x) = 5x³ + 10x² + 9x + 50x² + 100x + 90

F(x) = x(5x² + 10x + 9) + 10(5x² + 10x + 9)

F(x) = (x + 10)(5x² + 10x + 9)

Yes, (x + 10) is a factor of F(x) = 5x³ + 60x² + 109x + 90 and x = -10 is a solution.

Is X +10 a factor of F(x)= 5X^3 +60X^2+109X+90?-example-1
User Bay
by
7.9k points

Related questions

asked Dec 6, 2024 117k views
Spamdark asked Dec 6, 2024
by Spamdark
7.6k points
2 answers
3 votes
117k views
asked Sep 28, 2024 72.6k views
Jjpcondor asked Sep 28, 2024
by Jjpcondor
7.2k points
1 answer
1 vote
72.6k views
1 answer
1 vote
175k views