How do you factor 100x^2-9x^2?

Question

Also, can you helpme figure this...
How to write a polynomial function of least degreethat has real coefficients, a leading coefficient of 1, and...
a. -4,-1,3
b. -1, 3i
...as zeros.

I am sorry I meant 100x^2-9y^2

Answer 1

Aha! The famous difference of squares:

(10 - 3y)(10x + 3y)

In a., we will need a cubic equation to get three zeros.

y = x^3 + bx^2 + cx + d

Now y will be zero when x is -4, or -1, or 3.

0 = (-4)^3 + b(-4)^2 + c(-4) + d
0 = (-1)^3 + b(-1)^2 + c(-1) + d
0 = (3)^3 + b(3)^2 + c(3) + d

Solve three equations in three unknowns.

b. is impossible, because imaginary roots always appear in conjugate pairs, so if 3i is a root, -3i must be also.

Answer 2

100x^2 - 9x^2 = 91x^2