Answer:
C
Step-by-step explanation:
The expression given is a difference of cubes and factors as
a³ - b³ = (a - b)(a² + ab + b²)
8
= (2
)³ ⇒ a = 2
27
= (3y²)³ ⇒ b = 3y²
Hence 2 factors are
(2 - 3y²) and
((2)² + (2 × 3y²) + (3y²)²)
= (4
+ 6y² + 9
)
Hence the factored form of the expression is C
Answer:
I believe the answer is 3/7. Hope this helps!
Step-by-step explanation:
When roots of polynomials occur in radical form, they occur as two conjugates.
That is,
The conjugate of (a + √b) is (a - √b) and vice versa.
To show that the given conjugates come from a polynomial, we should create the polynomial from the given factors.
The first factor is x - (a + √b).
The second factor is x - (a - √b).
The polynomial is
f(x) = [x - (a + √b)]*[x - (a - √b)]
= x² - x(a - √b) - x(a + √b) + (a + √b)(a - √b)
= x² - 2ax + x√b - x√b + a² - b
= x² - 2ax + a² - b
This is a quadratic polynomial, as expected.
If you solve the quadratic equation x² - 2ax + a² - b = 0 with the quadratic formula, it should yield the pair of conjugate radical roots.
x = (1/2) [ 2a +/- √(4a² - 4(a² - b)]
= a +/- (1/2)*√(4b)
= a +/- √b
x = a + √b, or x = a - √b, as expected.
Answer:
The answer is they are congruent.
Step-by-step explanation:
They have two congruent sides and share one side, so they are congruent by SSS.
I hope this helps! :)
