Answer:
<h3>D. -1, 1</h3>
Step-by-step explanation:
If x-1 is a factor of x⁴ + 2x³ - 2x - 1, then x-1 =0 is a factor
if x-1 = 0
x = 1
To get other factors we will divide the polynomial by x-1
Find the division in the attachment
x⁴ + 2x³ - 2x - 1,/x-1 = x³ +3x²+ 3x + 1,
let x = -1 be a factor of the resulting expression
f(-1) = (-1)³ +3(-1)²+ 3(-1) + 1
f(-1) = -1 +3(1)-3 + 1
f(-1) =-1+1-3+3
f(-1) = 0
Since f(-1) =0, hence x+1 is a factor of the resulting polynomial'
Dividing x³ +3x²+ 3x + 1, by x+1 to reduce the power of the polynomial
x³ +3x²+ 3x + 1/x+1 = x²+2x+1
Factorizing x²+2x+1
= x²+2x+1
=x²+x+x+1
= x(x+1)+1(x+1)
= (x+1)(x+1)
if the function is equal to zero
x+1 = 0 and x+1 = 0
x = -1 twice
Hence the solutions to the polynomial are 1 and -1(three times)
Answer: 15m + 5n
Step-by-step explanation:
so, first off, we take the number outside of the parentheses and multiply it by everything that's inside of the parentheses.
(5)3m + 5(n)
then, we just multiply all of those together.
15m + 5n
<em>Question:</em>
The area of the kite is 48 cm². What are the lengths of the diagonals PR and QS?
________
<em>Solution:</em>
You can split the kite into two isosceles triangles: PSR and PQR.
Assume that both diagonals intersect each other at the point O.
• Area of the triangle PSR:
m(PR) · m(OS)
A₁ = ————————
2
(x + x) · x
A₁ = ——————
2
2x · x
A₁ = ————
2
A₁ = x² (i)
• Area of the triangle PQR:
m(PR) · m(PQ)
A₂ = ————————
2
(x + x) · 2x
A₂ = ——————
2
2x · 2x
A₂ = ————
2
4x²
A₂ = ———
2
A₂ = 2x² (ii)
So the total area of the kite is
A = A₁ + A₂ = 48
Then,
x² + 2x² = 48
3x² = 48
48
x² = ———
3
x² = 16
x = √16
x = 4 cm
• Length of the diagonal PR:
m(PR) = x + x
m(PR) = 2x
m(PR) = 2 · 4
m(PR) = 8 cm
<span>• </span>Length of the diagonal SQ:
m(SQ) = x + 2x
m(SQ) = 3x
m(SQ) = 3 · 4
m(SQ) = 12 cm
I hope this helps. =)
Tags: <em>polygon area triangle plane geometry</em>
Answer:
x= 5,-3
Step-by-step explanation:
Answer: Triangle A'B'C is an enlargement of triangle ABC
Step-by-step explanation: When figuring out whether a dilation of a triangle is an enlargement or reduction, you see if the scale factor is larger or smaller than 1. If the scale factor is less than 1, it's a reduction. If the scale factor is larger than 1, it's an enlargement. 4/3 > 1 so this means the triangle gets bigger and is an enlargement. This means triangle A'B'C is an enlargement of triangle ABC.
