Answer: Choice B
(x-1)(x^3+x^2+5x+6)
==========================================
Explanation:
The 1 in the upper left box means that x = 1 is a root of the original polynomial.
So this means x-1 is a factor of the original polynomial.
This is because x = 1 leads to x-1 = 0 after subtracting 1 from both sides.
-----------------
The 0 in the last position of the bottom row shows we got a remainder of 0.
Getting a remainder 0 tells us that (x-1) is a factor of the polynomial. This synthetic division table confirms our initial guess.
The other values in that bottom row (1, 1, 5, 6) form coefficients to the polynomial 1x^3+1x^2+5x+6, or simply x^3+x^2+5x+6
-------------------
So we know that (x-1) and (x^3+x^2+5x+6) are factors
Meaning that,
x^4+4x^2+x-6 = (x-1)(x^3+x^2+5x+6)
You can confirm this by expanding out the right hand side (distribution rule).
Answer:
12n-20
Step-by-step explanation:
None are left over, as 345/23 = 15, or 15 pieces of paper per classmate.
Answer:
12 feet
Step-by-step explanation:
As a ladder is leaning against a house, it forms right angle triangle. And for right angleΔ, we use Pythagoras theorem.i.e
P²+B²= H²
Where,
'P' is perpendicular i.e the distance from the top of the ladder to the ground
'B' is base i.e be the distance from the bottom of the ladder to the house
'H' is hypotenuse i.e 13
considering 'x' as perpendicular
So, base would be 'x-7'
Applying Pythagoras theorem,
x² + (x-7)²= 13²
x² +x² -14x +49 =169
2x² -14x -120= 0
x² -7x -60=0 ----> solving the quadratic equation
x² + 5x -12x-60=0
x(x+5) -12(x+5)=0
Either : x+5=0 => x=-5
OR: x-12=0 => x=12
We'll choose the positive length.
therefore , The distance from the bottom of the ladder to the house is 12 feet
