Answer: 8x
Step-by-step explanation:
Product stands for multiplication, so we need to use (×)
Let x = the number.
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The product of 8 and a number
8 × x=8x
Answer:
Answer: Third option is the right answer.
Step-by-step explanation:
First we the write the expression
Now teacher says that the product of these polynomials will result in the sum of 
Now the teacher ask if we put the value of a = 2x and b = 1 then what will be the expression look like.
![(2x+1)\left [ (2x)^{2}+(1^{2})-(2x)(1)\right ]](https://tex.z-dn.net/?f=%282x%2B1%29%5Cleft%20%5B%20%282x%29%5E%7B2%7D%2B%281%5E%7B2%7D%29-%282x%29%281%29%5Cright%20%5D)
=
So third option is looking like our expression.
Answer:
Step-by-step explanation:
9(2.3n+6)+10.45>43.7
(9*2.3n)+(9*6)+10.45>43.7
20.7n+54+10.45>43.7
20.7n+64.45>43.7
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.
