Problem 13
10p+10q factors to 10(p+q). If we apply the distributive property, we can distribute the 10 to each term inside (p and q) to get
10(p+q) = (10 times p)+(10 times q) = 10*p + 10*q = 10p+10q
so we get the original expression again. Here 10 is the GCF of the two terms.
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Plug p = 1 and q = 2 into the factored form
10*(p+q) = 10*(1+2) = 10*(3) = 30
As a check, let's plug those p,q values into the original expression
10*p+10*q = 10*1+10*2 = 10+20 = 30
We get the same output of 30
Answer: quotient is 2x^2 + 10x - 5
Solution:
The first polynomial is miswritten.
The right one is: 2x^3 + 4x^2 - 35x + 15.
So, the division is [2x^3 + 4x^2 - 35x + 15] / (x - 3)
The synthetic division uses the coeffcients and obviate the letters, but you have to be sure to respect the place of the coefficient.
So, in this case it is:
3 | 2 4 -35 15
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2 10 - 5 0
So, the quotient is 2x^2 + 10x - 5, and the remainder is 0.
I like to show it in this other way:
| 2 4 -35 15
|
|
3 | +6 +30 -15
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2 10 - 5 0
Of course they are the same coefficients and the answer continue being quotien 2x^2 + 10x - 5, remainder 0.
Answer:
Step-by-step explanation:
