-3
25x2 - 36y2 = ( 5x + 6y ) ( 5x - 6y )
Remainder Theorem:- When f(x) is divided by (x-a) the remainder is f(a) Tor example:- f(x) x3-2x2+5x+8 divided by x-2 f(2) 8-8+10+8 = 18 So the remainder is 18 if there is no remainder then the divisor is a factor of the dividend.
3x2 - 5x - 2 can be factored into (3x + 1) (x - 2)
10x ÷ 5x = 2
7
-3
I assume you meant x^4 + 5x^2 +10x + 12. The remainder is 28
If a polynomial is divided by x - c, we can use the Remainder theorem to evaluate the polynomial at c.The Remainder theorem:If the polynomial f(x) is divided by x - c, then the remainder is f(c).Example:Given f(x) = x^3 - 4x^2 + 5x + 3, use the remainder theorem to find f(2).Solution:By the remainder theorem, if f(x) is divided by x - 2, then the remainder is f(2).We can use the synthetic division to divide.2] 1 -4 5 32 -4 2__________1 -2 1 5The remainder is 5, so f(2) = 5Check:f(x) = x^3 - 4x^2 + 5x + 3f(2) = (2)^3 - 4(2)^2 + 5(2) + 3 = 8 - 16 + 10 + 3 = 5
From the Division Algorithm for Polynomials theorem,f(x) = q(x)g(x) + r(x) or we say:dividend = (quotient)(divisor) + (remainder)In our case,quotient = x^2 - 5x - 6; divisor = x - 3; and remainder = 5.Substitute what you know into the formula, and you will have:f(x) = (x^2 - 5x - 6)(x - 3) + 5f(x) = x^3 - 5x^2 - 6x - 3x^2 + 15x + 18 + 5f(x) = x^3 - 5x^2 - 3x^2 - 6x + 15x + 18 + 5f(x) = x^3 - 8x^2 + 9x + 23 (this is the required polynomial)
Yes, if there is no remainder after division, the divisor is a factor.
It is a quadratic polynomial.
x3-x2+5x-1 with remainder 7, which the final answer would be written as:x3-x2+5x-1+[7/(4x+3)]
-5x + 729
25x2 - 36y2 = ( 5x + 6y ) ( 5x - 6y )
x.x-5x+6
2x+5x-24 7x2-24
7,12,17,22,27 etc. in generalize form it is 5x+2, where x=1,2,3,4,.....