(x+1)(x+5)(x+2)
Polynomials are often writen from the highest to the lowest power, for example, x3 - 3x2 + 5x + 7.Polynomials are often writen from the highest to the lowest power, for example, x3 - 3x2 + 5x + 7.Polynomials are often writen from the highest to the lowest power, for example, x3 - 3x2 + 5x + 7.Polynomials are often writen from the highest to the lowest power, for example, x3 - 3x2 + 5x + 7.
x3 + 7x = 8x2x3 + 7x - 8x2 = 0 [subtract 8x2 from both sides]x(x2 + 7 - 8x) = 0 [factor out x]x(x-1)(x-7) = 0 [factor]Since the product of the three factors x, x-1, and x-7 equals zero, any of the three expressions could equal zero:x = 0x - 1 = 0, x = 1x - 7 = 0, x = 7Therefore, there are three solutions to the equation x3 + 7x = 8x2:x = 0x = 1x = 7Or, in set notation: x = {0,1,7}
Assumption 8x2 = eight times x squared Assumption: x3 is x to the third Assumption: y2 is y squared Answer 40 y to the fourth x to the fifth = 40 y4 x5
Usually the sum will have the same degree as the highest degree of the polynomials that are added. However, it is also possible for the highest term to cancel, for example if one polynomial has an x3, and the other a -x3. In this case, the sum will have a lower degree.
x(x+3)(x+5)
(x+1)(x+5)(x+2)
x2(x - 8)
Polynomials are often writen from the highest to the lowest power, for example, x3 - 3x2 + 5x + 7.Polynomials are often writen from the highest to the lowest power, for example, x3 - 3x2 + 5x + 7.Polynomials are often writen from the highest to the lowest power, for example, x3 - 3x2 + 5x + 7.Polynomials are often writen from the highest to the lowest power, for example, x3 - 3x2 + 5x + 7.
x3 + 7x = 8x2x3 + 7x - 8x2 = 0 [subtract 8x2 from both sides]x(x2 + 7 - 8x) = 0 [factor out x]x(x-1)(x-7) = 0 [factor]Since the product of the three factors x, x-1, and x-7 equals zero, any of the three expressions could equal zero:x = 0x - 1 = 0, x = 1x - 7 = 0, x = 7Therefore, there are three solutions to the equation x3 + 7x = 8x2:x = 0x = 1x = 7Or, in set notation: x = {0,1,7}
Assumption 8x2 = eight times x squared Assumption: x3 is x to the third Assumption: y2 is y squared Answer 40 y to the fourth x to the fifth = 40 y4 x5
2x3 - 7 + 5x - x3 + 3x - x3 = 8x - 7
Usually the sum will have the same degree as the highest degree of the polynomials that are added. However, it is also possible for the highest term to cancel, for example if one polynomial has an x3, and the other a -x3. In this case, the sum will have a lower degree.
1, 8, -5 and 4 One could argue that 4 is not a coefficient, but a term of it's own. On the other hand, if you follow the pattern in the polynomial, you could argue that it's a coefficient of x0.
Anything plus 0 is itself, so x3 + 0 is x3.
x3 + x2 + 4x + 4 = (x2 + 4)(x + 1)
x3 + 4x2 + x + 4 = (x + 4)(x2 + 1)