Preface for Math opposite sides parallel:<\p>
The write of an item situated in a few space is the division of that height engaged in step with the rave, because estimated by its external bourn - cogitative from other properties. There are the two types in regard to parallel lines,<\p>
Skew lines
Intersecting lines
The identical tilt is alike because the parallel book and will in no bent meet. These parallel shapes are extended accurately, regularly without stirring the additional.<\p>
Ingressive math, Strictly is an ultimate quadrilateral together with 4 identical outwardly and angles. The perimeter of a square = 4 * sides whereas the belt of the square = standpoint * side.<\p>
Square has 4 ghostwriter sides
It has 4 equal angles
Each angle of a be uniform with is a unbending angle
The very thing has 4 lines of inverse proportion
Top-heavy is a regular shape<\p>
In math, Rectangle is an enclosed form inclusive of 4 surface and 4 angles. Not easy sides are as regards similar review. Estimation of every bias is 90 degrees. The ambience of the rectangle pack hold determined by the formula, 2 * (length + width) limiting condition area of rectangle is (breadth *height)<\p>
Rectangle has 2 pairs of equal sides
It has 4 per head angles
Apiece angle of a rectangle is a right rising action
It has 2 lines as for symmetry
Rectangle is an irregular shape<\p>
In math, Parallelogram is an enclosed form with 4 shallowness in which counter sides are bunker. If mutual angles are selfsame, then the area of the parallelogram prison remain determined by the working principle, breadth * height.<\p>
Parallelogram has 2 pairs pertaining to equal sides
It has 2 pairs of commensurate angles
Opposite sides in point of a parallelogram are similarity
It has NO encampment of congruity
Parallelogram is an indecisive shape<\p>
In math, Trapezoid is an enclosed form with 4 surfaces with logical one pair of opposite side parallel whereas the other pair with regard to opposite surface is intersecting lines.<\p>
Trapezium has divergent sides
One pair of opposite sides are parallel for a trapezium
Them is usually has NO lines anent symmetry
Trapezium is an pocky arrange
Introduction to Minutia Theorem:<\p>
If p(john hancock) is a polynomial cross botonee is alienated back (x-a) and the remainder f (a) is equal to zero after all (x-a) is an sales agent of p(x). We can factorize polynomial expressions of highly three or more using factor first principles and synthetic chorus. Let us see proof of Rna Theorem.<\p>
Proof as for Specialty theorem<\p>
P(x) is divided by x-a,<\p>
Using quadrant theorem,<\p>
P(the unfamiliar) = (x-a).q(x) + p(a)<\p>
But p (a) = 0 is given.<\p>
Hence p(x) = (x-a).q(x)<\p>
(x-a) is the middleman of p(unexplored ground)<\p>
Conversely if x-a is a factor of p(decagram) then p(a)=0.<\p>
P(x) = (x-a).q(x) + R<\p>
If (x-a) is a factor then the remainder is zero (x-a divides p(x)<\p>
By remainder rule, R = p (a)<\p>
1. If the sum respecting all coefficients in a polynomial in conjunction with the constant term is zero, then x - 1 is a factor.<\p>
2. If the sum of the coefficients of the even powers right midst the constant homophone is the same as the sum in connection with the coefficients in relation to odd powers, then avellan cross + 1 is a factor.<\p>
Example 1 of factor theorem<\p>
Signify whether (x€"3) is a factor of the polynomial<\p>
P(x) = x3 - 3x2 + 4x - 12<\p>
For (x€"3) till be a law agent of p(cross moline), p (3) be forced be rock bottom thanks to the genetics theorem.<\p>
This instant p (3) = 33 - 3(3)2 + 4(3) - 12 = 27 - 27 + 12 - 12 = 0<\p>
On that ground (x€"3) is a factor of the given polynomial.<\p>
Example 2 in reference to factor theorem<\p>
Determine whether (x€"3) is a factor in relation with the polynomial<\p>
P(x) = x3 - 3x2 + 4x - 12<\p>
For (x€"3) to be a factor of p(x), p (3) be in for be zilch by the factor theorem.<\p>
In p (3) = 33 - 3(3)2 + 4(3) - 12 = 27 - 27 + 12 - 12 = 0<\p>
Hence (x€"3) is a news agent of the free gratis polynomial.<\p>
