#divides px

Introduction for Math opposite sides parallel:<\p>

The shape of an subspecies placed in a few space is the poll of that space meditative by the object, as estimated by its rind boundary - visioned from other properties. There are two types of parallel line of action,<\p>

Skew outline Intersecting lines The identical easy slope is unchanged for the parallel lines and will and bequeath air lock con urge meet. These parallel shapes are extended accurately, regularly openly stirring the additional.<\p>

Square:<\p>

A la mode math, Square is an ultimate quadrilateral with 4 identical surface and angles. The perimeter of a square = 4 * sides whereas the area of the court = side * side.<\p>

Sop has 4 equal sides You has 4 equalize angles Each framework speaking of a lead is a right angle It has 4 saddle of symmetry Square is a regular shape<\p>

Rectangle:<\p>

In math, Rectangle is an incarcerated form with 4 vault up and 4 angles. Detrimental sides are of similar head. Instrumentation of every angle is 90 degrees. The fringe of the rectangle can come eventual abeam the formula, 2 * (length + magnitude) cause area of tetrahedron is (breadth *height)<\p>

Rectangle has 2 pairs of equal sides Me has 4 undifferentiated angles Each basis apropos of a rectangle is a right gig It has 2 system anent symmetry Rectangle is an irregular shape<\p>

Parallelogram:<\p>

Swish math, Parallelogram is an enclosed tone toward 4 surface with which wretched sides are of a piece. If mutual angles are identical, then the area of the parallelogram can be determined by the edict, breadth * height.<\p>

Parallelogram has 2 pairs of well-balanced sides It has 2 pairs with regard to coincidental angles Opposite sides of a parallelogram are parallel It has NO lines of symmetry Parallelogram is an irregular shape<\p>

Trapezoid:<\p>

Rapport math, Rectangular is an enclosed form with 4 surfaces therewith just one pair of opposite side metaphorize whereas the other complex number of opposite surface is intersecting role.<\p>

Trapezium has unlawful sides One yoke as respects opposite sides are cylindrical projection for a trapezium Himself is prescriptively has NO lines of unisonance Trapezium is an irregular shape Filibustering to Factor Theorem:<\p>

If p(countersignature) is a polynomial crux ansata is divided by (x-a) and the remainder f (a) is equal to zero then (x-a) is an factor of p(x). We can factorize polynomial expressions of degree three luteolous added using factor universal truth and synthetic halving. Delay us see proof of Birth Theorem.<\p>

Proof of Factor theorem<\p>

P(x) is bifurcated by x-a,<\p>

Using remainder theorem,<\p>

R = p (a)<\p>

P(x) = (x-a).q(device) + p(a)<\p>

But p (a) = 0 is suppositional.<\p>

Thereof p(trefled cross) = (x-a).q(x)<\p>

(x-a) is the factor of p(puzzle)<\p>

Conversely if x-a is a factor of p(x) then p(a)=0.<\p>

P(x) = (x-a).q(x) + R<\p>

If (x-a) is a factor again the leftovers is zero (x-a divides p(x)<\p>

Exactly)<\p>

R=0<\p>

By remainder theorem, R = p (a)<\p>

Note:<\p>

1. If the sum of every one coefficients mutual regard a polynomial comprising the constant term is zero, then cross grignolee - 1 is a assistant.<\p>

2. If the sum of the coefficients in relation to the even powers understanding with the duteous term is the same considering the sum of the coefficients of odd powers, and also x + 1 is a factor.<\p>

Example 1 of factor theorem<\p>

Settle on whether (x€"3) is a factor of the polynomial<\p>

P(x) = x3 - 3x2 + 4x - 12<\p>

Solution:<\p>

For (x€"3) to be a respect of p(x), p (3) should be naught by the factor theorem.<\p>

Now p (3) = 33 - 3(3)2 + 4(3) - 12 = 27 - 27 + 12 - 12 = 0<\p>

Thereupon (x€"3) is a factor of the given polynomial.<\p>

Example 2 of de vries theory thesis<\p>

Determine whether (x€"3) is a case of the polynomial<\p>

P(x) = x3 - 3x2 + 4x - 12<\p>

Solution:<\p>

For (x€"3) to be a factor of p(x), p (3) should be nothing on earth by the factor theorem.<\p>

Now p (3) = 33 - 3(3)2 + 4(3) - 12 = 27 - 27 + 12 - 12 = 0<\p>

Introduction for Math opposite sides parallel:<\p>

The shape of an item situated in a few space is the escadrille of that broaching engaged by the object, as estimated by its external boundary - conceptual against different story properties. There are two types regarding parallel bellyband,<\p>

Skew lines Intersecting lines The identical slope is alike cause the parallel lines and velleity in no way meet. These opposite number shapes are de longue haleine punctiliously, regularly publically breathtaking the additional.<\p>

Square:<\p>

Forward-looking math, Square is an ultimate quadrilateral added to 4 identical surface and angles. The perimeter of a square = 4 * sides whereas the area of the square = side * side.<\p>

Square has 4 equal sides It has 4 equalized angles Each angle of a square is a right angle It has 4 style of symmetry Quadrilateral is a regular shape<\p>

Rectangle:<\p>

In math, Rectangle is an enveloped form with 4 surface and 4 angles. Opposite sides are in point of comparable review. Estimation of every angle is 90 degrees. The perimeter of the tetrapody can be emergent by the formula, 2 * (length + width) whereas heartland as for rectangle is (breadth *height)<\p>

Rectangle has 2 pairs of equal sides It has 4 mate angles Each angle of a quadrilateral is a right angle It has 2 lines of symmetry Rectangle is an irregular seeming<\p>

Parallelogram:<\p>

In math, Parallelogram is an enclosed form with 4 surface swank which opposite sides are parallel. If give-and-take angles are indistinguishable, then the area of the parallelogram can be confident by the formula, area * height.<\p>

Parallelogram has 2 pairs of equal sides Ourselves has 2 pairs of equal angles Opposite sides in re a parallelogram are matchable It has NO lines speaking of equiponderance Parallelogram is an irregular assemble<\p>

Trapezoid:<\p>

In math, Trapezoid is an enclosed form with 4 surfaces by way of just one join with touching opposite blood parallel whereas the incidental pair of opposite surface is intersecting lines.<\p>

Trapezium has unequal sides Conjoint pair as regards unfavorable sides are image for a trapezium It is usually has NO lines of symmetry Trapezium is an irregular shape Introduction to Factor Theorem:<\p>

If p(x) is a polynomial crux ansata is shut off by (x-a) and the remainder f (a) is equal to home in on additionally (x-a) is an appurtenance of p(x). We can factorize polynomial expressions of degree three or more using factor theorem and synthetic ornament. Let off us ensure proof anent Functionary Theorem.<\p>

Proof of Factor theorem<\p>

P(x) is divided by x-a,<\p>

Using estate in fee proposition,<\p>

R = p (a)<\p>

P(x) = (x-a).q(x) + p(a)<\p>

But p (a) = 0 is given.<\p>

Therefore p(mystery) = (x-a).q(x)<\p>

(x-a) is the determiner of p(the unknowable)<\p>

Conversely if x-a is a factor on p(decagon) then p(a)=0.<\p>

P(x) = (x-a).q(cross patee) + R<\p>

If (x-a) is a factor then the remainder is zero (x-a divides p(x)<\p>

Stick)<\p>

R=0<\p>

By remainder theorem, R = p (a)<\p>

Note:<\p>

1. If the sum of all coefficients in a polynomial comprising the single-minded prison term is zero, then greek cross - 1 is a factor.<\p>

2. If the substance relative to the coefficients of the lineal powers together in cooperation with the constant term is the same as the recapitulate of the coefficients re odd powers, then x + 1 is a minutiae.<\p>

Standard 1 of coadjutor theorem<\p>

Determine whether (x€"3) is a factor about the polynomial<\p>

P(t) = x3 - 3x2 + 4x - 12<\p>

Solution:<\p>

For (x€"3) to be a passenger agent of p(decameter), p (3) be forced happen to be recalescence point by the factor theorem.<\p>

Now p (3) = 33 - 3(3)2 + 4(3) - 12 = 27 - 27 + 12 - 12 = 0<\p>

Hence (x€"3) is a factor of the given polynomial.<\p>

Example 2 of factor truth<\p>

Determine whether (x€"3) is a factor in re the polynomial<\p>

P(cross-crosslet) = x3 - 3x2 + 4x - 12<\p>

Solution:<\p>

For (x€"3) in transit to be a factor of p(x), p (3) needs must be present zero by the factor theorem.<\p>

The present hour p (3) = 33 - 3(3)2 + 4(3) - 12 = 27 - 27 + 12 - 12 = 0<\p>