((((x 4 )+(2•(x 3 )))-7x 2 )-8x)+12 - Tiger Algebra

Step 1 :

Equation at the end of step 1 :

Step 2 :

Equation at the end of step 2 :

Step 3 :

Polynomial Roots Calculator :

3.1 Find roots (zeroes) of : F(x) = x4+2x3-7x2-8x+12Polynomial Roots Calculator is a set of methods aimed at finding values of x for which F(x)=0 Rational Roots Test is one of the above mentioned tools. It would only find Rational Roots that is numbers x which can be expressed as the quotient of two integersThe Rational Root Theorem states that if a polynomial zeroes for a rational number P/Q then P is a factor of the Trailing Constant and Q is a factor of the Leading CoefficientIn this case, the Leading Coefficient is 1 and the Trailing Constant is 12. The factor(s) are: of the Leading Coefficient : 1 of the Trailing Constant : 1 ,2 ,3 ,4 ,6 ,12 Let us test ....

The Factor Theorem states that if P/Q is root of a polynomial then this polynomial can be divided by q*x-p Note that q and p originate from P/Q reduced to its lowest terms In our case this means that x4+2x3-7x2-8x+12 can be divided by 4 different polynomials,including by x-2

Polynomial Long Division :

3.2 Polynomial Long Division Dividing : x4+2x3-7x2-8x+12 ("Dividend") By : x-2 ("Divisor")

Quotient : x3+4x2+x-6 Remainder: 0

Polynomial Roots Calculator :

3.3 Find roots (zeroes) of : F(x) = x3+4x2+x-6 See theory in step 3.1 In this case, the Leading Coefficient is 1 and the Trailing Constant is -6. The factor(s) are: of the Leading Coefficient : 1 of the Trailing Constant : 1 ,2 ,3 ,6 Let us test ....

The Factor Theorem states that if P/Q is root of a polynomial then this polynomial can be divided by q*x-p Note that q and p originate from P/Q reduced to its lowest terms In our case this means that x3+4x2+x-6 can be divided by 3 different polynomials,including by x-1

Polynomial Long Division :

3.4 Polynomial Long Division Dividing : x3+4x2+x-6 ("Dividend") By : x-1 ("Divisor")

Quotient : x2+5x+6 Remainder: 0

Trying to factor by splitting the middle term

3.5 Factoring x2+5x+6 The first term is, x2 its coefficient is 1 .The middle term is, +5x its coefficient is 5 .The last term, "the constant", is +6 Step-1 : Multiply the coefficient of the first term by the constant 1 • 6 = 6 Step-2 : Find two factors of 6 whose sum equals the coefficient of the middle term, which is 5 .

Step-3 : Rewrite the polynomial splitting the middle term using the two factors found in step 2 above, 2 and 3 x2 + 2x + 3x + 6Step-4 : Add up the first 2 terms, pulling out like factors : x • (x+2) Add up the last 2 terms, pulling out common factors : 3 • (x+2) Step-5 : Add up the four terms of step 4 : (x+3) • (x+2) Which is the desired factorization

Final result :