Reformatting the entry :

Changes make to her input should not influence the solution: (1): \"x2\" was changed by \"x^2\". 1 an ext similar replacement(s).

You are watching: One root of f(x) = 2x3 + 9x2 + 7x – 6 is –3. explain how to find the factors of the polynomial.

Step 1 :

Equation in ~ the finish of action 1 :

(((2 • (x3)) + 32x2) + 7x) - 6

action 2 :

Equation in ~ the end of action 2 : ((2x3 + 32x2) + 7x) - 6

Step 3 :

Checking because that a perfect cube :3.12x3+9x2+7x-6 is no a perfect cube

Trying to variable by pulling the end :

3.2 Factoring: 2x3+9x2+7x-6 Thoughtfully split the expression at hand into groups, each team having 2 terms:Group 1: 7x-6Group 2: 2x3+9x2Pull the end from each group separately :Group 1: (7x-6) • (1)Group 2: (2x+9) • (x2)Bad news no Factoring through pulling out fails : The groups have no usual factor and can no be included up to type a multiplication.

Polynomial root Calculator :

3.3 find roots (zeroes) of : F(x) = 2x3+9x2+7x-6Polynomial roots Calculator is a set of methods aimed at finding worths ofxfor i beg your pardon F(x)=0 Rational root Test is among the above mentioned tools. It would certainly only discover Rational Roots that is number x which have the right to be expressed as the quotient of 2 integersThe Rational source Theorem says that if a polynomial zeroes because that a rational numberP/Q then p is a aspect of the Trailing continuous and Q is a aspect of the leading CoefficientIn this case, the top Coefficient is 2 and also the Trailing consistent is -6. The factor(s) are: the the leading Coefficient : 1,2 of the Trailing constant : 1 ,2 ,3 ,6 Let united state test ....

See more: 500000 Yen To Usd ) - 500000 Japanese Yen (Jpy) To U

PQP/QF(P/Q)Divisor
-11 -1.00 -6.00
-12 -0.50 -7.50
-21 -2.00 0.00x+2
-31 -3.00 0.00x+3
-32 -1.50 -3.00
-61 -6.00 -156.00
11 1.00 12.00
12 0.50 0.002x-1
21 2.00 60.00
31 3.00 150.00
32 1.50 31.50
61 6.00 792.00

The element Theorem says that if P/Q is source of a polynomial climate this polynomial deserve to be divided by q*x-p note that q and p originate native P/Q reduced to its lowest state In our case this means that 2x3+9x2+7x-6can be separated by 3 various polynomials,including by 2x-1

Polynomial Long department :

3.4 Polynomial Long division splitting : 2x3+9x2+7x-6(\"Dividend\") By:2x-1(\"Divisor\")

dividend2x3+9x2+7x-6
-divisor* x22x3-x2
remainder10x2+7x-6
-divisor* 5x110x2-5x
remainder12x-6
-divisor* 6x012x-6
remainder0

Quotient : x2+5x+6 Remainder: 0

Trying to variable by splitting the center term

3.5Factoring x2+5x+6 The first term is, x2 its coefficient is 1.The center term is, +5x the coefficient is 5.The critical term, \"the constant\", is +6Step-1 : main point the coefficient of the very first term by the consistent 1•6=6Step-2 : find two components of 6 who sum equates to the coefficient that the center term, which is 5.

-6+-1=-7
-3+-2=-5
-2+-3=-5
-1+-6=-7
1+6=7
2+3=5That\"s it

Step-3 : Rewrite the polynomial separating the middle term using the two components found in step2above, 2 and also 3x2 + 2x+3x + 6Step-4 : add up the an initial 2 terms, pulling out choose factors:x•(x+2) include up the last 2 terms, pulling out usual factors:3•(x+2) Step-5:Add up the 4 terms of step4:(x+3)•(x+2)Which is the wanted factorization