Instructions for the Hour Calculator: 1. Enter the hours and minutes on the first column. See your totals on the second column. 2. OPTIONAL: Enter a Name and Date for your records. It will be included in the "Print" and "Email" versions. 3. OPTIONAL:
How does factor growth affect international trade and welfare of trading countries? Production: Labor and capital growth may increase the output of both the exportable and the importable by the same rate. This kind of growth is called neutral growth.
In the context of the HeckscherâOhlin model of international trade, open trade between two regions often leads to changes in relative factor supplies between the regions. This can lead to an adjustment in the quantities and types of outputs between
Almost everything will work again if you unplug it for a few minutes, including you. Anne Lamott
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Home / Calculators / Algebra I Calculators / Math Problem Solver (all calculators)
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RATIONAL ZEROS THEOREM CALCULATOR Calculators Math Games and Logic Puzzles
The calculator will find all possible rational roots of the polynomial, using the Rational Zeros Theorem. After this, it will decide which possible roots are actually roots. This is a more general case of the Integer (Integral) Root Theorem (when leading coefficient is `1` or `-1`). Steps are available.
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Solved Questions Enter a polynomial: 2x^4+x^3-15x^2-7x+7
Write all suggestions in comments below. Show steps CALCULATE
SOLUTION Your input: find rational zeros of 2x4 + x 3 − 15x 2 − 7x + 7. Since all coefficients are integer, we can apply the Rational Zeros Theorem. The trailing coefficient (coefficient of the constant term) is 7. Find its factors (with plus and minus): ±1, ± 7. These are the possible values for p. The leading coefficient (coefficient of the term with the highest degree) is 2. Find its factors (with plus and minus): ±1, ± 2. These are the possible values for q. p 1 1 7 7 Find all possible values of : ± , ± , ± , ± . q 1 2 1 2 Simplify and remove duplicates (if any), these are possible rational roots: ±1, ±
1 7 , ± 7, ± 2 2
. Next, check possible roots: if a is a root of the polynomial P(x) , the remainder from the division of P(x) by x − a should equal 0 . Check 1 : divide 2x4 + x 3 − 15x 2 − 7x + 7 by x − 1 .Quotient is 2x3 + 3x 2 − 12x − 19 and remainder is −12 (use synthetic division calculator to see the steps). Check −1 : divide 2x4 + x 3 − 15x 2 − 7x + 7 by x + 1 .Quotient is 2x3 − x 2 − 14x + 7 and remainder is 0 (use synthetic division calculator to see the steps). So, −1 is a root. 1 2 : divide 2x4 + x 3 − 15x 2 − 7x + 7 1 by x − 2 .Quotient is 2x3 + 2x 2 − 14x − 14 and remainder is 0 (use synthetic division calculator to see the steps). Check
1 2 is a root. So,
1 Check − 2 : divide 2x4 + x 3 − 15x 2 − 7x + 7 1 by x + 2 1 3 .Quotient is 2x − 15x + 2 27 and remainder is 4 (use synthetic division calculator to see the steps). Check 7 : divide 2x4 + x 3 − 15x 2 − 7x + 7 by x − 7 .Quotient is 2x3 + 15x 2 + 90x + 623 and remainder is 4368 (use synthetic division calculator to see the steps). Check −7 : divide 2x4 + x 3 − 15x 2 − 7x + 7 by x + 7 .Quotient is 2x3 − 13x 2 + 76x − 539 and remainder is 3780 (use synthetic division calculator to see the steps). 7 Check 2 : divide 2x4 + x 3 − 15x 2 − 7x + 7 7 by x − 2 77 .Quotient is 2x3 + 8x 2 + 13x + 2 567 and remainder is 4 (use synthetic division calculator to see the steps). 7 Check − 2 : divide 2x4 + x 3 − 15x 2 − 7x + 7 7 by x + 2 .Quotient is 2x3 − 6x 2 + 6x − 28 and remainder is 105 (use synthetic division calculator to see the steps).