# This is the standard form of a trinomial a x 2 b x c

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This is the standard form of a trinomial:ax^2+bx+cDiscriminant form is: b^2−4acIf the Discriminant is:Then there will be:Zero1 rational solutionPositive Perfect Square2 rational solutionsPositive Integer, Not a Perfect Square2 irrational solutionsNegative2 complex solutions
Factoring by Grouping (Four-Term Polynomials)factoring by groupingbecause pairs of terms are grouped together to factor the entire polynomial. The goal with this method is to find a common binomial that can be factored1. Factor the GCF.Determine if there is a GCF among all terms in the original polynomial and factor it, if one exists.2. Group the terms.Group the polynomial into two pairs—the first two terms and the last two terms.3. Factor the GCF from each group.Factor the GCF from the first pair of terms and then from the second pair of terms.4. Factor the common binomial.If common binomials do not exist, GCFs were factored accurately, and the expression cannot be rearranged, you have a prime polynomial.Don’t forget to check the factors for accuracy by distributing.Factoring Trinomials by GroupingWhat you've discovered is that the product of the middle two terms equals the product of the first andlast terms. Also, the sum of the middle two terms equals the middle term of the trinomial.Now let's use these ideas to factor the trinomial 6x2− 11x + 3 by grouping.First, check the result of the Discriminant. From the equation a = 6, b = −11, and c = 3.b2− 4ac(−11)2− 4(6)(3)121 − 72491. Factor the GCF.Determine if there is a GCF among all terms in the original polynomial and factor it, if one exists.2. Split the middle term.Multiply the leading coefficient and the constant.Find factors of this product that sum to the middle coefficient.Rewrite the polynomial with those factors replacing the middle term.
3. Factor by groupingThe four-term polynomial is split into two groups—the first pair and last pair of terms. Factor the GCF from each pair.Factor the common binomial.If common binomials do not exist and GCFs were factored accurately, you may have a prime polynomial.4. Check your work.Check the factors by distributing.02.03Perfect cube:geometrically, a perfect cube, or just cube, is a three-dimensional object whose length, width and height are all the same measurement; algebraically, a perfect cube is the product of three identical numbers or variables multiplied together. Example: the number 8 is a perfect cube since the cube root of 8 is 2. 2 • 2 • 2 = 8Cube root:a cube root is the number or variable which results from separating an expression into three identical groups which are multiplied togetherSums and Differences of CubesSum of Cubesa3+ b3= (a + b)(a2− ab + b2)quaDifference of Cubesa3− b3= (a − b)(a2+ ab + b2)Steps to Factoring the Sum/Difference of Cubes1.Factor the GCF.2.Identify the cube root of each term.oThe cube root of the first term will represent a in the pattern.oThe cube root of the second term will represent b in the pattern.3.Substitute a and b in the appropriate pattern.oDon’t forget to check the factors by multiplying!02.04 Lesson Summary
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