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    which term can be used in the blank of 36x3−22x2−__ so the greatest common factor of the resulting polynomial is 2x? select two options.

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    Factoring Polynomials: GCF Quiz Flashcards

    Study with Quizlet and memorize flashcards terms like Harriet earns the same amount of money each day. Her gross pay at the end of 7 workdays is 35h+56 dollars. Which expression represents her gross pay each day? 5h+8 8h+5 7h+11.2 11.2h+7, What is the completely factored form of the expression 16x2 + 8x + 32? 4(4x2 + 2x + 8) 4(12x2 + 4x + 28) 8(2x2 + x + 4) 8x(8x2 + x + 24), Which expression is equivalent to 10x2y + 25x2? 5x2(2y + 5) 5x2y(5 + 20y) 10xy(x + 15y) 10x2(y + 25) and more.

    Factoring Polynomials: GCF Quiz

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    Harriet earns the same amount of money each day. Her gross pay at the end of 7 workdays is 35h+56 dollars. Which expression represents her gross pay each day?

    5h+8 8h+5 7h+11.2 11.2h+7

    Click card to see definition 👆

    A.) 5h+8

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    What is the completely factored form of the expression 16x2 + 8x + 32?

    4(4x2 + 2x + 8) 4(12x2 + 4x + 28) 8(2x2 + x + 4) 8x(8x2 + x + 24)

    Click card to see definition 👆

    C.) 8(2x2 + x + 4)

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    Terms in this set (10)

    Harriet earns the same amount of money each day. Her gross pay at the end of 7 workdays is 35h+56 dollars. Which expression represents her gross pay each day?

    5h+8 8h+5 7h+11.2 11.2h+7 A.) 5h+8

    What is the completely factored form of the expression 16x2 + 8x + 32?

    4(4x2 + 2x + 8) 4(12x2 + 4x + 28) 8(2x2 + x + 4) 8x(8x2 + x + 24) C.) 8(2x2 + x + 4)

    Which expression is equivalent to 10x2y + 25x2?

    5x2(2y + 5) 5x2y(5 + 20y) 10xy(x + 15y) 10x2(y + 25) A.) 5x2(2y + 5)

    Six equilateral triangles are connected to create a regular hexagon. The area of the hexagon is 24a2 - 18 square units. Which is an equivalent expression for the area of the hexagon based on the area of a triangle?

    6(4a2 - 3) 6(8a2 - 9) 6a(12a - 9) 6a(18a - 12) A.) 6(4a2 - 3)

    What is the greatest common factor of 24s3, 12s4, and 18s?

    3 6 3s 6s D.) 6s

    What is the factored form of 8x2 + 12x?

    4(4x2 + 8x) 4x(2x + 3) 8x(x + 4) 8x(x2 + 4) B.) 4x(2x + 3)

    Which term can be used in the blank of 36x3−22x2−__ so the greatest common factor of the resulting polynomial is 2x? Select two options.

    2 4xy 12x 24 44y 2 3

    What is the greatest common factor of 42a5b3, 35a3b4, and 42ab4?

    7ab3 6a4b 42a5b4 77a8b7 A.) 7ab3

    What is the fully factored form of 32a3 + 12a2?

    4a2(8a + 3) 4a(8a2 + 3a) 12a2(3a + 1) 12a(3a2 + a) A.) 4a2(8a + 3)

    Mara carried water bottles to the field to share with her team at halftime. The water bottles weighed a total of 60x2 + 48x + 24 ounces. Which factorization could represent the number of water bottles and weight of each water bottle?

    6(10x2 + 8x + 2) 12(5x2 + 4x + 2) 6x(10x2 + 8x + 2) 12x(5x2 + 4x + 2)

    B.) 12(5x2 + 4x + 2)

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    Which term can be used in the blank of 36x3

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    Which term can be used in the blank of 36x3-22x2-underline so the greatest common factor of the resulting polynomial is 2x? Select two options. 2 4xy 12x 24 aav

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    Gauthmathier9893

    Grade 11 · 2021-06-11

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    Which term can be used in the blank of so the greatest common factor of the resulting polynomial is ? Select two options.

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    Gauthmathier5936

    Grade 11 · 2021-06-11

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    PRODUCTS AND FACTORS

    PRODUCTS AND FACTORS THE DISTRIBUTIVE LAW

    If we want to multiply a sum by another number, either we can multiply each term of the sum by the number before we add or we can first add the terms and then multiply. For example,

    In either case the result is the same.

    This property, which we first introduced in Section 1.8, is called the distributive law. In symbols,

    a(b + c) = ab + ac or (b + c)a = ba + ca

    By applying the distributive law to algebraic expressions containing parentheses, we can obtain equivalent expressions without parentheses.

    Our first example involves the product of a monomial and binomial.

    Example 1 Write 2x(x - 3) without parentheses.

    Solution

    We think of 2x(x - 3) as 2x[x + (-3)] and then apply the distributive law to obtain

    The above method works equally as well with the product of a monomial and trinomial.

    Example 2 Write - y(y2 + 3y - 4) without parentheses.

    Solution

    Applying the distributive property yields

    When simplifying expressions involving parentheses, we first remove the parentheses and then combine like terms.

    Example 3 Simplify a(3 - a) - 2(a + a2).

    We begin by removing parentheses to obtain

    Now, combining like terms yields a - 3a2.

    We can use the distributive property to rewrite expressions in which the coefficient of an expression in parentheses is +1 or - 1.

    Example 4 Write each expression without parentheses.

    a. +(3a - 2b) b. -(2a - 3b) Solution

    Notice that in Example 4b, the sign of each term is changed when the expression is written without parentheses. This is the same result that we would have obtained if we used the procedures that we introduced in Section 2.5 to simplify expressions.

    FACTORING MONOMIALS FROM POLYNOMIALS

    From the symmetric property of equality, we know that if

    a(b + c) = ab + ac, then ab + ac = a(b + c)

    Thus, if there is a monomial factor common to all terms in a polynomial, we can write the polynomial as the product of the common factor and another polynomial. For instance, since each term in x2 + 3x contains x as a factor, we can write the expression as the product x(x + 3). Rewriting a polynomial in this way is called factoring, and the number x is said to be factored "from" or "out of' the polynomial x2 + 3x.

    To factor a monomial from a polynomial:

    Write a set of parentheses preceded by the monomial common to each term in the polynomial.

    Divide the monomial factor into each term in the polynomial and write the quotient in the parentheses.

    Generally, we can find the common monomial factor by inspection.

    Example 1

    a. 4x + 4y = 4(x + y)

    b. 3xy -6y - 3y(x - 2)

    We can check that we factored correctly by multiplying the factors and verifying that the product is the original polynomial. Using Example 1, we get

    If the common monomial is hard to find, we can write each term in prime factored form and note the common factors.

    Example 2 Factor 4x3 - 6x2 + 2x.

    Solution We can write

    We now see that 2x is a common monomial factor to all three terms. Then we factor 2x out of the polynomial, and write

    2x( )

    Now, we divide each term in the polynomial by 2x

    and write the quotients inside the parentheses to get

    2x(2x2 - 3x + 1)

    We can check our answer in Example 2 by multiplying the factors to obtain

    In this book, we will restrict the common factors to monomials consisting of numerical coefficients that are integers and to integral powers of the variables. The choice of sign for the monomial factor is a matter of convenience. Thus,

    -3x2 - 6x

    can be factored either as

    -3x(x + 2) or as 3x(-x - 2)

    The first form is usually more convenient.

    Example 3 Factor out the common monomial, including -1.

    a. - 3x2 - 3 xy b. -x3 - x2 + x Solution

    Sometimes it is convenient to write formulas in factored form.

    Example 4 a. A = P + PRT = P(1 + RT) b. S = 4kR2 - 4kr2 = 4k(R2 - r2)

    4.3 BINOMIAL PRODUCTS I

    We can use the distributive law to multiply two binomials. Although there is little need to multiply binomials in arithmetic as shown in the example below, the distributive law also applies to expressions containing variables.

    We will now apply the above procedure for an expression containing variables.

    Example 1

    Write (x - 2)(x + 3) without parentheses.

    Solution

    First, apply the distributive property to get

    Now, combine like terms to obtain

    x2 + x - 6

    With practice, you will be able to mentally add the second and third products. Theabove process is sometimes called the FOIL method. F, O, I, and L stand for:

    1. The product of the First terms.

    2. The product of the Outer terms.

    3. The product of the Inner terms.

    4. The product of the Last terms.

    The FOIL method can also be used to square binomials.

    Example 2

    Write (x + 3)2 without parentheses.

    Solution

    First, rewrite (x + 3)2 as (x + 3)(x + 3). Next, apply the FOIL method to get

    Combining like terms yields

    x2 + 6x + 9

    When we have a monomial factor and two binomial factors, it is easiest to first multiply the binomials.

    Example 3

    Write 3x(x - 2)(x + 3) without parentheses.

    Solution

    First, multiply the binomials to obtain

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