Explanation Given Information: The polynomial is y 2 ( y + 1 ) − 4 y ( y + 1 ) − 21 ( y + 1 ) . Formula used: The factorization of a trinomial square is, A 2 − 2 A B + B 2 = ( A − B ) 2 The factorization of a difference of square is, A 2 − B 2 = ( A + B ) ( A − B ) Steps for factorization a trinomial by a c -Method are: Step 1: Factor out the greatest common factor, if any. Write the resultant trinomial as a x 2 + b x + c . Step 2: Multiply the coefficient of x 2 and the constant term c . Step 3: Determine p and q , the factors of the product a c , such that p q = a c and p + q = b . Step 4: Write the middle term, b, as the sum of the factors obtained in step (3). Step 4: Factor the expression be grouping. Step 5: Check the result by multiplying the factors obtained in step (4). Calculation: Consider the provided polynomial, y 2 ( y + 1 ) − 4 y ( y + 1 ) − 21 ( y + 1 ) . Factor out the common factor ( y + 1 ) from the provided polynomial as follows, y 2 ( y + 1 ) − 4 y ( y + 1 ) − 21 ( y + 1 ) = ( y + 1 ) ( y 2 − 4 y − 21 ) Factorize the polynomial y 2 − 4 y − 21 using the a c -Method as follows, Multiply the coefficient of y 2 , 1 and the constant term 21 , 1 × 21 = 21 Since, the coefficient of y is negative and product of coefficient of y 2 and constant term is positive. So, select negative factors of 21 . Thus, negative factors of 21 such that their sum is − 4 are − 7 and 3 , Therefore, y 2 − 4 y − 21 can be written as, y 2 − 4 y − 21 = y 2 − 7 y + 3 y − 21 Factor by grouping as follows, Group the first two terms and the last two terms as follows, y 2 − 4 y − 21 = y 2 − 7 y + 3 y − 21 = ( y 2 − 7 y )

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ISBN: 9780321997173

Author: Marvin L. Bittinger, Judith A. Beecher

Publisher: PEARSON

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Chapter 11.6, Problem 98ES

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To calculate: The factorization of the polynomial, y2(y+1)−4y(y+1)−21(y+1).

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Chapter 11.6, Problem 97ES

Chapter 11.6, Problem 99ES

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The factorization of the polynomial, y 2 ( y + 1 ) − 4 y ( y + 1 ) − 21 ( y + 1 ) .

Solution Summary: The author calculates the factorization of a polynomial by multiplying the coefficient of x2 and the constant term c.

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To calculate: The factorization of the polynomial, y2(y+1)−4y(y+1)−21(y+1).

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