Explanation Given Information: The provided polynomial is − 15 x 2 + 19 x − 6 . Formula used: Follow the steps as mentioned below to compute the factorization of a polynomial a x 2 + b x + c when a ≠ 1 by foil method. Step 1: Take the largest common factor as common, if possible. Step 2: Find the two first terms in a combination whose product will give a x 2 which will represent “ F” in the FOIL. Step 3: Find the two last terms in a combination whose product will give c which will represent “ L” in the FOIL. Step 4: Take the outer product by multiplying first and the last term obtained from step 2 and 3 also take the inner product by multiplying reaming inner terms obtained from step 2 and 3 then take the sum of results to get the value of b x which will represent “OI” in the FOIL. Step 5: Check the result by multiplication. Calculation: Consider the polynomial, − 15 x 2 + 19 x − 6 Take out the largest common factor − 1 as common, − 15 x 2 + 19 x − 6 = − 1 ( 15 x 2 − 19 x + 6 ) Now first compute the factors of 15 x 2 − 19 x + 6 , as, Take the combination of two terms, whose product is 15 x 2 , Combination of terms Product 3 x and 5 x 15 x 2 15 x and x 15 x 2 Write this combination in factor form, as, ( 3 x + ) ( 5 x + ) And ( 15 x + ) ( x + ) Take the possible pairs of two terms, whose product is 6 , Possible pairs Product of pairs 2 , 3 6 3 , 2 6 6 , 1 6 1 , 6 6 − 2 , − 3 6 − 3 , − 2 6 − 6 , − 1 6 − 1 , − 6 6 Here the sign of the middle term is negative and the sign of the last term is positive. So, select the negative pairs to keep the signs unchanged. Form the pair to get middle term − 19 by checking each possible pair via substituting the combination in the factor form, as, Trial Product Remark ( 3 x − 2 ) ( 5 x − 3 ) 15 x 2 − 9 x − 10 x + 6 = 15 x 2 − 19 x + 6 Middle term is − 19 , So, this pair is correct

9th Edition

ISBN: 9780321997173

Author: Marvin L. Bittinger, Judith A. Beecher

Publisher: PEARSON

See similar textbooks

Videos

Question

Chapter 11.3, Problem 51ES

To determine

To calculate: The factor of the polynomial −15x2+19x−6.

Expert Solution & Answer

Want to see the full answer?

Check out a sample textbook solution

See solution

Chapter 11.3, Problem 50ES

Chapter 11.3, Problem 52ES

Students have asked these similar questions

1. Consider the following system of equations: x13x2 + 4x3 - 5x4 = 7 -2x13x2 + x3 - 6x4 = 7 x16x213x3 - 21x4 = 28 a) Solve the system. Write your solution in parametric and vector form. b) What is a geometric description of the solution. 7 c) Is v = 7 in the span of the set S= [28. 1 HE 3 -5 3 ·6 ? If it is, write v 6 as a linear combination of the vectors in S. Justify. d) How many solutions are there to the associated homogeneous system for the system above? Justify. e) Let A be the coefficient matrix from the system above. Find the set of all solutions to Ax = 0. f) Is there a solution to Ax=b for all b in R³? Justify.

Answer questions 8.3.1 and 8.3.2 respectively

8.2.7 The brightness of a television picture tube can be evaluated by measuring the amount of current required to achieve a particular brightness level. A sample of 10 tubes results in x = 317.2 and s = 15.7. Find (in microamps) a 99% confidence interval on mean current required. State any necessary assumptions about the underlying distribution of the data. 8.2.8 An article in the Journal of Composite Materials (December 1989, Vol. 23(12), pp. 1200–1215) describes the effect of delamination on the natural frequency of beams made from composite laminates. Five such delaminated beams were subjected to loads, and the resulting frequencies (in hertz) were as follows: 230.66, 233.05, 232.58, 229.48, 232.58 Check the assumption of normality in the population. Calculate a 90% two-sided confidence interval on mean natural frequency.

Chapter 11 Solutions

Developmental Mathematics (9th Edition)

Ch. 11.1 - Objective 7.7d: Use the distributive laws to...Ch. 11.1 - Prob. 2SR Ch. 11.1 - Prob. 1DE Ch. 11.1 - Prob. 2DE Ch. 11.1 - Prob. 3DE Ch. 11.1 - Prob. 4DE Ch. 11.1 - Prob. 5DE Ch. 11.1 - Prob. 6DE Ch. 11.1 - Find the GCF. GS 24m5n6,12mn3,16m2n2,8m4n4 The...Ch. 11.1 - Prob. 8DE

Knowledge Booster

Learn more about

Need a deep-dive on the concept behind this application? Look no further. Learn more about this topic, subject and related others by exploring similar questions and additional content below.

The factor of the polynomial − 15 x 2 + 19 x − 6 .

Solution Summary: The author calculates the factorization of the polynomial ax2+bx+c by foil method.

Videos

To calculate: The factor of the polynomial −15x2+19x−6.

Want to see the full answer?

Chapter 11 Solutions