Problem 75 Find each product. In each case,... [FREE SOLUTION]

91影视

Introductory Algebra for College Students

Robert Blitzer

$Math Studyset 91影视 Explanations$ Math

6 Edition

Chapter 5: Problem 75

Find each product. In each case, neither factor is a monomial. $$\left(x-\frac{1}{2}\right)\left(4 x^{3}-2 x^{2}+5 x-6\right)$$

Short Answer

Expert verified

The product is $4 x^{4} - 4 x^{3} + 6 x^{2} - \frac{17}{2}x + 3$.

Step by step solution

Distribute First Term

Multiply the first term of the first factor with each term in the second factor: $x \times (4 x^{3}) = 4 x^{4}$, $x \times (-2 x^{2}) = -2 x^{3}$, $x \times (5 x) = 5 x^{2}$, $x \times (-6) = -6x$

Distribute Second Term

Multiply the second term of the first factor with each term in the second factor: $-\frac{1}{2} \times (4 x^{3}) = -2 x^{3}$, $-\frac{1}{2} \times (-2 x^{2}) = x^{2}$, $-\frac{1}{2} \times (5 x) = -\frac{5}{2}x$, $-\frac{1}{2} \times (-6) = 3$

Combine Like Terms

Combine like terms from Step 1 and Step 2 to get the final product: $4 x^{4}$ from step 1 and there is no matching term in step 2, $-2 x^{3}$ from step 1 and -2 $x^{3}$ from step 2 combine to give $-4 x^{3}$, $5 x^{2}$ from step 1 and $x^{2}$ from step 2 combine to give $6x^{2}$, $-6x$ from step 1 and $-\frac{5}{2}x$ from step 2 combine to give $-\frac{17}{2}x$, and the constant term from step 2 is 3

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91影视

Find each product. In each case, neither factor is a monomial. $$\left(x-\frac{1}{2}\right)\left(4 x^{3}-2 x^{2}+5 x-6\right)$$

Short Answer

Step by step solution

Distribute First Term

Distribute Second Term

Combine Like Terms

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