Book edition 7th Edition

Author(s) James Stewart, Lothar Redlin, Saleem Watson

Pages 948 pages

ISBN 9781337067508

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Short Answer

To factor the trinomial $x^{2} + 7 x + 10$ , we look for two integers whose product is ___ and whose sum is _. These integers are _ and _, so the trinomial factors as _____.

To factor the trinomial $x^{2} + 7 x + 10$ , we look for two integers whose product is 10 and whose sum is 7. These integers are 5 and 2 , so the trinomial factors as $x^{2} + 7 x + 10 = (x + 5) (x + 2)$

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Step by Step Solution

TABLE OF CONTENTS :

TABLE OF CONTENTS

Step 1. Apply the concept of factoring trinomials.

To factor a trinomial of the form $a x^{2} + b x + c$ , we note that

$(x + r) (x + s) = x^{2} + (r + s) x + r s$

So, we need to choose numbers r and s so that $r + s = b$ and $r s = c$ .

Step 2. Analyze the trinomial.

Given $x^{2} + 7 x + 10$

This is of the form $a x^{2} + b x + c$ where $b = 7$ and $c = 10$

The factorization of the trinomial will be $(x + r) (x + s) = x^{2} + (r + s) x + r s$

So, we need to choose numbers r and s so that $r + s = b$ and $r s = c$ .

Step 3. Find the integers to factor the trinomial.

We need to choose integers r and s so that $r + s = 7$ and $r s = 10$ .

By trial and error we find that the two integers are $r = 5, s = 2$

$r + s = 5 + 2 = 7$

$r s = 5 \cdot 2 = 10$

Step 4. Factor the trinomial.

The factorization of the trinomial is

$\begin{array}{l} x^{2} + 7 x + 10 = (x + r) (x + s) \\ \Rightarrow x^{2} + 7 x + 10 = (x + 5) (x + 2) \end{array}$

Polynomial	Type	Term	Degree
$- 2 x^{2} + 5 x - 3$

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Precalculus Mathematics for Calculus

Answers without the blur.

Short Answer

To factor the trinomial $x^{2} + 7 x + 10$ , we look for two integers whose product is ___ and whose sum is _. These integers are _ and _, so the trinomial factors as _____.

Step by Step Solution

Step 1. Apply the concept of factoring trinomials.

Step 2. Analyze the trinomial.

Step 3. Find the integers to factor the trinomial.

Step 4. Factor the trinomial.

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Precalculus Mathematics for Calculus

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Short Answer

To factor the trinomial x2+7x+10, we look for two integers whose product is _____ and whose sum is _____. These integers are _____ and _____, so the trinomial factors as _______.

Step by Step Solution

Step 1. Apply the concept of factoring trinomials.

Step 2. Analyze the trinomial.

Step 3. Find the integers to factor the trinomial.

Step 4. Factor the trinomial.

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To factor the trinomial $x^{2} + 7 x + 10$ , we look for two integers whose product is ___ and whose sum is _. These integers are _ and _, so the trinomial factors as _____.