Chapter 11: Q. 386 (page 1069)

In the following exercise, factor completely using the perfect square trinomials pattern.
$5 k^{3} - 70 k^{2} + 245 k$

Short Answer

Expert verified

The factorisation of the polynomial is

$5 k^{3} - 70 k^{2} + 245 k = 5 k {(k - 7)}^{2}$

Step by step solution

Step 1. Given information

The given polynomial is:

$5 k^{2} - 70 k^{2} + 245 k$

Step 2. Factorise the polynomial

We know that,

${(a - b)}^{2} = a^{2} - 2 a b + b^{2}$

For the polynomial $5 k^{3} - 70 k^{2} + 245 k$ , taking out $5 k$ as a common, we get:

$5 k (k^{2} - 14 k + 49)$

Now,

localid="1644658099435" $5 k [k^{2} - 14 k + 49] 5 k [{(k)}^{2} - 2 \times k \times 7 + 7^{2}] 5 k {(k - 7)}^{2} [u \sin g {(a - b)}^{2} = a^{2} - 2 a b + b^{2}]$

Thus, the factorisation of the polynomial is:

localid="1644657063485" $5 k^{3} - 70 k^{2} + 245 k = 5 k {(k - 7)}^{2}$

Step 3. check the answer

Multiplying the factors, we get:

$5 k^{3} - 70 k^{2} + 245 k = 5 k {(k - 7)}^{2} 5 k^{3} - 70 k^{2} + 245 k = 5 k (k^{2} - 14 k + 49) 5 k^{3} - 70 k^{2} + 245 k = 5 k^{3} - 70 k^{2} + 245 k$

This is true.

Unlock Step-by-Step Solutions & Ace Your Exams!

Full Textbook Solutions
Get detailed explanations and key concepts
Unlimited Al creation
Al flashcards, explanations, exams and more...
Ads-free access
To over 500 millions flashcards
Money-back guarantee
We refund you if you fail your exam.

Start your free trial

Over 30 million students worldwide already upgrade their learning with Vaia!

Recommended explanations on Math Textbooks

View all explanations

What do you think about this solution?

We value your feedback to improve our textbook solutions.

In the following exercise, factor completely using the perfect square trinomials pattern.
$5 k^{3} - 70 k^{2} + 245 k$

Short Answer

Step by step solution

Step 1. Given information

Step 2. Factorise the polynomial

Step 3. check the answer

One App. One Place for Learning.

Most popular questions from this chapter

Recommended explanations on Math Textbooks

Discrete Mathematics

Geometry

Logic and Functions

Probability and Statistics

Calculus

Applied Mathematics

Study anywhere. Anytime. Across all devices.

In the following exercise, factor completely using the perfect square trinomials pattern. 5k3−70k2+245k

Short Answer

Step by step solution

Step 1. Given information

Step 2. Factorise the polynomial

Step 3. check the answer

One App. One Place for Learning.

Most popular questions from this chapter

Recommended explanations on Math Textbooks

Discrete Mathematics

Geometry

Logic and Functions

Probability and Statistics

Calculus

Applied Mathematics

Study anywhere. Anytime. Across all devices.

In the following exercise, factor completely using the perfect square trinomials pattern.
$5 k^{3} - 70 k^{2} + 245 k$