factor The expression in the image is a quadratic polynomial: \[ 7y^2 - 4y - 3 \]This expression represents a quadratic equation in terms of the variable $ y $, where the coefficient of $ y^2 $ is 7, the coefficient of $ y $ is -4, and the constant term is -3.

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Advanced Engineering Mathematics

10th Edition

ISBN:9780470458365

Author:Erwin Kreyszig

Publisher:Erwin Kreyszig

Chapter2: Second-order Linear Odes

Section: Chapter Questions

Problem 1RQ

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Question

factor

The expression in the image is a quadratic polynomial:

\[ 7y^2 - 4y - 3 \]

This expression represents a quadratic equation in terms of the variable $ y $, where the coefficient of $ y^2 $ is 7, the coefficient of $ y $ is -4, and the constant term is -3.

Expert Solution

Step 1

The general form of a polynomial of degree n is given by $a_{0} y^{n} + a_{1} y^{n - 1} + \cdot \cdot \cdot + a_{n}$ , where $a_{0} \neq 0$ . The second-degree polynomials are called quadratic polynomials and their general form is $a_{0} y^{2} + a_{1} y + a_{2}$ .

According to the standard identity, any four numbers $a, b, c$ and d satisfy the condition $(a + b) (c + d) = a c + a d + b c + a d$ . Using the identity, the expression in the form $a c + a d + b c + b d$ can be factored as $(a + b) (c + d)$ .