Chapter 6: Q 102. (page 589)

Factor Trinomials of the Form $a x^{2} + b x + c$ Using Trial and Error.
$10 y^{2} - 53 y - 11$

Short Answer

Expert verified

The solution is $(2 y - 11) (5 y + 1)$ .

Step by step solution

Step 1. Given information

Consider the trinomial.

$10 y^{2} - 53 y - 11$

Step 2. Write the trinomial in descending order and then find greatest common factor.

The trinomial $10 y^{2} - 53 y - 11$ is given in descending order.

There is no greatest common factor.

Step 3. Find the factors of the first term and the last term.

The first term of the given trinomial is $10 y^{2}$ .

So, the factors of $10 y^{2}$ are as follows:

$10 y^{2} = y \cdot 10 y 10 y^{2} = 2 y \cdot 5 y$

The last term of the given trinomial is $- 11$ .

Since the last term of the given polynomial is negative, the factors of the last term will have opposite signs.

The factors of $- 11$ are as follows:

$\begin{array}{rcl} - 11 & = & 1 \cdot (- 11) \\ - 11 & = & (- 1) \cdot 11 \end{array}$

Step 4. Make a table for all the combination of factors of 10y2−53y−11.

Possible factors	Product
$(y + 1) (10 y - 11)$	$10 y^{2} - y - 11$
$(y - 11) (10 y + 1)$	$10 y^{2} - 109 y - 11$
$(y - 1) (10 y + 11)$	$10 y^{2} + y - 11$
$(y + 11) (10 y - 1)$	$10 y^{2} + 109 y - 11$
$(2 y + 1) (5 y - 11)$	$10 y^{2} - 17 y - 11$
$(2 y - 11) (5 y + 1)$	$10 y^{2} - 53 y - 11$
$(2 y - 1) (5 y + 11)$	$10 y^{2} + 17 y - 11$
$(2 y + 11) (5 y - 1)$	$10 y^{2} + 53 y - 11$

From the table, conclude that the combination localid="1644583284895" $(2 y - 11) (5 y + 1)$ is correct.

Step 5. Check by multiplying (2y-11)(5y+1).

$\begin{array}{rcl} (2 y - 11) (5 y + 1) & = & 10 y^{2} + 2 y - 55 y - 11 \\ = & 2 y^{2} - 53 y - 11 \end{array}$

Hence, the factor is $(2 y - 11) (5 y + 1)$ .

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Factor Trinomials of the Form $a x^{2} + b x + c$ Using Trial and Error.
$10 y^{2} - 53 y - 11$

Short Answer

Step by step solution

Step 1. Given information

Step 2. Write the trinomial in descending order and then find greatest common factor.

Step 3. Find the factors of the first term and the last term.

Step 4. Make a table for all the combination of factors of 10y2−53y−11.

Step 5. Check by multiplying (2y-11)(5y+1).

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Factor Trinomials of the Form ax2+bx+cUsing Trial and Error.10y2−53y-11

Short Answer

Step by step solution

Step 1. Given information

Step 2. Write the trinomial in descending order and then find greatest common factor.

Step 3. Find the factors of the first term and the last term.

Step 4. Make a table for all the combination of factors of 10y2−53y−11.

Step 5. Check by multiplying (2y-11)(5y+1).

One App. One Place for Learning.

Most popular questions from this chapter

Recommended explanations on Math Textbooks

Mechanics Maths

Probability and Statistics

Calculus

Logic and Functions

Pure Maths

Statistics

Study anywhere. Anytime. Across all devices.

Factor Trinomials of the Form $a x^{2} + b x + c$ Using Trial and Error.
$10 y^{2} - 53 y - 11$