Chapter 6: Q 113. (page 590)

Factor Trinomials of the Form $a x^{2} + b x + c$ using the ‘ac’ Method.

Short Answer

Expert verified

The solution is $(2 k - 3) (2 k - 5)$ .

Step by step solution

Step 1. Given information

The given trinomial is $4 k^{2} - 16 k + 15$ .

Step 2. Find greatest common factor.

There is no greatest common factor.

Step 3. Compare the given trinomial to ax2+bx+c and then find the product of ac.

The values are as follows:

$\begin{array}{rcl} a & = & 4 \\ b & = & - 16 \\ c & = & 15 \end{array}$

The product is as follows:

$\begin{array}{rcl} a c & = & 4 \cdot 15 \\ = & 60 \end{array}$

Step 4. Determine two numbers that multiply to ac and add to b.

Since the middle term in the given polynomial is negative, both factors will be negative.

Two numbers that multiply to $a c$ and add to $b$ are as follows:

localid="1644751587397" $\begin{array}{rcl} (- 6) (- 10) & = & 60 \\ = & a c \\ - 6 - 10 & = & - 16 \\ = & b \end{array}$

So, two numbers are $- 6$ and $- 10$ .

Now, split the middle term of the given trinomial $4 k^{2} - 16 k + 15$ as follows:

width="251">4k2-16k+15=4k2-6k-10k+15

Step 5. Factor by grouping.

$\begin{array}{rcl} 4 k^{2} - 16 k + 15 & = & 2 k (2 k - 3) - 5 (2 k - 3) \\ = & (2 k - 3) (2 k - 5) \end{array}$

Step 6. Check by multiplying (2k-3)(2k-5).

$\begin{array}{rcl} (2 k - 3) (2 k - 5) & = & 4 k^{2} - 10 k - 6 k + 15 \\ = & 4 k^{2} - 16 k + 15 \end{array}$

Hence, the factor is $\begin{array}{rcl} (2 k - 3) (2 k - 5) \end{array}$ .

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Factor Trinomials of the Form $a x^{2} + b x + c$ using the ‘ac’ Method.

Short Answer

Step by step solution

Step 1. Given information

Step 2. Find greatest common factor.

Step 3. Compare the given trinomial to ax2+bx+c and then find the product of ac.

Step 4. Determine two numbers that multiply to ac and add to b.

Step 5. Factor by grouping.

Step 6. Check by multiplying (2k-3)(2k-5).

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Factor Trinomials of the Form ax2+bx+cusing the ‘ac’ Method.

Short Answer

Step by step solution

Step 1. Given information

Step 2. Find greatest common factor.

Step 3. Compare the given trinomial to ax2+bx+c and then find the product of ac.

Step 4. Determine two numbers that multiply to ac and add to b.

Step 5. Factor by grouping.

Step 6. Check by multiplying (2k-3)(2k-5).

One App. One Place for Learning.

Most popular questions from this chapter

Recommended explanations on Math Textbooks

Calculus

Logic and Functions

Probability and Statistics

Mechanics Maths

Theoretical and Mathematical Physics

Applied Mathematics

Study anywhere. Anytime. Across all devices.

Factor Trinomials of the Form $a x^{2} + b x + c$ using the ‘ac’ Method.