Question
Factor the following expression. \[ \begin{array}{l}4 x^{2}-13 x+10 \\ (4 x-[?])(x-\square)\end{array} \]
Ask by Boone Ball. in the United States
Jan 21,2025
Real Tutor Solution
Tutor-Verified Answer
Answer
The factored form of the expression \(4x^{2} - 13x + 10\) is \((4x - 5)(x - 2)\).
Solution
To factor the quadratic expression \( 4x^{2} - 13x + 10 \), we look for two binomials of the form \((4x + a)(x + b)\) such that:
1. The product of \(a\) and \(b\) is \(10\).
2. The sum of \(4b\) and \(a\) is \(-13\).
Let's identify the values of \(a\) and \(b\):
1. Possible pairs \((a, b)\) that multiply to \(10\) are:
- \((-1, -10)\)
- \((-2, -5)\)
- \((-5, -2)\)
2. Check which pair satisfies \(4b + a = -13\):
- For \((-5, -2)\): \(4(-2) + (-5) = -8 - 5 = -13\)
This pair works, so the factored form is:
\[
(4x - 5)(x - 2)
\]
**Answer:**
\[
(4x - 5)(x - 2)
\]
Reviewed and approved by the UpStudy tutoring team
Like
error msg
Explain 
Simplify this solution Beyond the Answer
To factor the expression \(4x^2 - 13x + 10\), we need to find two numbers that multiply to \(4 \times 10 = 40\) and add to \(-13\). The pair of numbers that satisfy this condition is \(-8\) and \(-5\). This allows us to rewrite the expression as: \[ 4x^2 - 8x - 5x + 10 \] Now, we can group the terms: \[ (4x^2 - 8x) + (-5x + 10) \] Factoring out the common terms from each group gives us: \[ 4x(x - 2) - 5(x - 2) \] Now, we can factor out the common binomial \((x - 2)\): \[ (4x - 5)(x - 2) \] Thus, the factored form is: \[ (4x - 5)(x - 2) \] In your desired format, the answer is: \[ (4x - 5)(x - 2) \] where \([?] = 5\) and \([\square] = 2\).
