Answer:
d and e
Step-by-step explanation:
To factor 4x² + 17x - 15
Consider the factors of the product of the coefficient of the x² term and the constant term which sum to give the coefficient of the x- term, that is
product = 4 × - 15 = - 60 and sum = + 17
The factors are + 20 and - 3
Use these factors to split the middle term
4x² + 20x - 3x - 15 ( factor by grouping the first/second and third/fourth terms )
= 4x(x + 5) - 3(x + 5) ( take out the common factor (x + 5) )
= (x + 5)(4x - 3) → d/e
Factors of quadratic equation helps to write the quadratic equation in the form of product of its linear factors. All the factors of the given
[tex](x+5)\\(4x-3)[/tex]
The option D and option E are the correct option.
Given information
The given quadratic equation is,
[tex]4x^2+17x-15[/tex]
Factors of quadratic equation helps to write the quadratic equation in the form of product of its linear factors.
Equate the above equation to zero to find out the factors,
[tex]4x^2+17x-15=0[/tex]
Use the split the term method to solve further,
[tex]4x^2+20x-3x-15=0[/tex]
Group the above equation by taking out the common values,
[tex]\begin{aligned}4x^2+20x-3x-15&=0\\4x(x+5)-3(x+5)&=0\\(x+5)(4x-3)&=0\\\end[/tex]
Seprate the two factors of the given quadratic equation,
[tex](x+5)\\(4x-3)[/tex]
Hence all the factors of the given
[tex](x+5)\\(4x-3)[/tex]
Thus the option D and option E are the correct option.
Learn more about the factors of quadratic equation here;
https://brainly.com/question/529403
