Respuesta :
Answer:
2(2r + 1)(2r - 5)
Step-by-step explanation:
Given
8r² - 16r - 10 ← factor out 2 from each term
= 2(4r² - 8r - 5)
To factorise the quadratic
Consider the factors of the product of the coefficient of the r² term and the constant term which sum to give the coefficient of the r- term.
product = 4 × - 5 = - 20 and sum = - 8
The factors are + 2 and - 10
Use these factors to split the r- term
4r² + 2r - 10r - 5 ( factor the first/second and third/fourth terms )
= 2r(2r + 1) - 5(2r + 1) ← factor out (2r + 1) from each term
= (2r + 1)(2r - 5), so
4r² - 8r - 5 = (2r + 1)(2r - 5) and
8r² - 16r - 10 = 2(2r + 1)(2r - 5) ← in factored form
The factored form of the given quadratic equation 8r² - 16r - 10 will be 2(2r + 1)(2r - 5) .
What is a quadratic equation?
A quadratic equation is the second-order degree algebraic expression in a variable.
The standard form of this expression is ax² + bx + c = 0 where a. b are coefficients and x is the variable and c is a constant.
It is Given that
8r² - 16r - 10
= 2(4r² - 8r - 5)
To factorize the quadratic
Consider the factors of the product of the coefficient of the r² term and the constant term which sum to give the coefficient of the r- term.
The factors are + 2 and - 10
Use these factors to split the r- term
4r² + 2r - 10r - 5
= 2r(2r + 1) - 5(2r + 1)
= (2r + 1)(2r - 5),
4r² - 8r - 5 = (2r + 1)(2r - 5)
and
8r² - 16r - 10 = 2(2r + 1)(2r - 5)
The factored form of the given quadratic equation 8r² - 16r - 10 will be 2(2r + 1)(2r - 5) .
Learn more about quadratic equations;
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