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3 years ago

What is the correct factored form of x2 + 3x − 10?

Mathematics

2 answers:

Oksi-84 [34.3K]3 years ago

7 0

Answer:

(x + 5)(x - 2)

Step-by-step explanation:

To factorise the quadratic

Consider the factors of the constant term (- 10) which sum to give the coefficient of the x- term (+ 3)

The factors are + 5 and - 2, since

5 × - 2 = - 10 and 5 - 2 = + 3, thus

x² + 3x - 10 = (x + 5)(x - 2)

Anna71 [15]3 years ago

5 0

Answer:

(x+5)(x-2)

Step-by-step explanation:

To convert a quadratic equation into factored form, you need to go element by element with the given equation: x²+3x-10.

x²: you know you get that by multiplying x by x, so you start with (x±A)(X±B).

3x-10: two numbers when being added, you get 3 and when multiplying you get -10, those numbers are 5 and -2, so (x+5)(X-2).

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For what values of x will the function f(x) = 3x² + 13x - 10 equal zero?

Oduvanchick [21]

Answer:

x = - 5 , x = $\frac{2}{3}$

Step-by-step explanation:

the values of x that make f(x) zero are the zeros

to find the zeros let f(x) = 0 , that is

3x² + 13x - 10 = 0

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.

product = 3 × - 10 = - 30 and sum = + 13

the factors are + 15 and - 2

use these factors to split the x- term

3x² + 15x - 2x - 10 = 0 ( factor the first/second and third/fourth terms )

3x(x + 5) - 2(x + 5) = 0 ← factor out (x + 5) from each term

(x + 5)(3x - 2) = 0

equate each factor to zero and solve for x

x + 5 = 0 ⇒ x = - 5

3x - 2 = 0 ⇒ 3x = 2 ⇒ x = $\frac{2}{3}$

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