Question

An x-method chart shows the product a c at the top of x and b at the bottom of x. Above the chart is the expression a x squared b x c. Factor the trinomial 7x2 – 3x – 4. Which pair of numbers has a product of ac and a sum of b? What is the factored form of the trinomial?.

Answer 1

Factored form of an expression is writing it in the terms of multiplication of factors. The factors of given expression are: $(7x+4)$  and $(x-1)$

How to find the factors of a quadratic expression?

If the given quadratic expression is of the form $ax^2 + bx + c$,

then its factored form is obtained by two numbers alpha( α ) and beta( β) such that:

$b = \alpha + \beta \\ ac =\alpha - \beta$

The given expression is $7x^2 - 3x - 4$

Comparing it with the standard form of quadratic expression $ax^2 + bx + c$, we get: a = 7, b = -3, c = -4

ac = -28

-28 = -2 times 14

-28 = -7 times 4 (-7 + 4 = -3 = b)

Thus, $\alpha = -7, \beta = 4$

Thus, we get:

$7x^2 - 3x - 4 = 7x^2 - 7x + 4x - 4 = 7x(x-1) + 4(x-1) = (7x+4)(x-1)\\7x^2 - 3x - 4 = (7x+4)(x-1)$

Thus, The factors of given expression are: $(7x+4)$  and $(x-1)$

Learn more about factor of quadratic equation here:

brainly.com/question/26675692

Answer 2

Answer:

(x+2) (x+8)

2 nn 8

Step-by-step explanation: