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3 years ago

14

A linear function h(x) is represented by the equation 4x - 2y = 4 . What is the y-intercept of the function? Write the solution

as an ordered pair.

1 answer:

irina [24]3 years ago

6 0

4x-2y = 4

= -2y = 4-4x

= y = (4x + 4)/ 2

y = 2x - 2

h(x) = 2x-2

To find y-intercept, find h(0)

= 2(0) - 2 => -2

Y-intercept = (0,-2)

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Find the value of c so that (x-5) is a factor of the polynomial p(x)

liubo4ka [24]

I think the question is

Find the value of c so that (x-5) is a factor of the polynomial

$p(x) = x^3 + 2x^2 + cx + 10$

The other factor is going to be some quadratic. We can say a few things about its coefficients but let's start by saying in general it's

$q(x)= ax^2 + bx + k$

$p(x) = (x-5)q(x)$

$x^3 + 2x^2 + cx + 10 = (x-5)(ax^2 + bx+k) = ax^3 + (b-5a)x^2 + (k-5b)x - 5k$

Equating respective coefficients,

$a=1$

$b-5a = 2$

$k - 5b = c$

$-5k = 10$

so we get

$b = 2 + 5 = 7$

$k = 10/-5 = -2$

$c = k - 5b = 2 - 5(7)= -37$

Answer: -37

Check:

$(x^2 + 7x - 2)(x - 5) = x^3 + 2 x^2 - 37 x + 10\quad\checkmark$

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