Question

Can someone explain how to do this?

Answer 1

@Brainybeauty

Answer 2

So what is it that you don't understand?

Answer 3

How am I supposed to factor the polynomial so that I would be able to perform the zero product property on it to solve it?

Answer 4

Divide the equation by -4 and you will get 4t^2 -7t -2

Answer 5

factor out of 4, and then factor completely.

Answer 6

Quadratic formula, would be also an option if you haven't done factoring.

Answer 7

How did you know to use 4?

Answer 8

Completing the square ─ DO NOT SUGGEST.

Answer 9

Because you can see that in your equation (comparing to ax²+bx+c ) all a, b, and c are divisible by 4.

Answer 10

You mean it's the GCF?

Answer 11

Yep.

Answer 12

-16t²+28t+8=0
4(-4t²+7t+2)=0
-4t²+7t+2=0

Answer 13

I've seen before that you haven't done factoring, so I would suggest the quadratic formula.

Answer 14

I have learned factoring now. But I still don't know the quadratic formula.

Answer 15

\(\LARGE\color{blue}{ \frac{-b±\sqrt{b^2-4(a)(c)}}{2(a)} }\) comparing to


\(\LARGE\color{black}{ ax^2+bx+c=0 }\)

Answer 16

in your case, \(\LARGE\color{purple}{ -4t²+7t+2=0 }\)
a = - 4
b = 7
c = 2

Answer 17

This is what I learned about factoring from my lesson. This was the example:

2x^2 + 11x + 12

Factor pairs of 2: 1 and 2.
Factor pairs of 12: 1 and 12, 2 and 6, and 3 and 4.


"Once you’ve identified the factor pairs, you have to decide where to place the numbers in the binomial factors. The factors of the leading coefficient will go first in the binomials, and the factors of the ending number will go last. You can test out different combinations of the factor pairs by making sure you get the trinomial when you multiply the binomials together using the FOIL method."

All possible combinations:
(2x + 1) (x + 12)
(2x + 12) (x + 1)
(2x + 2) (x + 6)
(2x + 6) (x + 2)

Using FOIL, the correct answer was (2x + 3) (x + 4).

Answer 18

here is a method that works every time.
for a quadratic

\[ax^2 + bx + c = 0\]

take -4 as a common factor and you get

\[-4(4t - 7t - 2) = 0\]

so look at the quadratic...

multiply a and c so in your question its 4 and -2 = -8

find the factors of -8 that add to -7, the value of b

so its -8 and 1

then write the binomials as

(ax + factor 1)(ax + factor 2)
-------------------------- = 0
a

in your question its

(4t - 8)(4t + 1)
------------- = 0
4

remove any common factors in the binomials

4(t - 2)(4t + 1)
------------- = 0
4

cancel the common factor

(t - 2)(4t + 1) = 0

now you have the factored form of the quadratic

which is

-4(t -2)(4t + 1) = 0

and now you can do the rest of the question.

Answer 19

But how do I do it using the method I learned?

Answer 20

@tejasvir , what to you say?

Answer 21

about what

Answer 22

well its exactly the same... remove the common factor... -4

and you get

-4(4t^2 - 7t - 2)

find the factors of -2 since the middle term is negative the larger factor is also negative

so the factors you need are -2 and 1

next find the factors of 4t^2 either 2t and 2t or 4t and t

which pair give -7t as a product....

(t - 2)(4t + 1)

use foil to check

Answer 23

the reality is there are a lot of things to learn about factoring.... the sign of the b and c are critical to knowing what you have.