If x2 - 13x + 42 = (x + A)(x + B), then A + B = ?

Question

my options were -42, -1, 13, 42, or none of these..i put 42 and got it wrong but i have no idea why ??? am i suppose to factor it then multiply ?

Answer 1

First factor the left side so that it is in the form (X + A) (X + B)

x^2 -13x +42
=(X-6)(X-7).............{to factor, determine two numbers that multiply to equal 42 and add to equal -13}

This means that A=-6 and B=-7

Thusly, A + B = -6 +(-7) = - 13

Therefore, the option of "None of these" would be correct since negative 13 is not listed as a choice.

Answer 2

A+B= -13
A*B= +42

x^2 - 13x + 42
(X-6)(x-7)

Here's how to do the problem:

You know that each factor begins with x. Now you look at the sign before the third term: It's a +, so you know that
both signs will be the same. Then you look at the sign of the middle term, since it's a -, you know that both signs will be negative.

So now you want to look for two numbers that, when added will equal 13, and when multiplied will equal 42.
So maybe you should look at the 42. Let's see, 42 can be formed from 21*2, 14*3, 7*6. Which one of these sets of numbers can be added to equal 13? That's your answer.

You can test your answer by using thye FOIL method to see if you can use the reverse process to get your original equation back. Here's how:

(x-6)(x-7) = x^2 -7x -6x + 42

combine like terms and there you've proven your factoring to be correct.

Answer 3

Yes, you factor and multiply, at which point the X2 will cancel out leaving you with

-13X + 42 = AX + BX + AB

A + B = -13
A*B = 42

The numbers I get are A = -6 and B = -7 (or A = -7 and B = -6)

Answer 4

if you factor x^2 - 13x + 42 you get (x - 6)(x - 7) which is the same as (x + -6)(x + -7) so A = -6, B = -7, A + B = -13

Answer 5

x^2 + 13x + 40 2 Set this equivalent to 0, and then we can locate both roots for this polynomial. x^2 + 13x + 40 2 = 0 all of us do not ignore that x circumstances x provides us x^2, yet we opt to entice close elements of 40 2. there is two * 21, 6 * 7, 3 * 14... we opt to apply both elements, that once extra mutually, supply us thirteen. 6 + 7 = thirteen, so those are the elements we are going to use. (x + 6)(x + 7) = 0. Now we set both one among those equivalent to 0. x + 6 = 0 and x + 7 = 0. We subtract 6 from each and every area, and seven from each and every area, and we get: x = -6, and x = -7

Answer 6

Factoring x^2-13x+42 = (x - 6) (x - 7) = (x + -6)(x + -7)
so
A = -6 and B = -7
A+B= -13

Answer 7

x^2-13x+42 = x^2+(A+B)x+A*B

hence A+B=-13

Answer 8

Multiply out (x+A)(x+B). This gets you a polynomial with terms in x^2, x, and 1 (constant). Compare with the left hand side and note that only like terms can compare, so you can equate coefficients in x^2, x, and 1. This gets you your result.

Answer 9

The roots are -A and - B

The relationships between roots and coefficients are:

alpha + beta = - b / a
alpha beta = c/a

In this case, alpha = -A and beta = - B, a = 1, b = -13 and c = 43

So: A + B = - sum of the roots.

The sum of the roots is 13, so A + B = -13

Ana