Consider this expression. x^2 + x - 72

Replace the values of a and b to rewrite the given expression.

( x + a )( x + b )

We are to consider the given expression:

x² + x - 72

The above expression is a quadratic expression and the objective is to determine its roots in form of (x + a) (x + b)

In form of (x + a) (x + b), the values of the expression x² + x - 72 in form of (x + a) (x + b) are 9 and -8 respectively.

From the given expression;

x² + x - 72

So; we will look for two factors of 72 in such a way that if those factors are multiplied together; they will give -72 and the addition of those two numbers will give +1.

So, the factors of 72 are:

From the above factors;

∴

Our factors are:  (-8)  and (9)

From  x² + x - 72, we have:

x² + (-8x) + (9x) - 72 = 0

(x² - 8x) + (9x -72) = 0

Opening the brackets by factorization;

x(x -8) + 9(x -8) = 0

(x + 9) or (x - 8) = 0

(x + 9) (x - 8) = 0

Recall that, we are to replace the values of a and b with the roots derived from the expression x^2 + x - 72.

Therefore, we can conclude that the values of a and b are 9 and -8 respectively.

Learn more about quadratic equations here:

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Step-by-step explanation:

Hello, first we can develop (x+a)(x+b)

We know that this should be equal to

So, we can identify the coefficients of the like terms

1 = 1 (terms in

1 =  a + b (terms in x)

-72 = ab (constant term)

72 is 8 * 9 so, -72=9*(-8)

and we have 9 - 8 =1

so, a = 9 and b = -8

Thank you

step-by-step explanation:

a triangular prism is a 3 dimensional shape composed of triangles and rectangles. it is made from two triangular bases and three rectangular sides.