Question

Consider this expression.

x^2 + x - 72

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

( x + a )( x + b )

Answer 1

Answer:

Step-by-step explanation:

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

$(x+a)(x+b)=x(x+b)+a(x+b)=x^2+bx+ax+ab=x^2+(a+b)x+ab$

We know that this should be equal to

$x^2+x-72$

So, we can identify the coefficients of the like terms

1 = 1 (terms in $x^2)$

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

$\Large \boxed{\sf \bf \ x^2+x-72=(x+9)(x-8) \ }$

Thank you

Answer 2

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:

• 1, 2, 3, 6, 8, 9, 12, 36, 72

From the above factors;

• the multiplication of (-8) × (9) will give us  = -72
• and the addtion of -8 + 9 = +1

∴

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.

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