Question

Factorising Quadratic Expressions of the form
${ - 3b}^{2} + 76b - 25$
​

Answer 1

(3b-1) • (b-25)

Step-by-step explanation:

Factoring 3b2 - 76b + 25

The first term is, 3b2 its coefficient is 3 .

The middle term is, -76b its coefficient is -76 .

The last term, "the constant", is +25

Step-1 : Multiply the coefficient of the first term by the constant 3 • 25 = 75

Step-2 : Find two factors of 75 whose sum equals the coefficient of the middle term, which is -76 .

-75 + -1 = -76 That's it

Step-3 : Rewrite the polynomial splitting the middle term using the two factors found in step 2 above, -75 and -1

3b2 - 75b - 1b - 25

Step-4 : Add up the first 2 terms, pulling out like factors :

3b • (b-25)

Add up the last 2 terms, pulling out common factors :

1 • (b-25)

Step-5 : Add up the four terms of step 4 :

(3b-1) • (b-25)

Which is the desired factorization

Answer 2

Answer:

-3b²+76b-25 (Using splitting the middle term)

-3b²+75b+b-25

-3b(b-25)+1(b-25)

(-3b+1)(b-25)

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