Question

What should be multiplied to (3x – 5) to get 9x2 – 30x + 25?

Answer 1

Answer:

Step by step solution :

STEP

1

:

Equation at the end of step 1

(3x - 5) • ((32x2 - 30x) + 25) = 0

STEP

2

:

Trying to factor by splitting the middle term

2.1 Factoring 9x2-30x+25

The first term is, 9x2 its coefficient is 9 .

The middle term is, -30x its coefficient is -30 .

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

Step-1 : Multiply the coefficient of the first term by the constant 9 • 25 = 225

Step-2 : Find two factors of 225 whose sum equals the coefficient of the middle term, which is -30 .

-225 + -1 = -226

-75 + -3 = -78

-45 + -5 = -50

-25 + -9 = -34

-15 + -15 = -30 That's it

Step-3 : Rewrite the polynomial splitting the middle term using the two factors found in step 2 above, -15 and -15

9x2 - 15x - 15x - 25

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

3x • (3x-5)

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

5 • (3x-5)

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

(3x-5) • (3x-5)

Which is the desired factorization

Answer 2

SOLUTION

TO DETERMINE

The expression should be multiplied to (3x – 5) to get 9x² – 30x + 25

EVALUATION

By the given -

Product = 9x² – 30x + 25

One of the expression = 3x - 5

Let another expression = P

So by the given condition

P × ( 3x - 5 ) = 9x² – 30x + 25

$\displaystyle \sf{ \implies P = \frac{9 {x}^{2} - 30x + 25 }{(3x - 5)} }$

$\displaystyle \sf{ \implies P = \frac{{(3x)}^{2} - 2 \times 3x \times 5 + {5}^{2} }{(3x - 5)} }$

$\displaystyle \sf{ \implies P = \frac{{(3x - 5)}^{2} }{(3x - 5)} }$

$\displaystyle \sf{ \implies P = (3x - 5)}$

FINAL ANSWER

Hence the required algebraic expression

= 3x - 5

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