Question

$(x {}^{2} - 7x + 11) {x}^{2} { - 11x + 30} = 1$
Please solve this fast. ​

Answer 1

Answer:

STEP

1

:

Trying to factor by splitting the middle term

1.1 Factoring x2-7x+11

The first term is, x2 its coefficient is 1 .

The middle term is, -7x its coefficient is -7 .

The last term, "the constant", is +11

Step-1 : Multiply the coefficient of the first term by the constant 1 • 11 = 11

Step-2 : Find two factors of 11 whose sum equals the coefficient of the middle term, which is -7 .

-11 + -1 = -12

-1 + -11 = -12

1 + 11 = 12

11 + 1 = 12

Observation : No two such factors can be found !!

Conclusion : Trinomial can not be factored

Trying to factor by splitting the middle term

1.2 Factoring x2-11x+30

The first term is, x2 its coefficient is 1 .

The middle term is, -11x its coefficient is -11 .

The last term, "the constant", is +30

Step-1 : Multiply the coefficient of the first term by the constant 1 • 30 = 30

Step-2 : Find two factors of 30 whose sum equals the coefficient of the middle term, which is -11 .

-30 + -1 = -31

-15 + -2 = -17

-10 + -3 = -13

-6 + -5 = -11 That's it

Step-3 : Rewrite the polynomial splitting the middle term using the two factors found in step 2 above, -6 and -5

x2 - 6x - 5x - 30

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

x • (x-6)

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

5 • (x-6)

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

(x-5) • (x-6)

Which is the desired factorization