Question

8a⁴+2a²-45 what is the answer ​

Answer 1

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Step-by-step explanation:

The first term is, 8a4 its coefficient is 8 .

The middle term is, +2a2 its coefficient is 2 .

The last term, "the constant", is -45

Step-1 : Multiply the coefficient of the first term by the constant 8 • -45 = -360

Step-2 : Find two factors of -360 whose sum equals the coefficient of the middle term, which is 2 .

-360 + 1 = -359

-180 + 2 = -178

-120 + 3 = -117

-90 + 4 = -86

-72 + 5 = -67

-60 + 6 = -54

-45 + 8 = -37

-40 + 9 = -31

-36 + 10 = -26

-30 + 12 = -18

-24 + 15 = -9

-20 + 18 = -2

-18 + 20 = 2 That's it

Step-3 : Rewrite the polynomial splitting the middle term using the two factors found in step 2 above, -18 and 20

8a4 - 18a2 + 20a2 - 45

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

2a2 • (4a2-9)

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

5 • (4a2-9)

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

(2a2+5) • (4a2-9)

Which is the desired factorization