Question

cn the polynomial below be factored into a perfect square? if not select the best describes...64x^2+49x+8
a) the x^2 coefficient does not permit the factoring.
B) the x^2 coefficient does permit the factoring.
C)the constant value does not permit the factoring.
D)the polynomial may be factored into a perfect square.

Answer 1

im confused

Answer 2

i think c
because to permit factorising cosnta should be some how a multiple of some odd number

Answer 3

Okay, if a quadratic (the type of polynomial in your case) can be factored into a perfect square, it means it has repeated roots. Now to find out if it has repeated roots or not, we need to check the discriminant -

To check if a quadratic has real factors or not, check the Discriminant "D"

\[D = b^2 - 4ac\]

where 'a', 'b' and 'c' can be found out by comparing your quadratic with the standard form of the quadratic equation:
\[ax^2 + bx +c = 0\]

now, if:

\(D=0 \rightarrow\) One real root (REPEATED) (means its a whole square)
\(D>0 \rightarrow\)Two real and unequal roots
\(D<0 \rightarrow\) NO real roots

So, what do you think now for your polynomial \(64x^2+49x+8\) ??