Factor the trinomial. 32t3+32t2z+8tz2=

Question

Factor the trinomial.  32t3+32t2z+8tz2=

Thomas White · Accepted Answer

Step 1
Given that :
The trinomial polynomial is

32 t^{3} + 32 t^{2} z + 8 t z^{2}

.
Step 2
By using,
Factorization of polynomial :
Factors are the integers which are multiplied to produce an original number.
Step 3
To find the factors of the polynomial:
Consider,

32 t^{3} + 32 t^{2} z + 8 t z^{2} = (8 \times 4) t^{2} z + 8 t z^{2}

= 8 t (4 t^{2} + 4 t z + z^{2})

= 8 t (4 t^{2} + 4 t z + z^{2})

4 t^{2} + 4 t z + z^{2} = 4 t^{2} + 2 t z + 2 t z + z^{2}

= (4 t^{2} + 2 t z) + (2 t z + z^{2})

=2t(2t+z)+z(2t+z)
=(2t+z)(2t+z)
Factor of

4 t^{2} + 4 t z + z^{2} = (2 t + z) (2 t + z)

Step 4
To get,

32 t^{3} + 32 t^{2} z + 8 t z^{2} = 8 t (4 t^{2} + 4 t z + z^{2})

=8t(2t+z)(2t+z)
Then,
Factor of the polynomial

32 t^{3} + 32 t^{2} z + 8 t z^{2} = 8 t (2 t + z) (2 t + z)

Therefore,
Factors of the trinomial polynomial

32 t^{3} + 32 t^{2} z + 8 t z^{2} = 8 t (2 t + z) (2 t + z)

.

Factor the trinomial. 32t^{3}+32t^{2}z+8tz^{2}=

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