Factor 4a^4+23a^2+28

Math
4a4+23a2+28
Rewrite a4 as (a2)2.
4(a2)2+23a2+28
Let u=a2. Substitute u for all occurrences of a2.
4u2+23u+28
Factor by grouping.
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For a polynomial of the form ax2+bx+c, rewrite the middle term as a sum of two terms whose product is a⋅c=4⋅28=112 and whose sum is b=23.
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Factor 23 out of 23u.
4u2+23(u)+28
Rewrite 23 as 7 plus 16
4u2+(7+16)u+28
Apply the distributive property.
4u2+7u+16u+28
4u2+7u+16u+28
Factor out the greatest common factor from each group.
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Group the first two terms and the last two terms.
(4u2+7u)+16u+28
Factor out the greatest common factor (GCF) from each group.
u(4u+7)+4(4u+7)
u(4u+7)+4(4u+7)
Factor the polynomial by factoring out the greatest common factor, 4u+7.
(4u+7)(u+4)
(4u+7)(u+4)
Replace all occurrences of u with a2.
(4a2+7)(a2+4)
Factor 4a^4+23a^2+28

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