Find the HCF 3q^2-5q-28 , 7q^2-29q+4 , q^2-16

Math
3q2-5q-28 , 7q2-29q+4 , q2-16
Add 3q2 and 7q2.
10q2-5q-28-29q+4+q2-16
Add 10q2 and q2.
11q2-5q-28-29q+4-16
Subtract 29q from -5q.
11q2-34q-28+4-16
Add -28 and 4.
11q2-34q-24-16
Subtract 16 from -24.
11q2-34q-40
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=11⋅-40=-440 and whose sum is b=-34.
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Factor -34 out of -34q.
11q2-34(q)-40
Rewrite -34 as 10 plus -44
11q2+(10-44)q-40
Apply the distributive property.
11q2+10q-44q-40
11q2+10q-44q-40
Factor out the greatest common factor from each group.
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Group the first two terms and the last two terms.
(11q2+10q)-44q-40
Factor out the greatest common factor (GCF) from each group.
q(11q+10)-4(11q+10)
q(11q+10)-4(11q+10)
Factor the polynomial by factoring out the greatest common factor, 11q+10.
(11q+10)(q-4)
(11q+10)(q-4)
Find the HCF 3q^2-5q-28 , 7q^2-29q+4 , q^2-16

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