Let x = 834 + -150119/180. Let q(g) be the third derivative of 1/9*g**3 - 1/90*g**5 + 0*g + 0 + g**2 + x*g**6 - 1/36*g**4. Factor q(o).
2*(o - 1)**2*(o + 1)/3
Let h(y) be the first derivative of -y**6/9 + 13*y**5/15 - 5*y**4/2 + 28*y**3/9 - 4*y**2/3 + 24. Factor h(b).
-b*(b - 2)**3*(2*b - 1)/3
Let b(h) be the third derivative of 1/39*h**3 + 0 + 0*h + 2*h**2 - 1/455*h**7 - 1/39*h**4 + 1/195*h**5 + 1/195*h**6. Solve b(l) = 0.
-1, 1/3, 1
Factor 0*o + 3/4*o**2 - 1 - 1/4*o**3.
-(o - 2)**2*(o + 1)/4
Let z(w) be the first derivative of 2*w**3 + 6*w**2 - 3/4*w**4 + 10 - 24*w. What is f in z(f) = 0?
-2, 2
Suppose -2*q + 10*q**2 + 21 - 3*q**2 - 24 - 2*q**3 = 0. What is q?
-1/2, 1, 3
Let u be (14/(-4) - -3)*42. Let s(m) = -8*m**3 - 9*m**2 + m + 9. Let f(h) = h**3 + h**2 - 1. Let i(n) = u*f(n) - 3*s(n). Factor i(z).
3*(z - 1)*(z + 1)*(z + 2)
Let u be (1 - 20/12)*(-9 - -3). Let t(r) be the third derivative of 0*r**3 + 0*r**4 + 1/135*r**5 + 0 + 0*r - 1/540*r**6 + u*r**2 - 1/945*r**7. Factor t(f).
-2*f**2*(f - 1)*(f + 2)/9
Let j(u) = u + 6. Let r be j(-4). Determine v, given that 2*v + v + 0*v**2 + 2*v**2 - r - 3*v**2 = 0.
1, 2
Suppose 28 + 0 = 4*a. Let o = 10 - a. Factor 2*v - 3*v**2 + 3*v**2 - 2*v**o.
-2*v*(v - 1)*(v + 1)
Let q(i) = 2*i - 6*i + i**2 + i + 2. Let j(x) = 4*x - 3. Let t(p) = -2*j(p) - 3*q(p). Suppose t(c) = 0. What is c?
0, 1/3
Let j(d) be the third derivative of d**7/1260 - d**6/180 + d**4/8 + 3*d**2. Let c(k) be the second derivative of j(k). Determine s so that c(s) = 0.
0, 2
Suppose -k + 3 + 1 = 0. Determine w, given that k - 3*w**2 - 1 - w + w = 0.
-1, 1
Let q = 104 - 518/5. Let r = -13/33 - -461/165. Factor r*d**3 + 8/5*d**4 + 8/5*d**2 + q*d + 0 + 2/5*d**5.
2*d*(d + 1)**4/5
Let l(c) = c**3 - 2*c**2 - 3. Let p be ((-24)/14)/((-6)/21). Let a(y) = y**2 + 1. Let v(k) = p*a(k) + 2*l(k). Determine n so that v(n) = 0.
-1, 0
Let y(d) be the third derivative of 0*d + 0 + d**2 - 1/2*d**3 - 1/4*d**4 - 1/20*d**5. Factor y(b).
-3*(b + 1)**2
Let i(l) be the third derivative of -l**6/30 - l**5/15 + l**4/3 - 10*l**2. Find h such that i(h) = 0.
-2, 0, 1
Let q = 3943/7 + -563. Factor 4/7 - 2/7*p - q*p**2.
-2*(p - 1)*(p + 2)/7
Let u(w) be the first derivative of -5*w**4/16 + 15*w**2/8 + 5*w/2 - 13. Solve u(a) = 0.
-1, 2
Let h(m) be the first derivative of 1 + 0*m**5 + 0*m**2 - 1/126*m**7 + 0*m**3 + 2*m + 0*m**4 + 0*m**6. Let d(z) be the first derivative of h(z). Factor d(x).
-x**5/3
Let r = 45/89 - 1445/3738. Let x = r - -1/6. Factor 0 + x*p**3 - 6/7*p**2 + 4/7*p.
2*p*(p - 2)*(p - 1)/7
Let g(j) be the third derivative of -j**8/1176 + j**7/735 + j**6/420 - j**5/210 - 8*j**2. Factor g(o).
-2*o**2*(o - 1)**2*(o + 1)/7
Suppose -7*c = -2*c - 40. Suppose 0 = -4*a + c. Factor -v**3 - 3*v**a + v**4 - v**5 + 2*v**2 + 2*v**3.
-v**2*(v - 1)**2*(v + 1)
Let f be 14*22/(-960) + 2/6. Let o(x) be the third derivative of 3*x**2 - 1/40*x**6 + 0*x + 1/48*x**4 + 0 + 0*x**3 - f*x**5 - 1/120*x**7. Factor o(g).
-g*(g + 1)**2*(7*g - 2)/4
Let q = 28/5 - 107/20. Factor q*k**2 + k + 1.
(k + 2)**2/4
Let -m**4 + 2*m**2 - 1 + 1/2*m**5 - m**3 + 1/2*m = 0. Calculate m.
-1, 1, 2
Suppose 0 + 0*v + 9/4*v**2 - 3/4*v**3 = 0. Calculate v.
0, 3
Let b(l) be the first derivative of -1/21*l**6 - 8/21*l**3 + 8/35*l**5 + 4/7*l**2 - 3/14*l**4 + 0*l - 1. What is c in b(c) = 0?
-1, 0, 1, 2
Let j = 14 - 14. Let l be (0 - j) + 2/6. Factor l*g + 0 - 1/3*g**3 + 0*g**2.
-g*(g - 1)*(g + 1)/3
Let q = 22 + -22. Let c(r) be the second derivative of q - r + 1/3*r**4 + 1/3*r**3 - r**2. Determine y, given that c(y) = 0.
-1, 1/2
Let f(c) = 3*c**2 - c + 1. Suppose 5 = 6*m - m. Let a be f(m). Factor -11 - 2*b + b**a + 11 + b**2.
b*(b - 1)*(b + 2)
Let c(m) be the first derivative of -1/12*m**4 - 1/6*m**2 + 2/9*m**3 - 2 + 0*m. Determine h so that c(h) = 0.
0, 1
Let l(p) = -p**2 - 8*p + 3. Let h = -29 + 21. Let u be l(h). Suppose -4/5*b**u - 2/5*b + 0 - 6/5*b**2 = 0. What is b?
-1, -1/2, 0
Let z = 11 - 8. Factor 0*k**3 - 2 - 1 + 3*k - 3*k**z + 3*k**2.
-3*(k - 1)**2*(k + 1)
Let z(s) be the second derivative of s**7/12600 + s**6/1800 + s**5/600 + s**4/6 + 3*s. Let o(p) be the third derivative of z(p). Suppose o(i) = 0. Calculate i.
-1
Let x(a) = a**2 + 84*a - 399. Let i(b) = 10*b**2 + 755*b - 3590. Let w(s) = 6*i(s) - 55*x(s). Solve w(o) = 0 for o.
9
Let w(y) be the first derivative of y**6/16 - 3*y**5/40 - 15*y**4/32 + y**3/8 + 3*y**2/2 + 3*y/2 - 8. Factor w(k).
3*(k - 2)**2*(k + 1)**3/8
Suppose -35*k**5 + 112*k**4 - 38*k**5 + 25*k**5 + 56*k**4 + 9*k**2 - 75*k**3 = 0. Calculate k.
0, 1/4, 3
Let v(b) be the first derivative of -b**7/420 + b**6/180 + b**5/60 - b**4/12 + b**3/3 + 2. Let m(z) be the third derivative of v(z). Let m(n) = 0. Calculate n.
-1, 1
Let 48/7*t**2 - 74/7*t**3 - 8/7*t**5 + 6*t**4 - 8/7*t + 0 = 0. What is t?
0, 1/4, 1, 2
Let y be (-4)/32*(-2)/10. Let h(u) be the second derivative of u + 0 + y*u**5 + 0*u**3 + 0*u**2 - 1/24*u**4 + 1/60*u**6 - 1/84*u**7. Factor h(i).
-i**2*(i - 1)**2*(i + 1)/2
Let v = 54/85 + -4/17. Let j(f) be the first derivative of 0*f + 0*f**2 + 0*f**3 - v*f**5 - 3 - f**4. Factor j(h).
-2*h**3*(h + 2)
Let f(g) = 2*g**5 - 6*g**4 + 4*g**3 + 4*g**2 - 2*g - 2. Let s(q) = q**3 - q**2 + q - 1. Let k(v) = 2*f(v) - 4*s(v). Factor k(h).
4*h*(h - 2)*(h - 1)**2*(h + 1)
Let x(b) = -b**3 + 15*b**2 + 2. Let p be x(15). Solve -1/4*w - 1/4*w**p + 0 = 0.
-1, 0
Let n(d) = d**3 + 11*d**2. Let m be n(-11). Let v = 9/20 + 1/20. Factor -v*q + m + 1/2*q**2.
q*(q - 1)/2
Let t(v) = -v**3 + 7*v**2 - 4*v - 7. Let k be t(6). Suppose g + s = k*s - 20, -4*g = -s + 5. Factor 0*u + g - 2/5*u**2 + 6/5*u**3 + 2/5*u**5 - 6/5*u**4.
2*u**2*(u - 1)**3/5
Let r(x) be the second derivative of -x**7/126 + x**6/60 - x**4/72 - 5*x. Factor r(f).
-f**2*(f - 1)**2*(2*f + 1)/6
Let j(w) be the third derivative of -w**5/12 - 5*w**4/6 - 10*w**3/3 + 12*w**2. Factor j(x).
-5*(x + 2)**2
Factor -20*t**2 - 80*t**3 + 254*t - 254*t - 25*t**4 + 125*t**5.
5*t**2*(t - 1)*(5*t + 2)**2
Let m(w) = 2*w**5 - 24*w**4 - 45*w**3 - 44*w**2 - 19*w + 1. Let g(y) = y**5 - y**4 + y**2 + y + 1. Let r(c) = 5*g(c) - m(c). Let r(t) = 0. What is t?
-2, -1, -1/3
Let w(b) = -1. Let u(z) = 29*z**2 + 7*z - 47. Let j(a) = u(a) + 6*w(a). Let s(r) = 10*r**2 + 2*r - 18. Let x(d) = 6*j(d) - 17*s(d). Factor x(f).
4*(f - 1)*(f + 3)
Let u(x) = 4*x**3 + 3*x**2 - 3*x - 8. Let y(p) = 5*p**3 + 4*p**2 - 3*p - 9. Let c(v) = -4*u(v) + 3*y(v). Let m(h) be the first derivative of c(h). Factor m(a).
-3*(a - 1)*(a + 1)
Let d(q) be the second derivative of 0*q**2 + 2*q + 0*q**3 + 0*q**4 + 1/75*q**6 + 0*q**5 - 1/105*q**7 + 0. Factor d(v).
-2*v**4*(v - 1)/5
Let b(m) be the second derivative of -1/12*m**4 + m**2 + 1/30*m**5 + 0 - 1/3*m**3 + 2*m + 1/60*m**6. Let r(p) be the first derivative of b(p). Factor r(f).
2*(f - 1)*(f + 1)**2
Let v = -1 + 7. Factor -h**4 + 0*h**2 - 3*h - v*h**2 + 4*h**3 + 7*h - 1 + 0*h**4.
-(h - 1)**4
Let i(f) be the first derivative of -2*f**3/15 + f**2/5 - 7. Factor i(z).
-2*z*(z - 1)/5
Factor 1/3*b + 1/9*b**2 + 0.
b*(b + 3)/9
Let x(k) = -2*k + 18. Let q be x(8). Let -3/5*y**q + 3/5*y - 3/5*y**3 + 3/5 = 0. Calculate y.
-1, 1
Let k(q) be the second derivative of -q**5/210 + q**4/42 - q**3/21 - q**2 - 2*q. Let s(v) be the first derivative of k(v). Factor s(z).
-2*(z - 1)**2/7
Let s(k) be the first derivative of 2*k**5/45 + k**4/18 - 2*k**3/9 - 5*k**2/9 - 4*k/9 - 13. Suppose s(o) = 0. Calculate o.
-1, 2
Let h(j) be the third derivative of j**6/420 + 2*j**5/105 + 5*j**4/84 + 2*j**3/21 - 13*j**2. Find u such that h(u) = 0.
-2, -1
Let r(c) be the third derivative of c**6/150 - c**5/25 + 8*c**3/15 - 18*c**2. What is i in r(i) = 0?
-1, 2
Factor 0 + 12/5*y**2 - 72/5*y + 16/5*y**3 - 4/5*y**4.
-4*y*(y - 3)**2*(y + 2)/5
Let w(c) be the first derivative of -5*c**4/4 + 20*c**3/3 - 2. Factor w(t).
-5*t**2*(t - 4)
Let c = -213 - -653/3. Let x(w) be the first derivative of 12*w**2 + 8*w - c*w**3 + 2. Solve x(u) = 0.
-2/7, 2
Suppose 1 - 25*o**3 - 1 + 40*o**4 + 5*o**5 + 10*o**5 - 30*o**2 = 0. What is o?
-3, -2/3, 0, 1
Let r(l) = -11*l**4 + 8*l**3 - 2*l. Let q(t) = 111*t**4 - 81*t**3 + 21*t. Let s(f) = 2*q(f) + 21*r(f). Factor s(g).
-3*g**3*(3*g - 2)
Let b(n) be the second derivative of 0 - 16/9*n**2 - 4/45*n**5 - 1/135*n**6 - 4/9*n**4 + 2*n - 32/27*n**3. Solve b(w) = 0.
-2
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