et q(x) be the second derivative of 2*x**7/49 - 137*x**6/70 + 2643*x**5/70 - 2538*x**4/7 + 11421*x**3/7 - 2187*x**2/2 + 56*x + 1. Solve q(a) = 0.
1/4, 7, 9
Suppose -2*o = -8, -4*o = f - 3*o. Let n be 11/f - (3 + -6). Determine m so that n*m**3 - m**2 + 5/4*m - 1/2 = 0.
1, 2
Find z such that 112/3 - 8/3*z**2 - 446/3*z = 0.
-56, 1/4
Suppose -p - 4*p - 355 = 0. Let d = p - -74. Determine r, given that 4/3*r**d + 0*r**2 - 2/3*r**4 - 4/3*r + 2/3 = 0.
-1, 1
Let u(r) be the third derivative of -r**7/126 + 7*r**6/144 - r**5/8 + 19*r**4/24 + r**2 + 25. Let g(f) be the second derivative of u(f). What is l in g(l) = 0?
3/4, 1
Suppose -15 = 22*y - 27*y. Factor 1263*z**2 - 372*z + 519*z**2 + 24 - 1075*z**y - 3993*z**4 - 740*z**3.
-3*(z + 1)*(11*z - 2)**3
Let v = 51 + -47. Let g = 1 + 3. Factor -63*p + v - g*p**2 - 17*p**2 - 22 - 6*p.
-3*(p + 3)*(7*p + 2)
Let l(f) be the first derivative of -f**4/20 + 2*f**3/5 - 9*f**2/10 + 4*f/5 - 54. Factor l(r).
-(r - 4)*(r - 1)**2/5
Find r, given that 1728*r**3 + 780*r + 100 + 1591*r**2 - 1092*r**2 + 1517*r**2 = 0.
-5/12, -1/3
Suppose 0 + 9 = 3*t - 3*g, 2*t = 5*g + 9. Let f(q) be the second derivative of 0*q**t + 0*q**3 - 5*q + 0 + 1/40*q**5 + 0*q**4. Factor f(y).
y**3/2
Let q(r) be the third derivative of 0 + 0*r**3 + 0*r - 9*r**2 - 1/5*r**5 + 1/3*r**4 - 1/15*r**6. Factor q(b).
-4*b*(b + 2)*(2*b - 1)
Let l = 0 - -2. Let i be 1/(-5) + (-754)/(-290). Factor 12/5*y + 3/5*y**l + i.
3*(y + 2)**2/5
Factor -87 - 3*u**2 - 109 + 381 - 119 - 63*u.
-3*(u - 1)*(u + 22)
Let j(w) be the second derivative of -w**5/50 + 7*w**4/15 - 19*w**3/5 + 72*w**2/5 + 111*w. Factor j(m).
-2*(m - 8)*(m - 3)**2/5
Let m(f) be the first derivative of 0*f + 1/5*f**3 + 3/5*f**2 - 5. Let m(b) = 0. What is b?
-2, 0
Suppose -3*j = 2*o + 2, -3*j - j - 8 = 0. Let f be 1*o/(-5) - 16/(-40). Let 0 - 2/11*i**2 - 8/11*i**4 - 10/11*i**3 + f*i = 0. Calculate i.
-1, -1/4, 0
Let i(q) be the first derivative of 4*q + 4/3*q**3 - 5 + 4*q**2. Solve i(v) = 0.
-1
Let z(d) = d**3 - d**2 - d + 2. Let k be z(-2). Let r(c) = 4*c**2 + 2*c + 3. Let v(q) = 11*q**2 + 5*q + 8. Let j(n) = k*r(n) + 3*v(n). Let j(y) = 0. What is y?
0, 1
Let r(j) be the first derivative of -j**7/280 - j**6/20 - 3*j**5/10 - j**4 - 5*j**3/3 - 24. Let b(q) be the third derivative of r(q). Let b(y) = 0. Calculate y.
-2
Let h = 45 - 78. Let r be (2 - h/(-18)) + (-5)/(-10). Factor -r*m + 0 - 1/3*m**2.
-m*(m + 2)/3
Let o = -739/15 + 253/5. Let m(y) be the first derivative of o*y**3 - 4/5*y**5 + 0*y + 0*y**4 - 1/3*y**6 + y**2 - 4. Suppose m(r) = 0. Calculate r.
-1, 0, 1
Let l(d) be the first derivative of d**7/420 - d**6/90 + d**5/60 - d**3 - 9. Let x(f) be the third derivative of l(f). Factor x(a).
2*a*(a - 1)**2
Let p(t) be the second derivative of t**7/63 - 7*t**6/45 + 19*t**5/30 - 25*t**4/18 + 16*t**3/9 - 4*t**2/3 - 119*t + 1. Factor p(r).
2*(r - 2)**2*(r - 1)**3/3
Let p(i) be the second derivative of i**6/80 - 3*i**5/160 - i**4/4 + 3*i**3/4 - 112*i. Factor p(z).
3*z*(z - 2)**2*(z + 3)/8
Let q be (4 - 18)*(-1 + -3). Let k be -4*(-36)/q + -2. Solve 2/7*h**2 + k*h + 2/7 = 0.
-1
Let j(i) be the second derivative of 12*i + 15/8*i**4 + 1/2*i**2 + 13/60*i**6 - 19/12*i**3 - 41/40*i**5 + 0. Factor j(a).
(a - 1)**3*(13*a - 2)/2
Suppose -2*w = -6*w + 36. Let i(b) = -7*b**2 + 1 - 7 + 2*b**3 + 0*b + w*b. Let r(u) = 5*u**3 - 15*u**2 + 19*u - 13. Let s(h) = -13*i(h) + 6*r(h). Factor s(q).
q*(q + 1)*(4*q - 3)
Let u(g) be the third derivative of -g**5/105 + g**4/14 + 8*g**3/21 + 51*g**2 + 2*g. Suppose u(b) = 0. What is b?
-1, 4
Suppose 0*n + 0 - 32*n**2 - 2/5*n**5 + 6/5*n**4 + 48/5*n**3 = 0. Calculate n.
-5, 0, 4
What is u in 1085*u - 43*u**3 - 48 + 2*u**2 - 1113*u + 45*u**3 = 0?
-3, -2, 4
Factor 4/3 + 3600*n**2 + 36000*n**3 + 120*n.
4*(30*n + 1)**3/3
Let b(d) be the second derivative of -3*d**7/28 - 31*d**6/10 - 89*d**5/8 - 59*d**4/6 - 3*d**3 + 3*d - 21. Suppose b(r) = 0. What is r?
-18, -2, -1/3, 0
Let g(f) be the second derivative of f**10/6048 - f**9/3024 + f**4/6 + 5*f. Let d(n) be the third derivative of g(n). What is x in d(x) = 0?
0, 1
Let s(u) be the third derivative of -u**7/1260 - u**6/360 + u**5/120 + u**4/36 - u**3/9 + 2*u**2 + 34. Suppose s(i) = 0. Calculate i.
-2, 1
Suppose 4*l + 16 = -4*s - 16, 3*l + 14 = -s. Let v be ((-2)/(-2))/(s/(-20)). Solve -10*c**v - 2*c**5 + 4*c**3 - 2*c + 10*c**4 = 0 for c.
-1, 0, 1
Let q = -12717 - -12719. Determine d so that -6 - 9/2*d**q - 24*d + 21/2*d**4 + 24*d**3 = 0.
-2, -1, -2/7, 1
Factor 2*g**3 - 6*g**3 - 174*g**2 - 36*g + 198*g**2.
-4*g*(g - 3)**2
Let x be (-714)/(-135) - 3/(-27) - 5. Factor -1/5*w**3 - 1/5*w**2 + x*w + 0.
-w*(w - 1)*(w + 2)/5
Let p(c) be the third derivative of -3*c**6/140 + c**5/7 + 23*c**4/84 + 4*c**3/21 - 6*c**2 + 9*c. Factor p(i).
-2*(i - 4)*(3*i + 1)**2/7
Let h(j) be the third derivative of 0*j + 1/8*j**4 - 3/40*j**5 + 1/80*j**6 + 0*j**3 + 0 + 10*j**2. Factor h(i).
3*i*(i - 2)*(i - 1)/2
Let b(m) be the third derivative of m**9/52920 + m**8/7840 - m**4/12 - m**3/6 + 2*m**2 + 4*m. Let w(i) be the second derivative of b(i). Solve w(s) = 0 for s.
-3, 0
Let o(d) = 2*d**2. Let t be o(1). Let w be (-1)/(2/8*(-5 + 3)). Determine v so that 16*v - 27*v**t + 2*v**3 + 2*v**w - 8 + 15*v**2 = 0.
1, 2
Let j(m) be the second derivative of -m**7/945 + m**6/108 - 7*m**5/270 + m**4/36 + 27*m**2 - 29*m. Let h(s) be the first derivative of j(s). Factor h(p).
-2*p*(p - 3)*(p - 1)**2/9
Let z(u) be the third derivative of -u**6/360 - 17*u**5/180 - 7*u**4/36 + 16*u**3/9 - 46*u**2 + 6*u. Factor z(d).
-(d - 1)*(d + 2)*(d + 16)/3
Let g(r) = 3*r**3 - 3*r**2 + 12*r + 5. Let i(v) = -4*v**3 + 4*v**2 - 12*v - 6. Let k(y) = -6*g(y) - 5*i(y). Let k(z) = 0. What is z?
-2, 0, 3
Let r = 2 + 0. Let m be (-3)/r*(-8)/6. Factor -9*d**3 - 12*d**2 + 13*d**4 + 3*d**m - 16*d**4 - 3*d.
-3*d*(d + 1)**3
Let r = -128 + 128. Let g(t) = 2*t**2. Let h be g(1). Let 3*u**3 + r*u**3 - 5*u**4 + u**3 + 3*u**4 - h*u**2 = 0. What is u?
0, 1
Let u = 4041/20 + -202. Let z(b) be the second derivative of 1/6*b**3 + 0 + u*b**5 + 0*b**2 + 7*b + 1/6*b**4. Suppose z(s) = 0. Calculate s.
-1, 0
Solve 902*b**2 - 191*b**2 - 384*b**3 + 1098*b**2 - 486*b + 21*b**4 = 0.
0, 2/7, 9
Let y(k) be the first derivative of 0*k**3 + 0*k**5 - 1/240*k**6 - k**2 + 0*k - 4 + 1/48*k**4. Let i(q) be the second derivative of y(q). Factor i(z).
-z*(z - 1)*(z + 1)/2
Factor 0 + 0*t - 32/9*t**3 - 2/9*t**5 + 20/9*t**4 + 0*t**2.
-2*t**3*(t - 8)*(t - 2)/9
Let u be 8/(-126) + 4/14. Let c = -14521 + 130697/9. Let 2*o + 4/3*o**2 + u*o**3 + c = 0. Calculate o.
-4, -1
Let i = -46565 + 46570. Factor -10/3 + i*j**3 - 50/3*j**2 + 15*j.
5*(j - 2)*(j - 1)*(3*j - 1)/3
Let v(q) be the first derivative of q**6/18 + 19*q**5/15 + 19*q**4/3 + 80*q**3/9 - 32*q**2/3 - 112*q/3 + 109. Factor v(k).
(k - 1)*(k + 2)**3*(k + 14)/3
Let o(z) be the third derivative of -25*z**8/672 - z**7/28 + 49*z**6/120 + z**5/2 + z**4/6 - 147*z**2. What is m in o(m) = 0?
-2, -2/5, -1/5, 0, 2
Suppose 99/4*x + 27/2 - 14*x**3 + 4*x**4 - 15/4*x**2 = 0. Calculate x.
-3/4, 2, 3
Let j be 69 - (-1 - (0 + -2 - -2)). Factor -3 - 54*h**2 + 621*h**4 - 660*h**4 + 21*h + 9*h**5 - 4*h**3 + j*h**3.
3*(h - 1)**4*(3*h - 1)
Let r(j) = -j**2 + 16*j + 39. Let w be r(18). Factor 2*s**w - 6 - 2*s**2 + 7*s**3 + 15*s - 10*s**2 - 6*s**3.
3*(s - 2)*(s - 1)**2
Suppose 25*m - 83*m = -23*m - 10*m. Factor 0 + 0*b - 1/2*b**4 + m*b**2 + b**3.
-b**3*(b - 2)/2
Let x(a) be the first derivative of 3/2*a**2 - 4 - 5*a - 1/3*a**3 + 1/36*a**4. Let n(s) be the first derivative of x(s). Determine f so that n(f) = 0.
3
Let -23*q + 40 + 11*q**3 - 86*q**3 + 113*q - 55*q**2 = 0. Calculate q.
-4/3, -2/5, 1
Let w(v) = -6*v**3 - 7*v**2 + 4*v + 5. Let k(u) = u**2 - 2*u**3 + 2 - u**3 + 1 + 2*u - 5*u**2. Let o(l) = 5*k(l) - 3*w(l). Factor o(m).
m*(m + 1)*(3*m - 2)
Let o(n) = -n**4 - 44*n**3 - 5*n**2 + 47*n. Let a(k) = -8*k**4 - 308*k**3 - 36*k**2 + 330*k. Let y(w) = -6*a(w) + 44*o(w). Factor y(m).
4*m*(m - 22)*(m - 1)*(m + 1)
Let y be (0 - 12/21)/(1/(-7)). Let s(z) be the third derivative of 2*z**3 + 0*z - 1/20*z**5 + 0*z**y + 4*z**2 + 0. Factor s(c).
-3*(c - 2)*(c + 2)
Let -9/7*s**2 + 0 - 3/7*s**4 + 0*s + 3/7*s**5 - 15/7*s**3 = 0. Calculate s.
-1, 0, 3
Let x(u) be the first derivative of 1/360*u**5 + 0*u - 1/48*u**4 - 3/2*u**2 + 1