+ 0*m - 3/2*m**2. Determine r so that q(r) = 0.
0, 1
Let d = 2/4215 + 37921/29505. Solve 3/7*f**3 + d*f**2 - 3/7*f - 9/7 = 0.
-3, -1, 1
Let i be 8 + (1/(6/60))/(77/(-44)). Let 2/7*l**2 + 4/7*l - i = 0. Calculate l.
-4, 2
Let o be 6/(((-1)/(-3))/(24/36)). Suppose 2*m + o = -m, 0 = -5*i + 5*m + 40. Factor 0*y + 6/5*y**5 + 4/5*y**3 + 2*y**i + 0*y**2 + 0.
2*y**3*(y + 1)*(3*y + 2)/5
Let r(g) be the third derivative of g**8/504 + 13*g**7/315 + 29*g**6/90 + 53*g**5/45 + 85*g**4/36 + 25*g**3/9 + 154*g**2. Factor r(q).
2*(q + 1)**3*(q + 5)**2/3
Let a be 8/(-140) - (-2)/(-14). Let x = 9/20 + a. Factor -x - 1/4*r**2 + 1/2*r.
-(r - 1)**2/4
Let p be -215 + 193 + 12*2. Let q**4 + 4/5*q + 2/5*q**3 - 3*q**p + 4/5 = 0. What is q?
-2, -2/5, 1
Let o(v) = v - 7 + 1 + 48*v**2 + 1. Let a(s) = s**2 - s + 1. Let b(p) = p + 15. Let d be b(-13). Let m(j) = d*o(j) + 2*a(j). Factor m(f).
2*(7*f - 2)*(7*f + 2)
Let o(g) = 3*g**3 + g**2 - 60*g + 146. Let i(r) = 4*r**3 + r**2 - 62*r + 147. Let m(h) = 2*i(h) - 3*o(h). Factor m(b).
-(b - 4)**2*(b + 9)
Suppose 0 = 5*b + o - 23, -b = 3*b - 5*o - 1. Suppose 5*f - a - 14 = 0, -b*a = f - 9*a + 2. Factor 0*w + 0 - 1/4*w**f + 1/4*w**2.
-w**2*(w - 1)/4
Let c(d) = 3*d**3 + d**2 - 2*d + 1. Let z(t) = -16*t**3 - 46*t**2 + 278*t - 594. Let x(l) = 6*c(l) + z(l). Factor x(a).
2*(a - 7)**2*(a - 6)
Let m be ((-51)/408)/(1*-1). Let r(n) be the second derivative of 0 + 1/16*n**4 - 2*n + m*n**2 - 1/6*n**3. Find g such that r(g) = 0.
1/3, 1
Suppose 0 = -5*k + 3*c + 1, -5*c = 4*k - 6*c - 5. Let i = -1 + 7. Suppose 2*o**k - 4 - 9*o + 3 + 3*o + i*o**3 + 2*o**4 - 3 = 0. What is o?
-2, -1, 1
Let p(f) = 3*f**4 + 9*f**3 + 6*f**2 - 6*f - 6. Let n(k) = k**3 - k**2 + k + 1. Let l(i) = 6*n(i) + p(i). Factor l(q).
3*q**3*(q + 5)
Suppose -6 = 4*x - 18. Suppose -l = -x*m - 2*m + 6, -4*l = m - 18. Determine b, given that 2*b**5 + b**m - b**3 + b**4 + b**2 + 7*b**3 + 5*b**4 = 0.
-1, 0
Let b(k) = -k + 9. Let z be b(5). Factor 2*i**2 - z*i**2 + 80*i - 88*i.
-2*i*(i + 4)
Let s(j) be the first derivative of -2/15*j**5 - j**4 - 8/3*j**3 + 9 - 8/3*j**2 + 0*j. What is x in s(x) = 0?
-2, 0
Let p(q) be the second derivative of q**6/90 - q**5/30 + q**4/36 + 174*q. Let p(y) = 0. Calculate y.
0, 1
Let y = -624252/5 + 124851. Let a = -13/3 - -68/15. Factor a*u**3 - 1/5*u + y*u**2 - 3/5.
(u - 1)*(u + 1)*(u + 3)/5
Let w(v) be the first derivative of 1/12*v**4 + 0*v**3 + 2*v**2 + 0*v + 1/60*v**5 - 4. Let h(t) be the second derivative of w(t). Suppose h(l) = 0. What is l?
-2, 0
Let m(g) be the second derivative of -1/12*g**3 + 0 - 1/48*g**4 + 0*g**2 + 13*g. Suppose m(j) = 0. Calculate j.
-2, 0
Let p(g) be the first derivative of -g**6/10 + 6*g**5/25 - 3*g**4/20 + 305. Factor p(i).
-3*i**3*(i - 1)**2/5
Let b(v) be the third derivative of 81*v**6/140 + 9*v**5/14 - 8*v**4/7 + 4*v**3/7 + 68*v**2 - v. Factor b(k).
6*(k + 1)*(9*k - 2)**2/7
Solve 90*i**4 - 4*i**3 - i**3 - 91*i**4 + 6*i**2 + 3*i**3 + 3*i**3 = 0 for i.
-2, 0, 3
Let l = 391 - 386. Let i(u) be the first derivative of -54*u - 14/5*u**l - 27*u**2 + 12*u**3 + 5*u**4 - 2 + 1/3*u**6. Factor i(j).
2*(j - 3)**3*(j + 1)**2
Let w(x) be the first derivative of x**4/14 - 24*x**3/7 + 69*x**2/7 - 68*x/7 + 179. Solve w(j) = 0.
1, 34
Let p(o) be the third derivative of 0*o + 1/630*o**7 + 5/6*o**4 + 0 + 25*o**2 + 23/90*o**5 + 25/18*o**3 + 1/30*o**6. Suppose p(m) = 0. Calculate m.
-5, -1
Let z = 957 - 957. Determine k, given that 6/7*k**2 + 2/7*k**4 + 2/7*k + z + 6/7*k**3 = 0.
-1, 0
Let v(r) be the third derivative of -r**8/168 + 2*r**7/35 - 3*r**6/20 - 2*r**5/15 + r**4 + 180*r**2. Determine h, given that v(h) = 0.
-1, 0, 2, 3
Let i = 21/53 + 11/106. Factor -i*m**2 + 3/2 + m.
-(m - 3)*(m + 1)/2
Factor 2728*k**2 + 128/9 - 3040/9*k + 29791/9*k**4 - 71114/9*k**3.
(k - 2)*(31*k - 4)**3/9
Let q = -4 + 9. Let -643*a**3 + 647*a**3 - 2*a**q - a - a + 0*a**5 = 0. Calculate a.
-1, 0, 1
Suppose s + 27 = 23, b - s = 4. Let w(r) be the first derivative of 1 - 2/7*r + b*r**2 + 2/21*r**3. Suppose w(g) = 0. What is g?
-1, 1
Let u(c) be the third derivative of 0 - 17*c**2 + 0*c**4 + 0*c**3 + 1/75*c**5 + 4/525*c**7 + 0*c - 1/840*c**8 - 1/60*c**6. Solve u(t) = 0 for t.
0, 1, 2
Let i be (-12)/(-8) - (-5)/2. Suppose 3*h + 10 = 4*n - 2, -5*n = h - 15. Factor -2*b - b**3 - 5 + 3*b**3 + h*b**3 + b**4 + i.
(b - 1)*(b + 1)**3
Let p be (2/(-3))/((-2)/25). Let k = p - 8. Let 0*z + 1/3 - k*z**2 = 0. What is z?
-1, 1
Let b(m) be the second derivative of m**4/24 + 11*m**3/12 - 15*m**2 + m + 5. Suppose b(j) = 0. Calculate j.
-15, 4
Let s be 216/144*(-4)/(-3)*2. Let h(t) be the first derivative of -3/2*t**s + 3/5*t**5 + 2 + 0*t**3 + 3*t**2 - 3*t. Let h(f) = 0. What is f?
-1, 1
Find z such that 20/13*z**2 - 2/13*z**3 - 224/13 + 206/13*z = 0.
-7, 1, 16
Let v(n) be the first derivative of 2/7*n**4 - 4/21*n**3 + 11*n + 0*n**2 + 1/10*n**5 - 11. Let k(o) be the first derivative of v(o). Solve k(j) = 0 for j.
-2, 0, 2/7
Let u = -46749/2 + 23375. What is k in -u*k**2 - 1/6*k**5 + 1/2*k**4 + 1/3*k - 1/6*k**3 + 0 = 0?
-1, 0, 1, 2
Let o(d) be the third derivative of d**6/1080 + d**5/360 - d**4/36 - 3*d**3/2 + 8*d**2. Let f(s) be the first derivative of o(s). Factor f(a).
(a - 1)*(a + 2)/3
Let f = 4/73 + 65/146. Let j(g) be the second derivative of -5*g - 9/20*g**5 - f*g**3 - 3/4*g**4 - 1/10*g**6 + 0 + 0*g**2. Determine z so that j(z) = 0.
-1, 0
Let n(m) be the first derivative of -m**6/120 + 3*m**5/20 - 9*m**4/8 + 4*m**3/3 - 8. Let b(o) be the third derivative of n(o). Factor b(q).
-3*(q - 3)**2
Let t(j) be the third derivative of -j**6/160 + 13*j**5/60 - 109*j**4/96 + 5*j**3/2 - 263*j**2 + 2. Factor t(y).
-(y - 15)*(y - 1)*(3*y - 4)/4
Let w(z) = 100*z**2 - 270*z. Let c(m) = -m**3 + 102*m**2 - 273*m. Let b(t) = -5*c(t) + 4*w(t). Factor b(o).
5*o*(o - 19)*(o - 3)
Suppose 3*c - 42 = -12. Let l(w) = -2*w**3 + 14*w**2 - 10*w. Let h(f) = f**2 - f. Let m(p) = c*h(p) - l(p). Let m(o) = 0. Calculate o.
0, 2
Let z be 4*((-1869)/(-266) - 7). Let s(p) = -p**3 + 9*p**2 + 2*p - 18. Let n be s(9). Factor 2/19*w**2 + n + z*w.
2*w*(w + 1)/19
Let d be (-7)/14 - 22/(-28). Solve 6/7*h**3 + 1/7*h**2 + 0 - 2/7*h + 1/7*h**4 - d*h**5 = 0.
-1, 0, 1/2, 2
Let g(w) be the second derivative of -w**7/6300 - w**6/900 - w**4/6 - 12*w. Let r(f) be the third derivative of g(f). Factor r(h).
-2*h*(h + 2)/5
Find f such that 4/21*f + 2/21*f**2 - 16/21 = 0.
-4, 2
Let g(n) be the second derivative of 0*n**3 + 3/25*n**6 + 8/15*n**4 - 33*n + 12/25*n**5 + 0*n**2 + 1/105*n**7 + 0. Let g(m) = 0. What is m?
-4, -1, 0
Suppose -4*i = -246*v + 243*v + 35, -5*i = 3*v + 10. Factor 1/3*t + 0*t**2 + 0*t**4 + 1/3*t**v - 2/3*t**3 + 0.
t*(t - 1)**2*(t + 1)**2/3
What is d in -18/19*d + 16/19 + 2/19*d**2 = 0?
1, 8
Let p = 87/178 - -1/89. Factor 0 - 1/2*x**5 - p*x**4 + 1/2*x**2 + 0*x + 1/2*x**3.
-x**2*(x - 1)*(x + 1)**2/2
Let x(w) be the first derivative of -w**5 + 10*w**4 - 110*w**3/3 + 60*w**2 - 45*w + 575. Determine f so that x(f) = 0.
1, 3
Let o(i) be the third derivative of 25*i**8/336 - 4*i**7/21 - i**6/6 + 5*i**5/6 - 5*i**4/24 - 5*i**3/3 + 137*i**2. Factor o(c).
5*(c - 1)**3*(c + 1)*(5*c + 2)
Let l(d) = -d**3 - 12*d**2 - d - 4. Let z be l(-12). Factor 5*r**2 + 12*r**3 - z*r**3 + 4*r**4 + r + 4*r**3.
r*(r + 1)*(2*r + 1)**2
Suppose 0 = -3*r + 12, 3*n - 5*n + 16 = r. Suppose n*h = h + 150. Factor -8*d**3 - h*d - 7*d**3 + 9 + 36*d**2 + 3*d**4 - 3*d**3.
3*(d - 3)*(d - 1)**3
Let n be 8 + (12 - 484/33). Factor 4/3 + n*q + q**3 + 13/3*q**2.
(q + 2)**2*(3*q + 1)/3
Let l(d) be the first derivative of -2*d**3/15 - 24*d**2/5 + 10*d + 121. Factor l(b).
-2*(b - 1)*(b + 25)/5
Let a be ((-52)/8)/1 - 1/(-2). Let c(f) = -2*f**2. Let n(u) = u**2. Let d(i) = a*c(i) - 17*n(i). Factor d(y).
-5*y**2
Factor -4*v**2 - 54 + 0*v**3 + 63*v - 3*v**2 + 3*v**3 - 17*v**2.
3*(v - 3)**2*(v - 2)
Let x(c) be the first derivative of -c**6/6 - 24*c**5/25 - 2*c**4 - 26*c**3/15 - 3*c**2/10 + 2*c/5 + 92. Let x(m) = 0. Calculate m.
-2, -1, 1/5
Let c(a) be the first derivative of 2*a**5/15 - 14*a**3/9 - 2*a**2 + 211. Factor c(d).
2*d*(d - 3)*(d + 1)*(d + 2)/3
Let d = 19/66 - -1/22. Let l(q) be the second derivative of 0 + 1/6*q**4 + 6*q - d*q**3 - 2*q**2. Suppose l(a) = 0. Calculate a.
-1, 2
Let v(g) = 3*g. Let r be v(1). Let o(f) be the third derivative of -1/70*f**7 