r = -43 + 45. Let n(z) be the first derivative of 2 + r*z - 3/2*z**2 - 3*z**3. Factor n(y).
-(3*y - 1)*(3*y + 2)
Let q be 4 + (-5937)/1980 + -1. Let h(k) be the third derivative of q*k**6 - 1/132*k**4 + 0*k + 1/33*k**3 + 0 - k**2 - 1/330*k**5. Factor h(i).
2*(i - 1)**2*(i + 1)/11
Let r be 2*(-1 + 2 + -2). Let l(f) = -2*f - 1. Let b be l(r). Factor 8/5*w + 8/5*w**b - 2/5 - 2/5*w**4 - 12/5*w**2.
-2*(w - 1)**4/5
Let f(t) be the third derivative of t**6/40 + t**5/5 + t**4/2 - 13*t**2. Determine m, given that f(m) = 0.
-2, 0
Let y(k) = -9*k**4 + 36*k**3 - 240*k - 216. Let n(x) = 43 + 22*x + 2*x**4 - 7*x**3 + 2*x + 24*x. Let o(r) = 24*n(r) + 5*y(r). Let o(w) = 0. Calculate w.
-2, 2
Let m be (-6)/3*(0 + 2). Let z = m - -9. Factor z*v + 0 - 4*v**2 + 5*v**2 + 1 - 3*v.
(v + 1)**2
Let k(y) be the second derivative of y**7/7 + 4*y**6/15 + y**5/10 + 11*y. Determine q, given that k(q) = 0.
-1, -1/3, 0
Let u(r) be the third derivative of -r**6/210 - r**5/35 - r**4/21 + 14*r**2. Factor u(j).
-4*j*(j + 1)*(j + 2)/7
Let i(u) = u**2 + 9*u + 12. Let k be i(-9). Let s be k/(-8)*(-48)/81. Solve -4/3*g**2 - 2/9*g**4 - 2/9 - s*g**3 - 8/9*g = 0 for g.
-1
Let d be (((-30)/(-8))/5)/(9/8). Factor d*m**2 - 2/3*m + 0.
2*m*(m - 1)/3
Factor 3/8*w**5 + 0 + 0*w**4 + 0*w**2 + 3/8*w - 3/4*w**3.
3*w*(w - 1)**2*(w + 1)**2/8
Let i(k) be the second derivative of 5*k**4/24 + 5*k**3/12 + 29*k. Suppose i(b) = 0. Calculate b.
-1, 0
Suppose -2*f + 35 = -3*u + 14, -4*u - 17 = f. Factor 0*p - 1/3*p**2 + 0 + 1/3*p**4 + 0*p**f.
p**2*(p - 1)*(p + 1)/3
Let s(v) be the first derivative of 5*v**6/6 - 4*v**5 + 25*v**4/4 - 10*v**3/3 - 29. Suppose s(g) = 0. Calculate g.
0, 1, 2
Suppose -3*p + 4 + 8 = 0, 3*r + 13 = 4*p. Let v(l) = 1. Let q(y) = 2*y**2 - 2*y - 9. Let h(w) = r*q(w) + 5*v(w). Suppose h(m) = 0. What is m?
-1, 2
Let y(k) be the third derivative of k**5/150 + 4*k**4/15 + k**3 - k**2 - 2*k. Factor y(m).
2*(m + 1)*(m + 15)/5
Let m(u) = 2*u**2 - 2. Let n be m(2). Factor -6*p - 15*p**3 + 0*p - n + 24*p**2 + 3*p.
-3*(p - 1)**2*(5*p + 2)
Let u be 2/(-3) + (-7)/(-6). Suppose -h + 9 = 3*m, 7*h - 6*h = 0. Factor 0 + u*b + 0*b**2 - 1/2*b**m.
-b*(b - 1)*(b + 1)/2
Let -1/2*q**2 - 1/2*q + 1/2*q**4 + 0 + 1/2*q**3 = 0. What is q?
-1, 0, 1
Suppose 40*p**4 - 95*p**3 + 20 + 22*p**3 + 140*p**2 - 5*p**5 - 73*p**3 + 36*p**3 - 85*p = 0. What is p?
1, 4
Suppose 0 = -2*a - a + 3*x - 15, 0 = 5*a + x - 5. Let r(s) be the first derivative of -2 - 2/9*s**3 - 1/12*s**4 + a*s - 1/6*s**2. Factor r(u).
-u*(u + 1)**2/3
Let u(s) = s**4 + 5*s**3 - 2*s + 2. Let k(d) = d**4 + d**3 + d + 1. Let c(z) = -10*k(z) + 5*u(z). Find t such that c(t) = 0.
-1, 0, 2
Find b such that -6 - 110/3*b**2 - 26*b - 50/3*b**3 = 0.
-1, -3/5
Let k(s) be the first derivative of -1/3*s**5 - 7/6*s**2 - 4 + 7/12*s**4 + 1/3*s**3 + 2/3*s. Let k(p) = 0. Calculate p.
-1, 2/5, 1
Let z = 1/916473 + 7936656169/10081203. Let d = -786 + z. Factor 0 + 4/11*k + 54/11*k**3 + d*k**5 + 26/11*k**2 + 46/11*k**4.
2*k*(k + 1)**3*(7*k + 2)/11
Let z = -15 + 21. Let c be (z/9)/(1/9). What is f in f**2 - 2 - 2*f**3 + 7*f**2 + c - 10*f = 0?
1, 2
Let f = 119 - 831/7. Solve 2/7*z**2 - f*z**5 + 2/7*z**3 - 2/7*z**4 + 0 + 0*z = 0.
-1, 0, 1
Let k(r) be the first derivative of 1/9*r**2 - 2/9*r + 2/27*r**3 - 1/18*r**4 - 1. Factor k(z).
-2*(z - 1)**2*(z + 1)/9
Let t = -831/5 - -167. Let q = -3 - -5. Factor -6/5*m + t + 2/5*m**q.
2*(m - 2)*(m - 1)/5
Let f(d) be the second derivative of d**7/840 - d**5/40 + d**4/12 - 2*d**3/3 - d. Let j(x) be the second derivative of f(x). Factor j(v).
(v - 1)**2*(v + 2)
Let r = 25 - 16. Let b(w) = -w**2 + 9*w + 1. Let i(l) be the first derivative of -l**2 - 1. Let x(s) = r*i(s) + 2*b(s). Let x(n) = 0. What is n?
-1, 1
Let j(l) be the second derivative of -l**7/12 - l**6/2 - l**5/5 + 14*l**4/3 + 12*l**3 + 8*l**2 + 12*l. Find x such that j(x) = 0.
-2, -2/7, 2
Let k = 31 + -21. Let w(z) = z - 7. Let p be w(k). Suppose -1/2 - 1/2*c**4 + 1/2*c + 1/2*c**5 - c**p + c**2 = 0. Calculate c.
-1, 1
Let i(f) be the first derivative of 0*f**2 + 0*f**3 + 1/3*f**6 + 0*f - 1/2*f**4 + 0*f**5 + 6. Factor i(x).
2*x**3*(x - 1)*(x + 1)
Let u(j) be the third derivative of j**10/378000 - j**9/50400 + j**8/16800 - j**7/12600 - j**5/30 + j**2. Let r(z) be the third derivative of u(z). Factor r(w).
2*w*(w - 1)**3/5
Let t(c) be the second derivative of 6*c + 1/9*c**2 + 1/27*c**4 + 0 - 1/9*c**3. Suppose t(s) = 0. What is s?
1/2, 1
Let t(w) = 3*w + 4. Let n(v) = 3*v + 4. Let j(a) = -6*n(a) + 5*t(a). Let b be j(-3). Solve 3*h**4 + 0*h**b + 2*h**5 - h**4 = 0.
-1, 0
Suppose 5*d - 13 = -3. Let w be (5/(10/(-3)))/(-6). What is o in 1/4*o**4 + 1/4*o**5 + 0*o - w*o**3 - 1/4*o**d + 0 = 0?
-1, 0, 1
Let g(l) be the second derivative of -l**5/90 + l**4/108 + 2*l**3/27 + l**2/2 - 3*l. Let p(y) be the first derivative of g(y). Factor p(x).
-2*(x - 1)*(3*x + 2)/9
Let a(b) be the second derivative of 3*b**7/56 + b**6/5 + 3*b**5/20 + 6*b. Factor a(u).
3*u**3*(u + 2)*(3*u + 2)/4
Let a(c) be the second derivative of c**7/63 + c**6/15 + c**5/15 - c**4/9 - c**3/3 - c**2/3 - 3*c. Factor a(y).
2*(y - 1)*(y + 1)**4/3
Let h(v) be the first derivative of -2*v**6/3 + 12*v**5/5 - 2*v**4 + 3. Determine o, given that h(o) = 0.
0, 1, 2
Let m(w) be the third derivative of -w**7/42 - 5*w**6/24 - 2*w**5/3 - 5*w**4/6 + 3*w**2. Suppose m(a) = 0. Calculate a.
-2, -1, 0
Suppose 2*v - 3*v + 2 = 0. Let 2/7*y**v - 2/7 + 0*y = 0. Calculate y.
-1, 1
Let x(y) be the second derivative of y**7/420 - y**6/120 + y**5/120 - 2*y**2 - 4*y. Let j(z) be the first derivative of x(z). Factor j(p).
p**2*(p - 1)**2/2
Let q(v) be the first derivative of -1/2*v - 1/8*v**4 - 2/3*v**3 + 1/24*v**6 + 1/10*v**5 - 1 - 7/8*v**2. Determine d so that q(d) = 0.
-1, 2
Let v = -1/112 - -71/112. Let k = v + 1/24. Suppose 1/3*j**4 + 0*j + 0 + 0*j**2 - k*j**3 = 0. What is j?
0, 2
Let 0 - 1/5*m**2 - 2/5*m = 0. Calculate m.
-2, 0
Let x(j) be the second derivative of -j**7/126 - j**6/90 + j**5/30 + j**4/18 - j**3/18 - j**2/6 - 14*j. Factor x(d).
-(d - 1)**2*(d + 1)**3/3
Let s(u) be the third derivative of u**5/450 - u**4/60 + 9*u**2. Let s(h) = 0. What is h?
0, 3
Let c(z) be the first derivative of -4/21*z**3 + 2 + 4/7*z + 1/14*z**4 - 1/7*z**2. Suppose c(l) = 0. What is l?
-1, 1, 2
Factor -14*q + 14*q + 4*q**2 + 4*q**4 - 8*q**3.
4*q**2*(q - 1)**2
Let j(q) = -q**5 - q**4 - q**3 + q**2 + q + 1. Let u(d) = 4*d**5 + 6*d**4 + 3*d**3 - 7*d**2 - 3*d - 3. Let x(z) = 6*j(z) + 2*u(z). Factor x(s).
2*s**2*(s - 1)*(s + 2)**2
Let r = 1 + 1. Let q be 6/(r - -1) + 0. Factor -2*d**2 - q*d**3 + 4*d**2 + 0*d**3.
-2*d**2*(d - 1)
Suppose 0 = 70*v - 74*v. Find u such that -2/5*u**3 + 8/5*u + 0*u**2 + v = 0.
-2, 0, 2
Let u(m) be the second derivative of 1/36*m**4 + 0 + 4*m - 1/6*m**2 + 0*m**3. Factor u(h).
(h - 1)*(h + 1)/3
Factor -m**3 - 2*m**5 - 4*m**3 + 3*m**3 - 4*m**4 + 0*m**5.
-2*m**3*(m + 1)**2
Factor 11/4*x**4 + 0*x - 3/4*x**5 - x**2 - 2*x**3 + 0.
-x**2*(x - 2)**2*(3*x + 1)/4
Let t(o) be the first derivative of o**3/3 + o**2/2 - 17. Factor t(y).
y*(y + 1)
Let s(b) = -b**3 - 8*b**2 - 13*b - 6. Let a be s(-6). Let m(p) be the second derivative of 1/27*p**3 - 3*p + 1/27*p**4 + 0*p**2 + a + 1/90*p**5. Factor m(g).
2*g*(g + 1)**2/9
Let u(z) be the second derivative of 1/120*z**6 - 1/16*z**4 + 1/80*z**5 - 8*z + 1/4*z**2 - 1/24*z**3 + 0. Factor u(y).
(y - 1)**2*(y + 1)*(y + 2)/4
Suppose 8*u + 15 - 39 = 0. Let w(z) be the second derivative of 1/33*z**u + 2/11*z**2 - 1/66*z**4 + 0 - 2*z. Factor w(b).
-2*(b - 2)*(b + 1)/11
Factor -18*f**2 - 4*f - f**3 - 4*f**4 + 5*f**3 + 22*f**2.
-4*f*(f - 1)**2*(f + 1)
Let j(g) be the first derivative of 5 + 0*g + 12/5*g**5 - 1/2*g**6 + 4*g**3 - 9/2*g**4 - 3/2*g**2. What is u in j(u) = 0?
0, 1
Suppose 2 + 5 = -4*d + 3*f, d + 23 = 5*f. Solve 4/5*t**4 + 0 + 0*t - 2/5*t**3 + 0*t**d = 0 for t.
0, 1/2
Solve 7/3*y**4 + 8/3*y + 0 - 2*y**3 + y**5 - 4*y**2 = 0 for y.
-2, 0, 2/3, 1
Let v(z) = -z + 9. Let d be v(9). Let 5*h**2 + 0*h**2 - 4*h**2 + h**3 + d*h**2 = 0. Calculate h.
-1, 0
Let s(o) = -11*o**3 - 86*o**2 - 900*o - 2996. Let z(a) = -9*a**3 - 87*a**2 - 900*a - 2997. Let r(c) = 3*s(c) - 4*z(c). Factor r(d).
3*(d + 10)**3
Let g(z) be the third derivative of -z**8/280 - 2*z**7/105 - z**6/25 - z**5/25 - z**4/60 - 17*z**2. Let g(m) = 0. What is m?
