*m**3 + 18*m**2 + 4*m**3 - 24*m + 12 - 3*m**3.
-3*(m - 2)**2*(m - 1)
Factor -3*u**3 - 3*u**4 + 17*u**5 - 14*u**5 + 3*u**2 + 0*u**4.
3*u**2*(u - 1)**2*(u + 1)
Let d(b) be the second derivative of -b**6/105 + b**4/21 - b**2/7 - 4*b. Factor d(y).
-2*(y - 1)**2*(y + 1)**2/7
Let l(w) be the second derivative of -w**7/63 + w**6/15 - w**5/15 + 9*w. What is a in l(a) = 0?
0, 1, 2
Factor -10/11*y**2 - 4/11*y + 4/11*y**4 + 1/11*y**3 + 1/11*y**5 + 8/11.
(y - 1)**2*(y + 2)**3/11
Let w(x) be the first derivative of -5 + 0*x**2 + 0*x - 1/20*x**5 + 3/16*x**4 - 1/6*x**3. Factor w(q).
-q**2*(q - 2)*(q - 1)/4
Let l be (-10)/35 - 23/(-7). Factor 0*b + 2/7*b**2 + 0 + 2/7*b**l.
2*b**2*(b + 1)/7
Let j be (-1)/(1*1/(-4)). Find k, given that -2*k - 4*k**2 - 2*k**5 + 2 - 5*k**3 + 2*k**j + 6*k**3 + 3*k**3 = 0.
-1, 1
Let r(z) be the first derivative of -40/3*z**3 + 1 + 0*z - 4*z**2 + 8*z**5 - 21/2*z**4 + 25/3*z**6. Determine s so that r(s) = 0.
-1, -2/5, 0, 1
Let u = 766/9 - 85. Let j(k) be the third derivative of 0 + k**2 + u*k**4 + 0*k + 2/45*k**5 + 0*k**3 + 1/180*k**6. Factor j(m).
2*m*(m + 2)**2/3
Let v(k) be the second derivative of -k**6/45 - k**5/15 - k**4/18 + 7*k. Factor v(j).
-2*j**2*(j + 1)**2/3
Let q = 4555/3 - 1518. Factor q*o - 2/3 + 1/3*o**2.
(o - 1)*(o + 2)/3
Let d = 117/4 - 577/20. Let p(o) be the first derivative of d*o**5 + 0*o**2 + 0*o + 1 + 0*o**3 + 0*o**4 + 1/3*o**6. Suppose p(v) = 0. Calculate v.
-1, 0
Let l(j) be the second derivative of -j**8/6720 + j**6/1440 + j**3/3 - 3*j. Let b(i) be the second derivative of l(i). Factor b(n).
-n**2*(n - 1)*(n + 1)/4
Let u(s) be the second derivative of 1/24*s**4 + 0 - 2/3*s**3 + 4*s**2 - 8*s. What is x in u(x) = 0?
4
Let s(y) be the third derivative of -7*y**2 + 0*y**3 + 1/120*y**6 + 1/48*y**4 + 0*y - 1/40*y**5 + 0. Find u, given that s(u) = 0.
0, 1/2, 1
Let r = -9/13 + 67/78. Let x(c) be the first derivative of r*c**4 - 2/3*c + c**2 + 2 - 2/3*c**3. Factor x(m).
2*(m - 1)**3/3
Let s = 28/261 + -3/58. Let k(b) be the second derivative of -s*b**3 + 0*b**2 + 0*b**4 + 1/60*b**5 - b + 0. Factor k(f).
f*(f - 1)*(f + 1)/3
Let v(c) be the first derivative of -1 + 0*c - 1/5*c**5 - 7/12*c**4 - 1/6*c**2 - 5/9*c**3. Factor v(t).
-t*(t + 1)**2*(3*t + 1)/3
Let y(a) be the third derivative of -a**7/420 - 11*a**6/1620 - a**5/270 - a**3/6 + 3*a**2. Let h(b) be the first derivative of y(b). Factor h(p).
-2*p*(p + 1)*(9*p + 2)/9
Let t be -1*-2*(-4)/(-2). Factor 0*p - p**2 - t - p**2 - 6*p.
-2*(p + 1)*(p + 2)
Let l(w) = w**3. Let u(d) = 12*d**3 + 6*d**2. Let y(j) = -9*l(j) - u(j). Determine i, given that y(i) = 0.
-2/7, 0
Solve 158*j**2 + 182*j**3 + 26*j**4 + 60*j**4 + 8 - 5*j**3 + 60*j - 5*j**5 + 20*j**5 = 0 for j.
-2, -1, -2/5, -1/3
Let m(n) be the first derivative of -3*n**5/25 - 9*n**4/20 - n**3/5 + 9*n**2/10 + 6*n/5 + 8. Determine u, given that m(u) = 0.
-2, -1, 1
Let u(z) = -5*z**5 + 5*z**3 - 8*z**2 - 8*z - 8. Let f(k) = -3*k**5 + 3*k**3 - 5*k**2 - 5*k - 5. Let t(n) = 8*f(n) - 5*u(n). Determine s so that t(s) = 0.
-1, 0, 1
Suppose 6*x - 18 = -0. Suppose 0*j**x - 3*j**4 + 3*j**2 + 0 + 3/2*j**5 - 3/2*j = 0. What is j?
-1, 0, 1
Solve 2*j**5 - 8*j**2 + 4*j**2 + j - 3*j + 4*j**4 = 0 for j.
-1, 0, 1
Let l = 661/6 + -110. Let r(m) be the first derivative of l*m**2 - 1/12*m**4 - 1 + 0*m**3 + 0*m. Factor r(n).
-n*(n - 1)*(n + 1)/3
Let r(d) be the second derivative of d**6/1440 + d**5/480 - d**4/48 - d**3/3 + 2*d. Let m(s) be the second derivative of r(s). Solve m(g) = 0 for g.
-2, 1
Suppose 14*p + 24 = 52. Factor -2/5*b**4 + 6/5*b**3 + 0 + 2/5*b - 6/5*b**p.
-2*b*(b - 1)**3/5
Let u(t) = 2*t**5 - t**4 - 2*t**3 - 3*t**2 - t. Let j(k) = -k**5 + k**4 - k**3 + k**2 + k. Suppose -6*g - 3 = -3*g. Let c(m) = g*j(m) - u(m). Factor c(p).
-p**2*(p - 2)*(p + 1)**2
Let c = 8 + -5. Determine b, given that 4*b**2 - 2*b**5 - 6*b**4 + 10*b**2 - 5*b + 2*b**c - 8 + 5*b = 0.
-2, -1, 1
Let o = -5655/34 - -333/2. Let h = 26/51 - o. Suppose 1/3 + 0*t - h*t**2 = 0. Calculate t.
-1, 1
Let c(z) = 7*z**2 - 5*z + 3. Let l(t) = -3*t**2 + 3*t - 2. Let h(v) = -2*c(v) - 5*l(v). Let y be h(5). Let 4*f**3 + 2*f - 2*f**y + 6*f - 10*f**3 = 0. What is f?
-2, 0, 1
Let 6/17*w**4 + 0 + 0*w**3 + 2/17*w**5 - 8/17*w**2 + 0*w = 0. Calculate w.
-2, 0, 1
Factor 5*d**2 - 6*d**4 + 16*d**4 - d**2 - 14*d**4.
-4*d**2*(d - 1)*(d + 1)
Suppose 2*h - 25 = 3*q, q = 4*h - q - 30. Let n be -2 - 12/(-4 - -1). What is s in 2*s**h - 2*s**5 - 3*s**3 + 3*s**4 + s**n - s**5 = 0?
0, 1
Let t(v) be the first derivative of -2/5*v**3 - 11 + 2/25*v**5 + 2/5*v**2 + 0*v**4 + 0*v. Find u such that t(u) = 0.
-2, 0, 1
Let n(d) = -d**2 + 4*d - 2. Let a be n(2). Factor 9*q - 3 + 7*q**4 + 2*q**4 - 10*q**3 + 4*q**3 - 3*q**5 - 6*q**a.
-3*(q - 1)**4*(q + 1)
Let 2*d**5 + 3*d - 3*d - 2*d**3 + 2*d**2 + 0*d - 2*d**4 = 0. What is d?
-1, 0, 1
Let c(r) = r**2 + 2*r. Let k be c(-3). Let t(u) be the second derivative of 0*u**k + 0 - u + 1/100*u**5 + 0*u**2 + 0*u**4. Solve t(b) = 0.
0
Factor -8/5 + 2/5*g**2 + 0*g.
2*(g - 2)*(g + 2)/5
Find j such that -16*j - 12 - 21*j**2 - 7*j + 36*j**2 - j = 0.
-2/5, 2
Suppose 6 = -5*z + 21. Let s = -1 + z. Factor 0*a + 0 + 1/2*a**4 - a**3 + 0*a**s.
a**3*(a - 2)/2
Let m(q) = 3*q**3 - 5*q**2 + 3*q + 1. Let c be m(1). What is w in 0 - 4/5*w**c + 0*w + 2/5*w**4 + 2/5*w**3 = 0?
-2, 0, 1
Let s(k) be the first derivative of 0*k - 3/20*k**4 + 2/5*k**3 - 3/10*k**2 + 3. Let s(b) = 0. Calculate b.
0, 1
Let o(r) = -42*r**3 - 78*r**2 - 36*r + 15. Let b = -19 + 34. Let u(k) = -6*k**3 - 11*k**2 - 5*k + 2. Let f(y) = b*u(y) - 2*o(y). Factor f(z).
-3*z*(z + 1)*(2*z + 1)
Let q = -2 - -8. Suppose 2*l = -l + 12. Factor 4*t**2 + 0*t**2 - 4*t**4 - 6*t**3 - q*t**l.
-2*t**2*(t + 1)*(5*t - 2)
Let v(t) be the first derivative of -1 + 0*t**2 - 4*t + 1/3*t**3. Factor v(f).
(f - 2)*(f + 2)
Let s(w) be the first derivative of 8 + 1/12*w**3 + 3/4*w**2 + 9/4*w. Solve s(b) = 0 for b.
-3
Factor 4*z**3 + 3*z**4 + 5 - 5 + 5*z**2 - 2*z**4 + 2*z.
z*(z + 1)**2*(z + 2)
Factor 14/3*o**3 + 34/7*o - 26/3*o**2 - 6/7.
2*(o - 1)*(7*o - 3)**2/21
Factor 2/3*d + 0 + 1/3*d**3 - d**2.
d*(d - 2)*(d - 1)/3
Suppose -2*a + a = -2*t, 0 = 4*t + 3*a. Solve y**4 + t - 1/2*y**5 + 0*y**2 - 1/2*y**3 + 0*y = 0.
0, 1
Let v(c) be the third derivative of -c**6/60 - c**5/15 - 7*c**2. Factor v(q).
-2*q**2*(q + 2)
Let j(o) be the third derivative of o**8/30240 + o**7/3780 + o**6/1080 + o**5/20 + 3*o**2. Let t(p) be the third derivative of j(p). Let t(n) = 0. Calculate n.
-1
Factor 3/5*y**4 - 16/5*y**2 - 3/5 + 2/5*y**3 + 14/5*y.
(y - 1)**2*(y + 3)*(3*y - 1)/5
Let s(v) be the first derivative of 0*v**2 - 2 + 0*v**3 + 0*v - 3/4*v**4 - 3/5*v**5. Solve s(c) = 0 for c.
-1, 0
Suppose -4*v + 9 = -39. Let n = 20 - v. Factor -10 + n*t - t**2 + 2 - t**2.
-2*(t - 2)**2
Suppose -47*k + 41*k = -42. Let a(u) be the third derivative of 0*u - 1/630*u**k - 1/18*u**3 + 0 + 0*u**4 + 0*u**6 - 2*u**2 + 1/90*u**5. Factor a(m).
-(m - 1)**2*(m + 1)**2/3
Let u(t) = -5*t**4 - 10*t**3 + 5*t**2 + 15*t + 5. Let s(z) = -2*z**4 - 4*z**3 + 2*z**2 + 7*z + 3. Let b(c) = -5*s(c) + 3*u(c). Suppose b(r) = 0. Calculate r.
-2, -1, 0, 1
Let t(m) be the first derivative of 343*m**5/15 - 245*m**4/3 + 224*m**3/3 - 88*m**2/3 + 16*m/3 + 11. Factor t(q).
(q - 2)*(7*q - 2)**3/3
Suppose -1/4*p**3 - 1/4*p**4 + 0*p + 0*p**2 + 0 = 0. What is p?
-1, 0
Let l(b) be the third derivative of b**6/90 - b**5/15 + b**4/6 + 2*b**3/3 - 4*b**2. Let u(n) be the first derivative of l(n). Factor u(i).
4*(i - 1)**2
Let v be ((-66)/(-12) - 5)*7. Let a = -4 + 6. Solve 4*o**4 - 7/2*o**a - 23/2*o**3 + v*o - 1/2 + 8*o**5 = 0 for o.
-1, 1/4, 1
Let y(x) be the second derivative of x**5/12 - 2*x**4/9 + x**3/18 + x**2/3 - 23*x. Factor y(p).
(p - 1)**2*(5*p + 2)/3
Let s(k) be the third derivative of -9*k**2 + 1/48*k**4 + 1/120*k**5 + 0*k + 0 + 0*k**3. Suppose s(n) = 0. What is n?
-1, 0
Let d(s) = -2*s - 2. Let x be d(-1). Let i(k) be the first derivative of 3/2*k**4 + 2 + 2*k**3 + 2/5*k**5 + k**2 + x*k. Factor i(t).
2*t*(t + 1)**3
Let t(y) be the first derivative of -y**8/840 - y**7/840 + y**6/72 - y**5/60 - 2*y**3/3 + 4. Let m(b) be the third derivative of t(b). Factor m(p).
-p*(p - 1)*(p + 2)*(2*p - 1)
What is f in 33*f - 5 + 11 + 48*f**2 + 20*f**3 + f**3 = 0?
-1, -2/7
Determine z, given that 10*z**4 + 2*z**2 + 2*z**5 - 6*