first derivative of -w**5/5 + w**3 - w**2 - 18. Suppose u(b) = 0. What is b?
-2, 0, 1
Let d(h) = 98*h**3 + 61*h**2 + 8*h - 5. Let o = -5 - -8. Let s(t) = 49*t**3 + 31*t**2 + 4*t - 3. Let g(m) = o*d(m) - 5*s(m). Let g(r) = 0. Calculate r.
-2/7, 0
Let t(m) be the first derivative of -2*m**3/45 + 2*m**2/5 - 6*m/5 + 24. Factor t(s).
-2*(s - 3)**2/15
Let d(o) be the second derivative of -o**5/25 + 2*o**3/5 - 4*o**2/5 - 6*o. Factor d(b).
-4*(b - 1)**2*(b + 2)/5
Let r be 0/(-5 - -5 - -2). Determine k, given that r + 2/7*k**3 + 8/7*k + 8/7*k**2 = 0.
-2, 0
Let i = 0 - -2. Suppose 0 = 5*w - 4*w - 4. Factor 3/4*f**i - 3/4*f**3 + 1/4*f**w - 1/4*f + 0.
f*(f - 1)**3/4
Let l(v) be the third derivative of 0*v + 7/60*v**6 - 2*v**2 + 1/35*v**7 - 1/6*v**4 + 0 - 5/168*v**8 - 1/10*v**5 + 0*v**3. Suppose l(m) = 0. What is m?
-1, -2/5, 0, 1
Let n = -224521/12 - -18698. Let s = n - -37/3. What is j in 0*j**2 + 0 - s*j + 1/4*j**3 = 0?
-1, 0, 1
Let z(w) = -4*w**3 - 2*w + 13. Let v(m) = 3*m**3 - 7*m + 15. Let c(q) = -4*q**3 + 8*q - 16. Let f(h) = 6*c(h) + 7*v(h). Let r(s) = 7*f(s) - 5*z(s). Factor r(n).
-(n - 1)**2*(n + 2)
Let v be (-48)/50*5/(-2). Factor -3*g - 6/5 - 3/5*g**3 - v*g**2.
-3*(g + 1)**2*(g + 2)/5
Let p(l) be the third derivative of l**7/70 + l**6/40 - l**5/20 - l**4/8 + 11*l**2. Factor p(h).
3*h*(h - 1)*(h + 1)**2
Let h(r) = r**2. Let o be h(-2). Let d be 10/3 - (-8)/12. Factor -d*b**2 - 6*b**4 + 2*b**o + 2*b + 8*b**2 - 2*b**5.
-2*b*(b - 1)*(b + 1)**3
Let s(g) be the first derivative of 2 + 0*g**2 + 2/15*g**3 + 0*g. Factor s(r).
2*r**2/5
Let c(x) = -10*x + 3. Let o be c(0). Let s be ((-2)/4)/((-5)/2). Suppose 0 + 0*d**2 - s*d**o + 1/5*d**4 + 0*d = 0. Calculate d.
0, 1
Let g(y) be the first derivative of 2*y**3/27 + 4*y**2/9 + 2*y/3 + 8. Factor g(j).
2*(j + 1)*(j + 3)/9
Let q(r) be the first derivative of 1/9*r**2 + 4/27*r**3 + 1/18*r**4 + 0*r - 1. Solve q(m) = 0.
-1, 0
Let z be ((-16)/6)/2 - (-12 - -10). Find d such that 0*d**2 + 0*d - 4/3*d**3 + 0 + 2/3*d**5 + z*d**4 = 0.
-2, 0, 1
Let -8/9*l - 2/9*l**2 - 2/3 = 0. What is l?
-3, -1
Suppose 5 = u - m + 3*m, -3*m - 25 = -5*u. Let r(a) be the third derivative of 0 + 1/40*a**u + 1/12*a**3 + a**2 + 0*a + 1/240*a**6 + 1/16*a**4. Factor r(l).
(l + 1)**3/2
Let k = -10 - -9. Let r = 3 - k. Solve w**2 + 3*w**3 + 0*w**2 - 3*w + w**4 + 2 - r = 0 for w.
-2, -1, 1
Factor 0*u - 4/3 + 1/3*u**2.
(u - 2)*(u + 2)/3
Let f = 1955/21 + -93. Let t(l) be the first derivative of 8/7*l - 4/7*l**2 + f*l**3 + 2. Factor t(x).
2*(x - 2)**2/7
Let p = -92/35 + 24/7. Factor -p*d**2 + 0 - 2*d**3 - 8/5*d**4 + 0*d - 2/5*d**5.
-2*d**2*(d + 1)**2*(d + 2)/5
Let c = -283/11550 + 12/385. Let s(i) be the third derivative of 1/20*i**4 + 2*i**2 - 2/15*i**3 - c*i**5 + 0 + 0*i. Let s(w) = 0. What is w?
1, 2
Suppose -2*m + 12 = -6*m. Let r = -1 - m. Let 0*j - 4/7*j**3 + 2/7*j**r + 0 + 2/7*j**4 = 0. Calculate j.
0, 1
Let o(t) be the third derivative of t**7/1785 + t**6/1020 - t**5/255 + 9*t**2. Let o(n) = 0. What is n?
-2, 0, 1
Suppose f = -4*w + 4*f - 9, 12 = -5*w + 4*f. Factor 3/2*y**4 - 3*y**2 + 0*y**3 + w*y + 3/2.
3*(y - 1)**2*(y + 1)**2/2
Suppose -10*t - t - 4*t = 0. Find s, given that 3/4*s + 3/4*s**2 + t = 0.
-1, 0
Let w(m) = m**3 - 5*m**2 + 3*m + 4. Let q be w(4). Let g = q + 1. Suppose v**2 - g - 5 + 5 = 0. What is v?
-1, 1
Let u be (-5 + 1)*(-4)/32. Let b(c) be the first derivative of 10/9*c**3 + 0*c - u*c**4 - 2/3*c**2 - 1. Factor b(y).
-2*y*(y - 1)*(3*y - 2)/3
Determine b so that -2/5*b**2 + 0 + 2/5*b = 0.
0, 1
Suppose 5*n = -2*v - 7, -2*v = -v + 2*n + 2. Factor -m**4 - 7*m**3 - 6*m**2 - m**3 - m**v + 2*m**3 - 2*m.
-2*m*(m + 1)**3
Let i(g) be the first derivative of -6*g**3 - 27*g**2 - 54*g - 6 - 1/2*g**4. Suppose i(t) = 0. Calculate t.
-3
Let v(d) = 10*d**2 - 5*d - 15. Let j(g) = 5*g**2 - 2*g - 7. Let z(l) = -5*j(l) + 2*v(l). Find a such that z(a) = 0.
-1, 1
Let y = 2/117 + 220/819. Factor 0 + 2/7*p - y*p**2.
-2*p*(p - 1)/7
Let b(h) = -21*h**2 + 25*h + 15. Let s(g) = 4*g**2 - 5*g - 3. Let z(o) = -6*b(o) - 33*s(o). Factor z(p).
-3*(p - 3)*(2*p + 1)
Let n = 1 + -1. Let p be 0 + n/(-1 + 4). Let 2*h**4 - 2*h**2 + p + 2/3*h**5 + 2/3*h**3 - 4/3*h = 0. Calculate h.
-2, -1, 0, 1
Solve -134 - 3*q**2 - 53 + 79 + 36*q = 0.
6
Suppose -55*x + 164 = -14*x. Factor -3/4*d**3 + 3/4*d + 3/8*d**x + 0 - 3/8*d**2.
3*d*(d - 2)*(d - 1)*(d + 1)/8
Let b(t) = -6*t**3 + 6*t. Let h(a) = 5*a**3 + a**2 - 5*a - 1. Let g be -1*(2 + 0 + 0). Let i(u) = g*b(u) - 3*h(u). Factor i(x).
-3*(x - 1)*(x + 1)**2
Let l(h) = h**2 - 7. Let k be l(-3). Determine i, given that 6/7*i + 4/7 - 2/7*i**3 + 0*i**k = 0.
-1, 2
Let k(x) be the first derivative of 7*x**3/3 - 13*x**2/2 - 2*x + 12. Determine j so that k(j) = 0.
-1/7, 2
Let g(q) = -7*q**5 - 2*q**4 + 5*q**3 + 2*q**2 - 2. Let n(j) = 29*j**5 + 9*j**4 - 20*j**3 - 9*j**2 + 9. Let b(k) = 9*g(k) + 2*n(k). Factor b(t).
-5*t**3*(t - 1)*(t + 1)
What is d in 4*d**3 - 8/7*d + 0 + 20/7*d**2 = 0?
-1, 0, 2/7
Let l = 32 - 23. Let v = l - 6. Factor -t**3 - t**2 + 0*t**v + 0*t**2.
-t**2*(t + 1)
Determine i, given that 9/4*i**3 + 0 + 3/4*i**2 + 0*i - 3*i**4 = 0.
-1/4, 0, 1
Let f be 0/1*(-5 - -4). Suppose 3*j + 16 = 5*d, -d - 5*j + 3*j = 2. Factor f + 0*i - 1/2*i**d.
-i**2/2
Let a(b) be the second derivative of -7*b**6/10 + 41*b**5/20 + 3*b**4/2 - 6*b**3 + 4*b**2 - 30*b. Suppose a(f) = 0. What is f?
-1, 2/7, 2/3, 2
Solve -4*d - 6*d**2 + 6*d**4 + 2*d + d + 3*d**5 - 2*d = 0 for d.
-1, 0, 1
Let s(q) = -q + 3. Let j be s(4). Let o = j - -4. What is v in -v + 1 + 4 - 4 - o*v**2 + 3*v = 0?
-1/3, 1
Suppose 0 + 16*h**2 + 140/3*h**3 - 16*h**4 + 4/3*h**5 - 48*h = 0. What is h?
-1, 0, 1, 6
Let l(x) be the first derivative of 49*x**4/10 + 28*x**3/3 - 52*x**2/5 + 16*x/5 + 5. Let l(b) = 0. What is b?
-2, 2/7
Let p(v) be the first derivative of -v**4/4 - v**3/3 + 2*v**2 + 4*v - 22. Factor p(t).
-(t - 2)*(t + 1)*(t + 2)
Let o(t) = -t - t**2 + 11 - 2*t**2 - 4. Let u(f) = -f**2 + 3. Let n = 2 + -7. Let j(v) = n*u(v) + 2*o(v). Factor j(l).
-(l + 1)**2
Let t(b) be the first derivative of -6*b**3/7 + b**2 + 4*b/7 + 6. Suppose t(v) = 0. What is v?
-2/9, 1
Let y(w) be the third derivative of 1/630*w**7 + 0*w + 0 + 0*w**4 + 1/1008*w**8 - 1/180*w**5 - 1/360*w**6 + 0*w**3 + 4*w**2. Factor y(j).
j**2*(j - 1)*(j + 1)**2/3
Let t(d) = d**3 - d**2 + 2. Let b(z) = -2*z**3 + z**2 - 3. Let n be 1 + 0 + -1 - -2. Let u(g) = n*b(g) + 3*t(g). Factor u(p).
-p**2*(p + 1)
Let i(q) be the first derivative of q**6/180 + q**5/30 + q**4/12 - q**3 + 4. Let k(l) be the third derivative of i(l). Factor k(h).
2*(h + 1)**2
Let v(d) be the second derivative of 0 - 1/14*d**4 - 1/7*d**3 - 1/70*d**5 + 5*d - 1/7*d**2. Factor v(w).
-2*(w + 1)**3/7
Let c(m) = -m**4 - m**3 - m**2 + 2. Let h(y) = -11*y**4 - 42*y**3 - 21*y**2 - 3*y - 2. Let z(b) = -c(b) - h(b). Solve z(f) = 0 for f.
-3, -1/3, -1/4, 0
Let a = -23/9 + 25/9. Determine i, given that -4/9*i - 2/9 - a*i**2 = 0.
-1
Let m(j) be the third derivative of -j**6/60 + j**5/9 - 7*j**4/27 + 8*j**3/27 + 4*j**2. Factor m(z).
-2*(z - 2)*(3*z - 2)**2/9
Let p be 19 + 3/(4 - 1). Let w be p/35*(-7)/(-2). What is k in -k**2 + w*k**2 - 2*k**2 = 0?
0
Let l = 560/867 - -6/289. Factor 0 - 2/3*a**4 + l*a + 2/3*a**2 - 2/3*a**3.
-2*a*(a - 1)*(a + 1)**2/3
Let m(o) be the second derivative of -o**6/60 + o**5/40 + o**4/24 - o**3/12 - 5*o. Determine p, given that m(p) = 0.
-1, 0, 1
Let v(u) be the third derivative of 1/20*u**5 + 0*u**4 + 0 + 0*u + 6*u**2 - 1/112*u**8 - 1/70*u**7 + 1/40*u**6 + 0*u**3. Let v(o) = 0. Calculate o.
-1, 0, 1
Let w(n) = -19 - 15*n + 4*n - n + 4*n**2. Let b(o) = -o**2 + 4*o + 6. Let f = -1 + 5. Let p(a) = f*w(a) + 14*b(a). Factor p(y).
2*(y + 2)**2
Let c(z) be the second derivative of 0 - 1/6*z**3 + 0*z**2 + z - 1/24*z**4. Let c(l) = 0. What is l?
-2, 0
Suppose 3*p + 3*a - 15 = 0, -2*p - p = -4*a - 50. Let j = p + -8. Factor -4/7*i**3 + 2/7*i**4 + 0 + 4/7*i - 2/7*i**j.
2*i*(i - 2)*(i - 1)*(i + 1)/7
Let j = -7/200 - -4/25. Let u(a) be the first derivative of -1/12*a**3 + 1/20*a**5 - 2 + 0*a - 1/16*a**4 + j*a**2. Let u(y) = 0. Calculate y.
-1, 0, 1
Factor 1/3 - 1/3*m**2 + 0*m.
-(m - 1)*(m + 1)/3
Let h(n) be the first derivative of 2*n**5/25 + 2*n**4/5 - 2*n**3/3 + 38. Factor h(i).
2*i**2*(i - 1)*(i + 5)/5
Let x(h) = 3*h**2 - 11*h - 1. Let g be x(4). F