b?
-1, 0, 1
Let l = 66 - 18. Suppose l*p = 46*p. Factor 2/7*r**2 + p - 2/7*r.
2*r*(r - 1)/7
Let k(u) be the third derivative of u**8/320 + u**7/168 - u**6/120 - 7*u**4/24 - 12*u**2. Let t(j) be the second derivative of k(j). Factor t(f).
3*f*(f + 1)*(7*f - 2)
Factor -324/5 + 32/5*v**2 + 18*v + 2/5*v**3.
2*(v - 2)*(v + 9)**2/5
Let q(t) be the third derivative of t**8/112 - 6*t**7/35 + 21*t**6/40 + 49*t**5/10 - 2*t**2 - 8*t. Factor q(l).
3*l**2*(l - 7)**2*(l + 2)
Let w(m) be the first derivative of -m**3/21 - 31*m**2/14 - 487. Suppose w(o) = 0. What is o?
-31, 0
Let g = -2965/24 + 999/8. Suppose 20/3*i**4 - g*i**2 + 28/3*i**3 + 4/3*i**5 - 32/3*i - 16/3 = 0. What is i?
-2, -1, 1
What is h in 3/7*h**3 - 60/7*h - 57/7*h**2 + 0 = 0?
-1, 0, 20
Suppose 10 = 5*w, 0 = 3*m + 2*w + 9 - 37. Suppose 0*j - 2*j = 5*f - 85, j + 10 = f. Factor f*y - 9*y - m*y + 2*y**3.
2*y*(y - 1)*(y + 1)
Suppose 2*b - 40 = -5*c + c, -4*c + 5*b = -12. Solve -12*n**3 - 4*n**5 + 27 + c*n**2 - 27 - 4*n**2 + 12*n**4 = 0.
0, 1
Suppose -5*s + 40 = -5*i, -150*s + 146*s - 5*i - 4 = 0. Factor -1/2*c**2 - s*c - 8.
-(c + 4)**2/2
Factor 28*w**3 - 96*w**3 + 484*w**3 - 153*w**2 + 14*w**4 + 33*w**2.
2*w**2*(w + 30)*(7*w - 2)
Let o = -11/47 + 331/611. Let v(n) be the first derivative of -2 + 0*n + 165/26*n**4 + o*n**2 - 32/13*n**3 - 242/65*n**5. Factor v(x).
-2*x*(x - 1)*(11*x - 2)**2/13
Suppose 736/5*s - 67712/5 - 2/5*s**2 = 0. What is s?
184
Suppose -d + 49 = 1. Factor 2*q**2 - 37*q + 65*q - d*q + 50.
2*(q - 5)**2
Determine d, given that -2/15*d**3 + 0 + 2/15*d**2 + 4/15*d = 0.
-1, 0, 2
Let f be (1332/1035 - 1) + (-2)/23. Let p(r) be the first derivative of 1/5*r**4 + 0*r - 1/15*r**6 - 8 - f*r**2 + 0*r**5 + 0*r**3. Factor p(w).
-2*w*(w - 1)**2*(w + 1)**2/5
Suppose -44*z + 91 = -41. Let l(v) be the third derivative of 1/15*v**6 + v**4 + 0 - 4/3*v**z + 1/2*v**5 + 0*v - 12*v**2. Determine c, given that l(c) = 0.
-2, 1/4
Let m(y) = 2*y**4 - 17*y**5 + 16*y**5 - 3*y**4. Let o(g) = -8*g**5 - 6*g**4 + 3*g**3 - 5*g**2 + 2*g. Let s(d) = -21*m(d) + 3*o(d). Solve s(t) = 0.
-2, 0, 1
Let o(i) be the first derivative of i**8/1680 + i**7/840 - i**6/180 - i**3 + 12. Let u(v) be the third derivative of o(v). Find z such that u(z) = 0.
-2, 0, 1
Let s = -98 - -102. Suppose -u = -s*u - u. Factor -1/4*q**4 + u + 1/4*q**2 + 1/4*q**5 - 1/4*q**3 + 0*q.
q**2*(q - 1)**2*(q + 1)/4
Factor 6*d**5 + 145*d + 335*d**2 + 4521*d**3 - 4186*d**3 + 14*d**5 + 145*d**4 + 20.
5*(d + 1)**3*(d + 4)*(4*d + 1)
Factor 2/3*n**3 + 2/9*n**4 + 0*n + 4/9*n**2 + 0.
2*n**2*(n + 1)*(n + 2)/9
Let r(c) = -6*c**3 - 12 - 1 - 55*c - 30*c**2 - 4. Let z(t) = -2*t**3 - 10*t**2 - 18*t - 6. Let g(s) = 2*r(s) - 7*z(s). Factor g(w).
2*(w + 1)*(w + 2)**2
Let h(j) be the second derivative of -j**4/3 + 100*j**3/3 - 1250*j**2 - j + 4. Factor h(a).
-4*(a - 25)**2
Let x be 3/((3/(-5))/(-3)*(-45)/(-6)). Suppose -9/2*f**x - 1/4*f**4 + 0*f + 2*f**3 + 27/4 = 0. What is f?
-1, 3
Let d = -6376 + 6376. Factor -3/4*i + 9/8*i**2 + 0*i**3 - 3/8*i**4 + d.
-3*i*(i - 1)**2*(i + 2)/8
Let j(r) be the second derivative of -r**4/27 - 64*r**3/27 + 7*r + 3. Suppose j(g) = 0. Calculate g.
-32, 0
Let h(w) = -w - 4. Let g be h(-7). What is m in 4*m + 4*m**2 + 4*m - 5 + 6 + g = 0?
-1
Let d(m) be the third derivative of m**6/960 - 29*m**5/240 + 113*m**4/192 - 7*m**3/6 - 187*m**2. Factor d(p).
(p - 56)*(p - 1)**2/8
Let o(j) be the third derivative of j**10/680400 + j**9/45360 - 41*j**5/60 - 35*j**2. Let l(p) be the third derivative of o(p). Factor l(x).
2*x**3*(x + 6)/9
Let j(u) be the second derivative of u**6/120 + u**5/40 - u**4/12 - u**3/12 + 3*u**2/8 - u + 10. Find p such that j(p) = 0.
-3, -1, 1
Suppose 0*q - 21 = -3*q. Factor -q*r - 58 - 3*r - 5*r**2 + 53.
-5*(r + 1)**2
Let c(i) be the first derivative of 1/5*i**4 + 3 + 0*i**5 + 0*i - 1/5*i**2 - 1/15*i**6 + 0*i**3. Factor c(g).
-2*g*(g - 1)**2*(g + 1)**2/5
Determine u so that -69*u - 2212 - 4*u**2 - 99*u + 448 = 0.
-21
Let h(l) be the second derivative of 0 + 0*l**2 + 1/24*l**4 + 0*l**3 - 2*l. Solve h(a) = 0 for a.
0
Suppose 89 = 3*f - 1. Let n = f - 57/2. Factor 3*w + n*w**2 - 9/2.
3*(w - 1)*(w + 3)/2
Let z(d) be the second derivative of d**6/10 - 3*d**5/20 - 7*d**4/4 + 13*d**3/2 - 9*d**2 - 39*d. Determine i, given that z(i) = 0.
-3, 1, 2
Suppose -6*s = -9 - 3. Determine w so that 4*w**s - 4*w - 2 + 9 - 7 = 0.
0, 1
Suppose 31*d - 14*d = 16*d. Let h be (-19)/(152/(-48)) - (1 + d). Solve 0 - 3*y**2 + 0*y**3 - 3/2*y**h + 3*y**4 + 3/2*y = 0.
-1, 0, 1
Let x(z) = -36*z - 1. Let v be x(-1). Let f = -23 + v. Factor -q + q**2 + 0*q**2 + f - 14.
(q - 2)*(q + 1)
Let o(t) be the third derivative of -t**4/24 + 7*t**3/6 - 6*t**2. Let a be o(5). Factor 0*l - 4*l + l**2 + 3*l**a + 0*l**2.
4*l*(l - 1)
Let c be (6 - ((-52)/(-5) - 4))*-5. Let q(k) be the third derivative of -1/20*k**5 + 0 + 1/4*k**4 + 3/2*k**3 + 0*k - 7*k**c. Suppose q(v) = 0. What is v?
-1, 3
Let -29/6*l**3 - 3*l - 3/2*l**4 - 1/6*l**5 - 13/2*l**2 + 0 = 0. What is l?
-3, -2, -1, 0
Let w(k) = k**4 - k**3 - k. Let z(m) = -25*m**4 + 55*m**3 + 45*m**2 - 15*m - 40. Let u be 3*(-12)/(-9)*5. Let g(d) = u*w(d) + z(d). Find b such that g(b) = 0.
-1, 1, 8
Suppose -8*w + w - 42 = 0. Let z = w + 11. Factor -50*u**z + 24*u**2 - 6*u - 6*u + 17*u**3 - 60*u**4 + 4*u + 5*u**3.
-2*u*(u + 1)**2*(5*u - 2)**2
Factor -35*p**2 - 3*p**3 - 85*p - 34*p**3 - 45 + 42*p**3.
5*(p - 9)*(p + 1)**2
Let r = 4801/6 - 800. Let q(i) be the second derivative of 1/9*i**3 + 0 + 0*i**2 + 10*i - 2/15*i**5 - r*i**4. Suppose q(h) = 0. What is h?
-1, 0, 1/4
What is h in 45/4 + 1/2*h**2 - 33/4*h = 0?
3/2, 15
Let a(b) be the third derivative of b**6/30 - 62*b**5/15 - 127*b**4/6 - 128*b**3/3 + 230*b**2 + 2. Let a(v) = 0. Calculate v.
-1, 64
Let q(i) be the first derivative of i**4/2 - i**3/3 - 3*i**2/2 + 2*i + 7. Let p be q(2). Determine s, given that -3 + 19 - p - 2*s - 2*s**2 - 4 = 0.
-2, 1
Let b(n) be the second derivative of 5/6*n**3 - 10*n - 3 + 5/12*n**4 + 0*n**2. Solve b(h) = 0 for h.
-1, 0
Suppose 14 = -k + 3*k. Let b = 10 - k. Let 4*u**4 + 18*u**2 + 2*u**2 - 13*u**3 - 8*u - b*u**3 = 0. Calculate u.
0, 1, 2
Let s be 1 - (-2 - -1)*2. Suppose 8*k + 6 - 2 - 4 - 8*k**s - 20*k**4 + 20*k**2 = 0. Calculate k.
-1, -2/5, 0, 1
Let c(i) be the third derivative of -i**5/100 - i**4/20 - 484*i**2. Factor c(n).
-3*n*(n + 2)/5
Let o(d) be the third derivative of d**5/150 + 17*d**4/10 + 867*d**3/5 - 18*d**2 - 2*d. Factor o(v).
2*(v + 51)**2/5
Let y be (-202)/756 + (-13 - (-93)/7). Let i(n) be the second derivative of y*n**4 - 2/27*n**3 + 4*n + 0*n**2 + 0. Factor i(r).
2*r*(r - 2)/9
Let s(c) be the first derivative of 30*c**2 + 26*c**3 + 80*c**4 - 23*c**3 - 2 + 5*c + 77*c**3. Suppose s(a) = 0. Calculate a.
-1/4
Factor 15/8*b + 3/8 - 9/4*b**2.
-3*(b - 1)*(6*b + 1)/8
Let j(c) be the second derivative of c**7/273 - 2*c**6/65 + 4*c**5/65 + c**4/13 - 3*c**3/13 + 161*c. Solve j(p) = 0 for p.
-1, 0, 1, 3
Let r(l) be the first derivative of -l**2 + 15 - 3/5*l**5 - 2*l**3 - 1/12*l**6 - 13/8*l**4 + 0*l. Factor r(k).
-k*(k + 1)**2*(k + 2)**2/2
Let l(r) be the second derivative of r**4/48 - 181*r**3/12 + 32761*r**2/8 - 418*r. Factor l(b).
(b - 181)**2/4
Let q = 104 - 43. Let t = 64 - q. Solve 2/3*f**t + 4/3 - 4/3*f**2 - 2/3*f = 0 for f.
-1, 1, 2
Let j(h) be the second derivative of -h**6/24 - h**5/12 + 5*h**4/12 + h**2/2 - 2*h. Let x(a) be the first derivative of j(a). Solve x(b) = 0 for b.
-2, 0, 1
Let f(v) = 3*v**2 + 87*v + 1848. Let i(d) = 2*d**2 + d - 1. Let k(y) = 4*f(y) - 4*i(y). Factor k(u).
4*(u + 43)**2
Let n(l) be the first derivative of 4*l**5/35 - 38*l**4/7 + 1444*l**3/21 - 35. Factor n(a).
4*a**2*(a - 19)**2/7
Let u(l) = 9*l - 13 - l + 7*l**2 - l**3 + 2*l. Let o be u(8). Factor -4/5*w**2 + 0 + 2/5*w**o + 2/5*w.
2*w*(w - 1)**2/5
Factor 1/4*s**2 + 1 + 5/4*s.
(s + 1)*(s + 4)/4
Let j(r) be the third derivative of 0*r + 12*r**2 + 0*r**4 + 0 - 1/30*r**5 + 0*r**3. Suppose j(t) = 0. What is t?
0
Let k = -584 + 587. Let b(h) be the second derivative of -4*h**2 + 0 - 2/3*h**k - 1/24*h**4 + 14*h. Factor b(l).
-(l + 4)**2/2
Let w(m) be the third derivative of 3*m**8/224 + m**7/28 + m**6/40 - m**2 - 16*m. Factor w(l).
3*l**3*(l + 1)*(3*l + 2)/2
Let a(d) = 5 - 2*d - 8*d - d**3 - 14*d + 8*d**2 + 8*d. Let w be a(5). Let -2/9*i**2 + 2/3*i + w = 0. 