 be j(29). Let b(z) be the first derivative of -2*z**2 + 8/3*z**g + 7 + z**4 - 8*z. Suppose b(u) = 0. What is u?
-2, -1, 1
Let 4/13*u**3 - 8/13*u**2 + 0 - 16/13*u + 2/13*u**4 = 0. Calculate u.
-2, 0, 2
Let r(f) = 26*f**3 - 56*f**2 - 11. Let i(p) = 9*p**3 - 19*p**2 - 4. Suppose 0 = -3*g - 16 + 4. Let c(q) = g*r(q) + 11*i(q). Solve c(v) = 0.
0, 3
Solve -3*g**2 + 6*g**2 + 3 - 31 + 18*g - 5*g**2 = 0 for g.
2, 7
Suppose -20 = -4*j, -4*w + j + 4*j - 17 = 0. Factor -i**w + 0 - 4 + 0*i**2 + 5*i.
-(i - 4)*(i - 1)
Let j be 7 + 4/(-4 - -3). Determine u so that 2*u**2 + 2*u**3 - u**5 - 2*u**j + 2*u**3 + u**3 = 0.
-1, 0, 2
Suppose 54*w - 53*w - 3 = 0. Factor -7*m**2 + 12*m**2 + 2*m**w - 4*m**3 + 1 + 0 - 4*m.
-(m - 1)**2*(2*m - 1)
Suppose o = -5*p - 4, 0 = -4*p - 15*o + 14*o - 4. Factor 3/2*k**5 + p*k**3 + 3*k**4 + 0 - 3*k**2 - 3/2*k.
3*k*(k - 1)*(k + 1)**3/2
Let g = 622/1035 + -1/1035. Solve g*a**5 - 117/5*a**2 + 54/5*a - 27/5*a**4 + 87/5*a**3 + 0 = 0.
0, 1, 2, 3
Let a(m) = -m**2 - 10*m + 15. Let r be (2/(-3))/((-8)/(-132)). Let v be a(r). Let -6*y**3 + 3*y**v + 0*y**3 + y**3 + 2*y**3 = 0. Calculate y.
0, 1
Let k(z) be the second derivative of -z**7/2940 + z**6/210 + z**5/60 + 7*z**3/2 - 7*z. Let w(b) be the second derivative of k(b). Determine f so that w(f) = 0.
-1, 0, 7
Let k(z) = 2*z + 330 - z**2 + z - 2*z**4 - 8*z**3 - 317. Let t(w) = w**2 - w + 1. Let q(j) = k(j) - 5*t(j). Suppose q(l) = 0. Calculate l.
-2, -1, 1
Let z(b) = -b**3 - b - 1. Let j(m) = 12*m**3 - 12*m**2 + 16*m + 8. Let c(x) = -x**3 - 6*x**2 + 2*x + 4. Let t be c(-6). Let u(n) = t*z(n) - j(n). Factor u(y).
-4*y*(y - 2)*(y - 1)
Suppose -20 = 2*b - 5*o, -b - 4*o - 5 = -21. Suppose 9*a = -b*a. Factor -1/5*c**2 + a - 4/5*c.
-c*(c + 4)/5
Find i such that 93*i**4 + 32 - 69*i - 12*i**5 - 22*i**4 - 24*i**3 - 63*i + 231*i**3 - 40*i**2 = 0.
-2, -1, 1/4, 2/3, 8
Let h(s) be the third derivative of s**8/168 + 4*s**7/105 + s**6/60 - s**5/5 + 68*s**2. What is f in h(f) = 0?
-3, -2, 0, 1
Let b(k) = k**3 - 17*k**2 - 28*k - 187. Let g be b(19). Factor 0*s**2 + 2/7*s**4 + 0*s + 0*s**g + 0 - 1/7*s**5.
-s**4*(s - 2)/7
Let n(x) be the second derivative of 1/15*x**6 + 0 + 1/10*x**5 - 1/3*x**3 + 0*x**2 - 1/6*x**4 + x. Solve n(d) = 0 for d.
-1, 0, 1
Let t = 56 + -53. Factor -p**t - 357*p**2 + 357*p**2 + 4*p.
-p*(p - 2)*(p + 2)
Let j(q) be the third derivative of -q**5/15 + 7*q**4/6 - q**2 + 59*q. Find w such that j(w) = 0.
0, 7
Let t(d) be the first derivative of -d**5 + 15*d**4/4 + 5*d**3/3 - 15*d**2/2 + 249. Factor t(r).
-5*r*(r - 3)*(r - 1)*(r + 1)
Let s be 2238/670 + 3*14/21. Let k = s - -4/67. Let 3/5*j**3 + 9*j - 21/5*j**2 - k = 0. Calculate j.
1, 3
Suppose -15 = -2*x + 4*t + 13, 4*x = 4*t + 56. Suppose -4*v = -3*q - 3*v + 10, 5*v - x = -q. Let 54*z**2 + 2*z**q - 58*z**2 + 2 + 0*z**4 = 0. Calculate z.
-1, 1
Let n be (-1)/(-10) + -4*(-14)/140. Determine p so that -n*p**2 + 0*p + 1/2 = 0.
-1, 1
Suppose 0 = -4*h - z + 61, 2*z + 2*z + 26 = 2*h. Factor 1 + 412*d**4 + 13*d**3 - 408*d**4 + h*d**2 + 7*d + 0.
(d + 1)**3*(4*d + 1)
Let c = -41 + 40. Let v be 0 + (-2 - c) + 5. Factor 4*z**3 + 8*z + 2/3*z**v + 8/3 + 26/3*z**2.
2*(z + 1)**2*(z + 2)**2/3
Factor -102*a + 5802*a**2 - 2*a**3 - 52 - 2*a**3 + 6*a**3 - 5850*a**2.
2*(a - 26)*(a + 1)**2
Let h(l) be the first derivative of -3*l**5/80 + 3*l**4/16 + 20*l + 20. Let w(k) be the first derivative of h(k). Let w(j) = 0. What is j?
0, 3
Let z(y) be the third derivative of -y**7/840 + 7*y**6/480 - 3*y**5/40 + 5*y**4/24 - y**3/3 + y**2 - 7. Factor z(s).
-(s - 2)**3*(s - 1)/4
Let z(h) = -h**5 + 3*h**4 - h**3 - 3*h**2 - 2*h - 2. Let d(p) = -p**4 + p**3 + p**2 + p + 1. Let f = -133 - -134. Let m(u) = f*z(u) + 2*d(u). Factor m(b).
-b**2*(b - 1)**2*(b + 1)
Let c be (-213)/1917 + 16/63. Factor -1/7*h + c*h**5 - 2/7*h**2 + 0 + 2/7*h**4 + 0*h**3.
h*(h - 1)*(h + 1)**3/7
Let r(g) be the first derivative of 2*g**3/21 + 64*g**2/7 - 130*g/7 - 1067. Factor r(k).
2*(k - 1)*(k + 65)/7
Let i(u) = -u - 9*u**3 + 18*u**3 - 8 - 8*u**3. Let v(t) = -3. Let l(g) = 3*i(g) - 8*v(g). Factor l(y).
3*y*(y - 1)*(y + 1)
Suppose -12 = f + 4*c, -3*f - 4*c - 52 = -7*f. Suppose 5*w + 0*i + 5*i - 20 = 0, f = 5*w + 2*i. Find t such that 1/3*t**3 + 0 + w*t**2 - 1/3*t = 0.
-1, 0, 1
Let r(c) = c**2 + 7*c + 2. Let x be r(-7). Factor 449*a**2 - 25*a**3 - 8 - 24*a + 7*a**3 - 399*a**x.
-2*(a - 2)*(a - 1)*(9*a + 2)
Let j be -5 + (9 - 5 - -5). Suppose q**2 - j*q**3 + 3*q**4 - 11*q**3 - q**2 = 0. Calculate q.
0, 5
Let n(a) be the third derivative of -a**7/420 - a**6/90 - 5*a**4/4 + 24*a**2. Let s(d) be the second derivative of n(d). Let s(f) = 0. What is f?
-4/3, 0
Let t(o) be the second derivative of 5*o**7/42 + 7*o**6/10 - o**5/4 - 19*o**4/4 + 6*o**3 - 274*o. Factor t(s).
s*(s - 1)*(s + 3)**2*(5*s - 4)
Let v(u) be the second derivative of 1/6*u**4 + 11*u + 1/5*u**3 - 9/5*u**2 - 3 + 1/50*u**5. Find y such that v(y) = 0.
-3, 1
Let q(t) be the second derivative of t**4/8 + 76*t**3 + 17328*t**2 - 2*t + 344. Let q(y) = 0. What is y?
-152
Factor -5/4*k**4 + 5/4*k - 5/4*k**3 + 5/4*k**2 + 0.
-5*k*(k - 1)*(k + 1)**2/4
Let l(q) be the third derivative of -q**5/540 - 5*q**4/216 - 32*q**2 + 2*q. Let l(b) = 0. Calculate b.
-5, 0
Let r(d) = -7*d**2 + 33*d - 46. Let z(y) = 36*y**2 - 165*y + 228. Let t(x) = 21*r(x) + 4*z(x). Determine i so that t(i) = 0.
2, 9
Let a(y) = y**3 + y + 1. Let s(m) = 570*m + 15*m**2 + 25 + 7*m**3 - 613*m + 2. Let w(u) = 2*a(u) - s(u). What is o in w(o) = 0?
-5, 1
Factor 0*y + 8*y**2 + 16/3*y**3 + 0 + 2/3*y**4.
2*y**2*(y + 2)*(y + 6)/3
Let n be (-10)/84 - 84/(-294). Let z(b) be the third derivative of 0*b - 5*b**2 - 1/60*b**5 - n*b**3 + 1/12*b**4 + 0. Factor z(a).
-(a - 1)**2
Factor -2/3*f**2 - 2 - 8/3*f.
-2*(f + 1)*(f + 3)/3
Let o(y) = -10*y**5 + 10*y**4 + 55*y**3 + 15*y**2 - 100*y - 5. Let x(p) = p**5 - p**4 + p**3 + p**2 + 4*p + 1. Let v(z) = -o(z) - 5*x(z). Factor v(h).
5*h*(h - 4)*(h - 1)*(h + 2)**2
Let p(m) be the second derivative of 2*m**4/27 - 37*m**3/27 + m**2 + 216*m. Suppose p(u) = 0. Calculate u.
1/4, 9
Let m(j) be the second derivative of -3/20*j**5 - 3/16*j**4 + 9/8*j**3 + 22*j + 0 - 3/4*j**2. Factor m(d).
-3*(d - 1)*(d + 2)*(4*d - 1)/4
Let s = 29306 + -29303. Factor -3/8*h + 3/8*h**s + 9/8*h**2 - 9/8.
3*(h - 1)*(h + 1)*(h + 3)/8
Let y(d) be the second derivative of -2*d**6/15 - 5*d**5/2 - 26*d**4/3 - 20*d**3/3 - 7*d - 5. Let y(b) = 0. What is b?
-10, -2, -1/2, 0
Let t = 1/6 - 1/30. Let a(r) be the first derivative of -2 - 1/5*r**2 + 0*r - t*r**3. Factor a(g).
-2*g*(g + 1)/5
Let x(r) be the second derivative of 1/9*r**2 - 1/90*r**6 + 0 + 1/36*r**5 - 20*r - 5/54*r**3 + 1/108*r**4. Determine y so that x(y) = 0.
-1, 2/3, 1
Solve 135*f**4 - 704*f**3 - 416*f**2 + 1088*f + 184 - 20*f**5 + 138 + 197*f**4 + 34 + 92 = 0.
-1, -2/5, 2, 14
Let u(b) be the first derivative of -1/15*b**3 - 20 + 3/5*b - 1/5*b**2. Factor u(g).
-(g - 1)*(g + 3)/5
Let n(a) be the second derivative of -a**4/42 + 13*a**3/21 - 22*a**2/7 - 2*a + 4. Factor n(p).
-2*(p - 11)*(p - 2)/7
Factor -320*m**2 + 1 + 96*m**4 + 65*m + 1 + 235*m**3 - 2 - 76*m**4.
5*m*(m - 1)*(m + 13)*(4*m - 1)
Factor -87*x**3 + 44*x**3 + 6 + 7*x + 42*x**3.
-(x - 3)*(x + 1)*(x + 2)
Let y be ((-21)/420)/(6/(-16)). Let o(l) be the second derivative of 1/9*l**4 - 4/9*l**3 + 0 - l**2 + 1/45*l**6 + y*l**5 + 7*l. Solve o(z) = 0 for z.
-3, -1, 1
Let a(p) be the second derivative of 0 + 8/3*p**3 + 15*p - 10*p**2 + 1/3*p**4. Factor a(n).
4*(n - 1)*(n + 5)
Factor -10/3*x - 11*x**2 - 3*x**4 + 52/3*x**3 + 0.
-x*(x - 5)*(x - 1)*(9*x + 2)/3
Factor 0 - 1/9*r**4 + 0*r - 1/9*r**5 + 5/9*r**3 - 1/3*r**2.
-r**2*(r - 1)**2*(r + 3)/9
Let a(k) be the third derivative of k**8/84 + 2*k**7/21 + 7*k**6/30 + k**5/5 + 2*k**2. Factor a(n).
4*n**2*(n + 1)**2*(n + 3)
Let v = 1611 - 1609. Determine y so that -3*y**4 + 4/3*y**3 + 3/2*y**5 - 1/6*y + 0 + 1/3*y**v = 0.
-1/3, 0, 1/3, 1
Determine m, given that 112*m - 36/5*m**4 + 52*m**3 - 96/5 - 632/5*m**2 = 0.
2/9, 2, 3
Let s(o) be the first derivative of o**3/6 + 3*o**2/4 - 43. Suppose s(p) = 0. Calculate p.
-3, 0
Let c(w) be the second derivative of -2/3*w**4 - 1 + w + 12/5*w**2 + 22/15*w**3. Let c(s) = 0. Calculate s.
-2/5, 3/2
Let q(k) be the first derivative of 3*k**6/80 - 7*k**5/40 - 17*k**4/48 - k**3/4 + 3*k**2 - 33. Let t(u) be the se