y such that 0 - 36/7*y**v + 12/7*y - 18/7*y**4 + 39/7*y**3 + 3/7*y**5 = 0.
0, 1, 2
Let -61440000 - 3/2*t**4 + 480*t**3 + 3072000*t - 57600*t**2 = 0. What is t?
80
Let k(a) be the first derivative of -a**3/2 - 95*a**2/4 + 16*a - 141. Suppose k(b) = 0. What is b?
-32, 1/3
Let -5*a**2 + 54 - 20*a - 5*a + 94 - 36 + a**3 + 13 = 0. What is a?
-5, 5
Let r(s) be the second derivative of -s**7/1050 - s**6/150 - s**5/50 - s**4/30 - s**3/30 + 9*s**2 + 10*s. Let j(v) be the first derivative of r(v). Factor j(o).
-(o + 1)**4/5
Let s(a) = -4*a**4 + 4*a**3 + 3*a**2 - 3. Let k(p) = 44*p**4 - 44*p**3 - 32*p**2 + 32. Suppose -2*o - o + 9 = 0. Let h(i) = o*k(i) + 32*s(i). Factor h(n).
4*n**3*(n - 1)
Let k(b) be the second derivative of 7*b**5/30 - b**4/3 + 8*b**2 + 24*b. Let s(d) be the first derivative of k(d). Factor s(c).
2*c*(7*c - 4)
Let -12*h**4 - 379*h**2 - 191*h**3 + 18*h**4 - 122*h - 7*h**4 - 67*h = 0. Calculate h.
-189, -1, 0
Determine d so that 1/2*d**4 + 3249/2*d**2 - 57*d**3 + 0 + 0*d = 0.
0, 57
Let m(v) be the third derivative of 0*v**5 + 0*v + 0 - 1/35*v**7 + 1/40*v**6 + 0*v**4 + 0*v**3 + 1/112*v**8 - 27*v**2. Suppose m(r) = 0. What is r?
0, 1
Find m, given that -10*m - 35*m**2 - 25*m**4 - 8*m**3 - 2*m**5 - 34*m**3 - 3*m**3 - 3*m**5 = 0.
-2, -1, 0
Suppose 1/4*f**2 + 0*f + f**3 + 1/2*f**5 + 0 + 5/4*f**4 = 0. Calculate f.
-1, -1/2, 0
Let p(f) be the third derivative of -18*f**2 - 3/16*f**4 - 1/8*f**3 - 1/16*f**5 + 0*f + 0. Factor p(b).
-3*(b + 1)*(5*b + 1)/4
Let k be 31/(-8) - (-11 + 6). Factor -3/8*u + 3/8 - 15/8*u**2 - k*u**3.
-3*(u + 1)**2*(3*u - 1)/8
Let k be (21/42)/((6/16)/3). Factor 0*w**2 + 0*w + 3/7*w**3 - 3/7*w**k + 0.
-3*w**3*(w - 1)/7
Let d(v) be the first derivative of 2/63*v**3 + 4 + 0*v**2 - 8/21*v. Factor d(z).
2*(z - 2)*(z + 2)/21
Let r(j) = -2*j + 16. Let c be r(8). Let u(s) be the second derivative of 10*s + 1/6*s**4 + 2/3*s**3 + c - 3*s**2. Determine d so that u(d) = 0.
-3, 1
Suppose 0 = 2*t - 5*w + 21, 3*t = w + 2*w - 9. Suppose -9/4*c**t + 15/4*c**3 - 27/4*c + 0 - 3/4*c**4 = 0. What is c?
-1, 0, 3
Suppose 0 = -3*c + 7 + 5. Factor c*j - 79 - 2*j**3 + 2*j**2 + 42 + 37.
-2*j*(j - 2)*(j + 1)
Let t(v) = -v**2 - 3*v. Let q(f) = f**2 + 2*f. Let p(n) = 5*q(n) + 6*t(n). Let g(z) = -z. Let b(j) = 12*g(j) - 3*p(j). Factor b(k).
3*k*(k + 4)
Suppose -3*g - 5*p = -5, -g = g + p - 15. Suppose -u + 6 = -g*w + 6*w, w + 11 = 5*u. What is d in 0*d**u + 0 - 1/3*d**4 - 2/3*d**3 + 0*d = 0?
-2, 0
Let y be 8/(-13 - (-24 - -7)). Let x be (1 - (-1)/(-5))/1. Suppose -x*s - 2/5*s**4 + 2/5 + 4/5*s**3 + 0*s**y = 0. Calculate s.
-1, 1
Let a(z) be the second derivative of z**6/900 + z**5/150 + z**4/60 - 10*z**3/3 - 11*z. Let x(d) be the second derivative of a(d). Factor x(y).
2*(y + 1)**2/5
Let l = -36 - -43. Solve -11*p**2 + 9*p**2 + 5*p - l*p = 0.
-1, 0
Let v(t) = t**2 + 8*t - 3. Let n be v(-6). Let l be (-1)/(n/(-18))*-5. Solve l*w**3 + w - 4*w + 0*w - 3*w**5 = 0 for w.
-1, 0, 1
Let v(t) be the second derivative of t**6/70 - 9*t**5/140 + 2*t**3/7 - 3*t - 49. Factor v(c).
3*c*(c - 2)**2*(c + 1)/7
Let n(h) = -4*h**3 + 3*h + 2. Let a be n(-1). Suppose -a*q + 0*q + 6 = 0. Factor q*f + 5*f**3 - 3*f**3 + 3*f - 7*f.
2*f*(f - 1)*(f + 1)
Let j(o) = -2*o + 6. Let t be j(6). Let d = t - -8. Factor -7*c**5 - 6*c**3 + d*c**4 + c**4 + 10*c**5.
3*c**3*(c - 1)*(c + 2)
Let t be 834/(-21) + 4/(-14). Let g = t + 40. Let g + 0*w + 0*w**2 - 3/2*w**3 = 0. What is w?
0
Suppose 2/3*n**2 - 148/3*n + 2738/3 = 0. What is n?
37
Let q(y) be the first derivative of -8/3*y**3 - 4*y**4 - 8*y - 2/3*y**6 + 16/5*y**5 + 10*y**2 - 6. Factor q(w).
-4*(w - 2)*(w - 1)**3*(w + 1)
Let q(r) = -r + 30 + 13 - 42 - r**2. Let z(k) = -k - 7. Let l be z(-6). Let d(u) = -2*u**2 - 2*u + 3. Let h(j) = l*d(j) + 3*q(j). Let h(y) = 0. Calculate y.
-1, 0
Suppose 38/17*b + 20/17 - 2/17*b**3 + 16/17*b**2 = 0. Calculate b.
-1, 10
Let g(h) be the first derivative of 12 + 20/3*h**3 + 0*h + 15/2*h**2 - 5/4*h**4 - 2*h**5. Factor g(n).
-5*n*(n + 1)**2*(2*n - 3)
Let o = 54 + -118. Let b be 24/(-36) + o/(-60). Factor 4/15 - 2/3*m**2 + b*m.
-2*(m - 1)*(5*m + 2)/15
Let l = 695 - 692. Let z(c) be the third derivative of -1/90*c**5 - 1/12*c**4 + 11*c**2 + 0*c - 2/9*c**l + 0. Factor z(s).
-2*(s + 1)*(s + 2)/3
Factor 1/3 - 1/2*f + 1/6*f**2.
(f - 2)*(f - 1)/6
Let -14/5*p**3 + 16/5 - 46/5*p**2 + 44/5*p = 0. What is p?
-4, -2/7, 1
Let h(b) = -b**5 - b**3 - b**2 + b. Let a(y) = 10*y**5 - 12*y**4 + 32*y**3 - 12*y**2 - 2*y. Let i(q) = a(q) + 8*h(q). What is d in i(d) = 0?
0, 1, 3
Factor 102 + 10*f**2 - 130 + 24*f + 7*f**3 + 50*f**2 + f**3.
4*(f + 1)*(f + 7)*(2*f - 1)
Factor -i - 1/2*i**3 - 3/2*i**2 + 0.
-i*(i + 1)*(i + 2)/2
Suppose 5*n = 3*n + 8. Suppose k = n + 4. Factor -21*q**2 + 5 - 4 + 3 + k*q.
-(3*q - 2)*(7*q + 2)
Let i(n) = 3*n**2 + 3*n + 6. Suppose 0 = -4*k + 12 - 28. Let w(d) = 13*d**2 + 11*d + 25. Let m(p) = k*w(p) + 18*i(p). Factor m(s).
2*(s + 1)*(s + 4)
Let l(n) be the second derivative of -n**8/13440 + n**7/5040 + n**4/4 + 8*n. Let a(j) be the third derivative of l(j). Factor a(d).
-d**2*(d - 1)/2
Let c(f) be the second derivative of -f**9/1512 + f**7/210 - f**5/60 - 17*f**3/6 + 19*f. Let h(o) be the second derivative of c(o). Factor h(x).
-2*x*(x - 1)**2*(x + 1)**2
Let 1/3*b**2 - 23/3*b + 22/3 = 0. Calculate b.
1, 22
Factor -16000*v + 2401/4*v**5 + 22540*v**3 + 26600*v**2 - 40000 + 25039/4*v**4.
(v - 1)*(7*v + 20)**4/4
Let d(k) be the third derivative of -k**8/336 - k**7/105 + k**6/40 + k**5/15 - k**4/6 - 8*k**2 + 4. Factor d(w).
-w*(w - 1)**2*(w + 2)**2
Let x(c) be the third derivative of -35*c**2 + 1/330*c**5 + 0 + 0*c + 0*c**3 + 1/66*c**4. What is n in x(n) = 0?
-2, 0
Let f(z) be the first derivative of 7/15*z**5 - 8 - 7/12*z**4 + 0*z + 0*z**2 - 1/9*z**6 + 2/9*z**3. Determine v so that f(v) = 0.
0, 1/2, 1, 2
Let d(r) = -12*r**2 + 564*r - 20164. Let g(t) = -14*t**2 + 563*t - 20164. Let x(f) = -5*d(f) + 4*g(f). Factor x(n).
4*(n - 71)**2
Let n be ((-6)/10)/((-21)/70). Factor -5/4*f**4 + 0 + 0*f + 0*f**3 + 0*f**n.
-5*f**4/4
Let o(j) = -j**2 - j - 1. Let n(t) = -9*t + 11. Let d(m) = -n(m) + o(m). Determine u, given that d(u) = 0.
2, 6
Let j = -285 - -281. Let z be j - (160/(-25) - -2). Factor -2/5*l**3 + 2/5*l**2 + z*l - 2/5.
-2*(l - 1)**2*(l + 1)/5
Let w = 289 + -287. Let i(y) be the third derivative of 9*y**w - 1/30*y**5 + 1/36*y**4 + 0*y**3 + 0 + 0*y. Factor i(z).
-2*z*(3*z - 1)/3
Let z(w) = 4*w**2 - 64*w + 80. Let c(s) = s**2 - 13*s + 16. Let n = 39 + -55. Let x(l) = n*c(l) + 3*z(l). Factor x(a).
-4*(a - 2)**2
Suppose -43 = 3*c - 0*i - 5*i, -2*i + 10 = 0. Let z(h) = -h + 1. Let r(j) = -j**2 - 7*j + 8. Let v(q) = c*z(q) + r(q). Factor v(k).
-(k - 1)*(k + 2)
Let r be 1/(4/(-56)*2). Let z = -5 - r. Factor -k**4 - 23*k**z + 2*k**4 + 23*k**2.
k**4
Let y(s) be the first derivative of -s**4/2 - 8*s**3 + 16. Factor y(o).
-2*o**2*(o + 12)
Let j(c) be the third derivative of -5/12*c**4 - 5/6*c**3 + 0 - c**2 - 1/12*c**5 + 0*c. Find l such that j(l) = 0.
-1
Let k be (-6)/12*(0 - 0). Suppose k = 5*a - 376 - 364. Suppose -148*q - 3 + a*q + 3*q**2 = 0. Calculate q.
-1, 1
Suppose -5130 = 20*b - 5170. Factor 12/11 - 6*t + 30/11*t**b.
6*(t - 2)*(5*t - 1)/11
Suppose -341 + 80 = -5*l - j, -l - j + 53 = 0. Find y such that 4*y**3 + 4 + 8*y**2 - 4 + 56*y - l*y = 0.
-1, 0
Let i(y) be the second derivative of 1/6*y**3 + 0*y**2 + 0 + 15*y - 1/12*y**4. Factor i(o).
-o*(o - 1)
Let z(c) be the second derivative of -c**7/91 - 4*c**6/195 - c**5/130 + 14*c + 1. Factor z(t).
-2*t**3*(t + 1)*(3*t + 1)/13
What is c in -2725888/3 + 30976*c - 352*c**2 + 4/3*c**3 = 0?
88
Let t = -937 - -941. Factor -5/4*j - 1/2 - 3/4*j**2 + 1/4*j**t + 1/4*j**3.
(j - 2)*(j + 1)**3/4
Suppose 17 = 5*d + l, 4*d + 2*l + 2 = 6*d. Suppose -4*y + 4 = 0, -d*y + 32 = 5*h - 16. Factor 3/2*w**4 + 6 + h*w**3 + 39/2*w**2 + 18*w.
3*(w + 1)**2*(w + 2)**2/2
Let y(c) be the second derivative of 0*c**2 + 0*c**4 - 1/30*c**6 - 3*c + 0*c**5 + 0*c**3 + 0. Suppose y(s) = 0. Calculate s.
0
Let u = 2218 + -2214. Let z(x) be the first derivative of -1/2*x**4 + 0*x + 2/3*x**3 + 2*x**2 - u. Solve z(o) = 0 for o.
-1, 0, 2
Let b(x) = -13*x**4 + 387*x**3 + 536*x**2 + 125*x - 11. Let s(k) = 3*k**4 - 97*k**3 - 134*k**2 - 31*k + 3. Let p(v) = -6*b(v) - 22*s(v). Solve p(z) = 0.
-1, -1/3, 0, 17
Let 