t d(f) = -36*f - 35. Let t be d(-1). Factor -t + 2*n - 1/4*n**2 - 3/4*n**3.
-(n - 1)*(n + 2)*(3*n - 2)/4
Suppose 1/4*n**5 - 3/4*n**3 + 0 - 11/2*n - 11/4*n**4 + 35/4*n**2 = 0. What is n?
-2, 0, 1, 11
Factor -1/2*m**3 + 25/2*m - 3/2*m**2 - 21/2.
-(m - 3)*(m - 1)*(m + 7)/2
Suppose 4*b - 2*h = -b + 9, -4*h - 3 = -5*b. Suppose 3*l + 3*f = -3, 4*l - 6*f - 17 = -b*f. Solve 2*g - 7*g**3 + 18*g**3 + 20*g**l + 5*g - 2 = 0.
-1, 2/11
Let f = -27 - -33. Determine j so that 3*j - 22*j**3 - 12*j**4 + f*j - 12*j**2 - 11*j = 0.
-1, -1/2, -1/3, 0
Let z(r) be the first derivative of 2*r**5/45 - r**4/3 + 10*r**3/27 - 65. Factor z(y).
2*y**2*(y - 5)*(y - 1)/9
Let j(i) be the second derivative of -2*i**6/15 - 3*i**5 - 74*i**4/3 - 88*i**3 - 144*i**2 - 2*i - 132. Factor j(q).
-4*(q + 1)*(q + 2)*(q + 6)**2
Let n(x) be the second derivative of -x**7/42 - 2*x**6/5 + x**5/10 + 2*x**4 - x**3/6 - 6*x**2 - 171*x. Suppose n(f) = 0. What is f?
-12, -1, 1
Let n(u) be the third derivative of u**7/105 - u**6/20 + u**4/3 + u**2 - 37*u. Factor n(p).
2*p*(p - 2)**2*(p + 1)
Suppose -23*m + 50 = -18*m. Let y be m/4 + -3 + (-11)/(-6). Let -y + 32/3*g - 64/3*g**2 = 0. What is g?
1/4
Let t(f) be the first derivative of -32/5*f + 26 - 49/5*f**4 - 56/3*f**3 + 104/5*f**2. Factor t(l).
-4*(l + 2)*(7*l - 2)**2/5
Let o(m) be the first derivative of m**6/30 + 9*m**5/25 + 3*m**4/2 + 46*m**3/15 + 33*m**2/10 + 9*m/5 - 69. Factor o(s).
(s + 1)**3*(s + 3)**2/5
Factor -5/3*u**2 + 5*u + 30.
-5*(u - 6)*(u + 3)/3
Let z(g) be the third derivative of -1/4*g**5 + 5/3*g**3 + 0 + 1/12*g**6 - 5/8*g**4 + 0*g - 13*g**2. Factor z(v).
5*(v - 2)*(v + 1)*(2*v - 1)
Let g(r) = 2*r**2 + 5*r - 1. Let f be g(-3). Factor -3/4*b + 1/4*b**f + 1/2.
(b - 2)*(b - 1)/4
Let t = -22 + 22. Let i(o) be the second derivative of 4*o + t - 3/2*o**3 + 1/3*o**4 + o**2. What is r in i(r) = 0?
1/4, 2
Let o be 0/(-3)*(-2)/(-4). Let y be (8/12 + o)*3. Solve -9 + s**2 - 6*s**y - 21*s - 7*s**2 = 0 for s.
-1, -3/4
Let z(h) = -109*h + 654. Let k be z(6). Factor 2/19*q**2 + k + 18/19*q.
2*q*(q + 9)/19
Let b(k) = -27*k + 301. Let y be b(11). Determine f, given that -12/7*f + 15/7*f**5 + 0 - 36/7*f**2 - 3/7*f**3 + 36/7*f**y = 0.
-2, -1, -2/5, 0, 1
Suppose 63 = d + 61. Let v(k) be the third derivative of 0*k**3 - 1/8*k**4 + 1/20*k**5 + 0 + 0*k + 9*k**d. Let v(t) = 0. What is t?
0, 1
Let f(t) be the first derivative of t**4/10 + 64*t**3/15 + 116*t**2/5 + 224*t/5 + 251. Let f(c) = 0. Calculate c.
-28, -2
Let y(z) = 11*z**3 - 11*z**2 + 5*z. Let a(q) = -6*q**2 + 7*q**3 + q + 2*q**3 - 3*q**3 + 2*q. Let n(k) = -5*a(k) + 3*y(k). Determine w so that n(w) = 0.
0, 1
Suppose -3*z = -5*m - 10, 4*z + 40 = 2*m + 44. Factor 4/3*l**2 - 4/3*l**4 + z - 8/3*l**3 + 8/3*l.
-4*l*(l - 1)*(l + 1)*(l + 2)/3
Suppose 4*j - 3*d - 10 = 0, 9*d - 13*d = -j - 4. Factor -2/9*x**3 + 2/3*x**2 - 2/9*x**j + 4/9 + 10/9*x.
-2*(x - 2)*(x + 1)**3/9
Let o(h) be the third derivative of -h**6/120 - 3*h**5/20 - 5*h**4/8 + 25*h**3/6 - 55*h**2. Determine l, given that o(l) = 0.
-5, 1
Let h(k) be the second derivative of -5*k**7/42 - k**6/6 + 3*k**5/4 + 25*k**4/12 + 5*k**3/3 - 172*k. Factor h(u).
-5*u*(u - 2)*(u + 1)**3
Let f(h) be the third derivative of -h**5/60 + h**4/12 + h**3/2 + h**2. Let y be f(0). Solve -2*i**3 + 4*i**y - 6*i + i**3 + 3*i**2 = 0.
-2, 0, 1
Let r(m) be the second derivative of -3*m**5/20 + 59*m**4/4 - 420*m**3 - 1350*m**2 - 10*m + 1. Solve r(o) = 0 for o.
-1, 30
Let o(j) = -4*j**3 + 20*j**2 + 9*j. Let b be (-1 - 0)*(-2 - -4). Let f(d) = d**3 - 4*d**2 - 2*d. Let u(m) = b*o(m) - 11*f(m). Suppose u(q) = 0. Calculate q.
-2/3, 0, 2
Let d(j) be the second derivative of 2/15*j**3 - 8/5*j**2 + 33*j + 1/30*j**4 + 0. Factor d(y).
2*(y - 2)*(y + 4)/5
Let i(a) be the first derivative of 10*a + 6 + 1/16*a**4 + 1/4*a**3 + 3/8*a**2. Let d(m) be the first derivative of i(m). Factor d(b).
3*(b + 1)**2/4
Let y(j) = -41*j - 572. Let q be y(-14). Determine i so that 0*i - 8/3*i**4 + 4/3*i**3 + 0*i**q + 4/3*i**5 + 0 = 0.
0, 1
Let y(w) be the first derivative of w**4/4 - w**2/2 + 2*w - 17. Let s(r) = 3*r**3 - 3*r + 7. Let t(j) = -6*s(j) + 21*y(j). Suppose t(l) = 0. What is l?
-1, 0, 1
Factor 433*d**2 - 5*d**5 - 10*d**3 - 15*d**4 + 427*d**2 - 860*d**2.
-5*d**3*(d + 1)*(d + 2)
Let n(o) be the second derivative of 0 + 1/6*o**4 + 1/10*o**5 - 1/3*o**3 + 10*o - o**2. Determine c, given that n(c) = 0.
-1, 1
Let g = -229 + 232. Let d(y) be the first derivative of 0*y + 0*y**g + 5 + 1/10*y**4 - 1/5*y**2. Suppose d(n) = 0. Calculate n.
-1, 0, 1
Let k = -10828 - -10848. Factor 0 + 8/3*x**2 - 49/3*x**5 - k*x**3 + 0*x + 42*x**4.
-x**2*(x - 2)*(7*x - 2)**2/3
Suppose -302 + 272 = -5*h. Let i(w) be the third derivative of 7/60*w**h - 3*w**2 + 0 - 4/3*w**3 + 2/3*w**4 + 19/30*w**5 + 0*w. Factor i(d).
2*(d + 1)*(d + 2)*(7*d - 2)
Let o(p) = 16*p**2 - 22*p + 2. Let a(w) = w**3 + w**2 - w + 1. Let b(n) = -2*a(n) + o(n). Factor b(d).
-2*d*(d - 5)*(d - 2)
Factor 3*g**4 + 0 + 6*g**2 + 15/2*g**3 + 3/2*g.
3*g*(g + 1)**2*(2*g + 1)/2
Suppose -3*z - 2*z = 2*i + 10, -3*i = -4*z - 8. Suppose 0 = -5*r - 25, 2*w + 8 + i = -4*r. Determine d so that -d + 2*d**2 - w*d + 4*d + 5*d = 0.
-1, 0
Let b(l) = 2*l**2 - 26*l - 22. Let g(j) = j**2 - 27*j - 23. Let c(u) = 5*b(u) - 6*g(u). Factor c(d).
4*(d + 1)*(d + 7)
Let g(f) be the third derivative of 0 - 32*f**2 + 3/2*f**4 + 0*f**3 + 1/84*f**8 - 4/5*f**5 + 8/105*f**7 + 0*f - 1/15*f**6. Factor g(p).
4*p*(p - 1)**2*(p + 3)**2
Suppose n + 2*r - 152 = 0, 0 = 3*n - 0*n + 5*r - 456. Suppose -74*j**3 - 85*j**2 - 73*j**3 - 320 + n*j**3 + 400*j = 0. What is j?
1, 8
Let z = -17 + 22. Factor 2*g**4 + 4*g + 3 - 3 - 2*g**z - 321*g**3 - 10*g**2 + 327*g**3.
-2*g*(g - 1)**3*(g + 2)
Let a(w) = 3*w**2 + w - 2. Let z be a(-3). Suppose -3*i + z = 4*x, 3*x = -4*i - 2*x + 28. Factor -8*n**2 - n + 4*n**i + 3*n**2.
-n*(n + 1)
Let g = -147 - -151. Let s = 31 - 29. Factor 0 - 6/7*n**s - 2/7*n**g - 6/7*n**3 - 2/7*n.
-2*n*(n + 1)**3/7
Let j(h) = -4*h**2 + 104*h - 6. Let c(o) = -2*o**2 + 102*o - 4. Let k(f) = 3*c(f) - 2*j(f). Factor k(n).
2*n*(n + 49)
Let t(d) be the third derivative of -d**7/42 + 7*d**6/3 - 196*d**5/3 - 508*d**2. Find n such that t(n) = 0.
0, 28
Let o be (-38)/57*(-45)/35. Find i, given that 17/7*i - 5/7*i**2 - o = 0.
2/5, 3
Let o(h) be the first derivative of -2*h**5/15 - 11*h**4/12 - 19*h**3/9 - 5*h**2/3 + 2. Factor o(w).
-w*(w + 1)*(w + 2)*(2*w + 5)/3
Factor 0 + 0*p - 20/3*p**2 + 4/3*p**3.
4*p**2*(p - 5)/3
Factor -8*q - 127*q**4 - 4*q**2 - 133*q**4 + 264*q**4 + 8*q**3.
4*q*(q - 1)*(q + 1)*(q + 2)
Let -60/7*k - 4/7*k**3 + 0 - 32/7*k**2 = 0. What is k?
-5, -3, 0
Let t be (-7)/(595/(-102)) - 8/(-10). Let r(c) be the first derivative of -2*c + 0*c**t - 2/5*c**5 + 4/3*c**3 + 0*c**4 + 7. Factor r(d).
-2*(d - 1)**2*(d + 1)**2
Suppose -8*o = -4*o - 2*o. Let l(a) be the third derivative of -1/90*a**5 + a**2 + 0 + 0*a**3 + 1/315*a**7 + o*a**4 + 0*a + 0*a**6. Let l(y) = 0. What is y?
-1, 0, 1
Let u(t) be the first derivative of -9 - 1/7*t**4 + 1/35*t**5 + 0*t**2 + 4/21*t**3 + 9*t. Let f(l) be the first derivative of u(l). Let f(o) = 0. What is o?
0, 1, 2
Let y(r) be the first derivative of 5*r**4/4 - 10*r**3 + 55*r**2/2 - 30*r - 129. Solve y(k) = 0.
1, 2, 3
Let a be (-16)/(-8) - (-2)/1. Suppose -2*t + a + 4 = 0. Find v such that 3*v**t + 8*v**3 - 3*v**4 + 4*v**4 - 13*v**2 + v**2 = 0.
-3, 0, 1
Let l(q) be the third derivative of q**6/40 + 33*q**5/5 + 726*q**4 + 42592*q**3 + 126*q**2. Suppose l(p) = 0. Calculate p.
-44
Let p(y) be the first derivative of 35/2*y**4 + 5 + 34/3*y**3 - 3*y + 4*y**2 + 25/6*y**6 + 55/4*y**5. Let g(d) be the first derivative of p(d). Factor g(u).
(u + 1)*(5*u + 2)**3
Let n(d) be the second derivative of d**7/13860 - d**6/1980 - d**5/220 + 8*d**4/3 + 3*d. Let c(a) be the third derivative of n(a). Let c(h) = 0. Calculate h.
-1, 3
Let x = 54 - 49. Factor -2*y**2 - 12*y**5 - 4*y**4 + x + 5*y**3 + 13*y**5 - 5.
y**2*(y - 2)*(y - 1)**2
Let u(i) be the third derivative of i**10/7560 + i**9/945 + i**8/336 + i**7/315 + 3*i**4/8 - 21*i**2. Let a(n) be the second derivative of u(n). Factor a(s).
4*s**2*(s + 1)**2*(s + 2)
Let l = -63 + 65. Factor -3*o + 55*o**3 - 3*o**4 + 12*o + 15*o**l - 52*o**3.
-3*o*(o - 3)*(o + 1)**2
Let z(n) = -2*n**2 - 17*n - 23. Let p(x) = -x**2 - 16*x - 24. Let b(