 y**4 + y**t + 0.
y**2*(y + 1)**3/3
Let c(q) = -q**2 + 5*q - 1. Suppose 5*r + 0*r + 4*a = 28, 5*r - 16 = 2*a. Let p be c(r). Find m such that -16/5*m + 8/5*m**2 + 4/5*m**p - 32/5 = 0.
-2, 2
Let k(i) be the first derivative of i**5/15 - 7*i**4/12 - i**3 + 7*i**2/6 + 8*i/3 - 154. Factor k(t).
(t - 8)*(t - 1)*(t + 1)**2/3
Let y be (-2)/(4 - 75/18). Factor -28*p**2 + 10*p**2 + 6*p + 8*p**2 + y*p**2 + 4.
2*(p + 1)*(p + 2)
Let k(b) = b**2 + 6*b - 3. Let a be k(-7). Suppose z - a*f + 5 = 0, -3 = 2*z - 2*f - 5. Solve -1/2*u**2 + 0 + 1/2*u**z + 0*u = 0.
0, 1
Let f(t) be the first derivative of -1/39*t**6 + 1/13*t**4 + 4/13*t + 33 - 4/65*t**5 + 16/39*t**3 + 7/13*t**2. Determine x, given that f(x) = 0.
-1, 2
Let p(l) be the first derivative of 3/14*l**2 + 1/7*l**3 + 20 - 6/7*l. Find i, given that p(i) = 0.
-2, 1
Factor -2/7*h**4 + 0*h + 2*h**3 + 0 - 20/7*h**2.
-2*h**2*(h - 5)*(h - 2)/7
Suppose 25 = 92*k - 251. Let 2*a - 4 + a**2 - 1/2*a**k = 0. Calculate a.
-2, 2
Suppose 16 = 3*g + 13*l - 8*l, -5*g - 4*l + 18 = 0. Let h = -369 - -5537/15. What is m in 4/15 + h*m**g - 2/5*m = 0?
1, 2
Factor -675 - 5/3*p**3 - 285*p - 115/3*p**2.
-5*(p + 5)*(p + 9)**2/3
Let p(w) = w**3 - w**2 + 2. Let v(a) = 8*a**3 - 8*a**2 + 17. Suppose -3*x - 15 = -2*q - 129, -275 = 5*q - 5*x. Let f(n) = q*p(n) + 6*v(n). Factor f(g).
-3*g**2*(g - 1)
Let n(s) be the second derivative of 2*s**6/75 - 2*s**5/25 - s**4/5 - 3*s. Factor n(m).
4*m**2*(m - 3)*(m + 1)/5
Let q be (-1496)/(-48) + 2/6. What is v in -3/2 - 15/4*v + q*v**2 = 0?
-1/6, 2/7
Let b be -2*(-6 + (-5 - -4)). Let i(f) = f**3 + 9*f**2 + 7*f - 5. Let c be i(-8). Let b*m**2 - 42*m**2 + 18*m + 32*m**c - 20*m**2 = 0. What is m?
0, 3/4
Let x(g) be the third derivative of g**7/168 + g**6/72 - g**5/12 - 8*g**3/3 - 14*g**2. Let h(b) be the first derivative of x(b). Factor h(w).
5*w*(w - 1)*(w + 2)
Let v(t) be the first derivative of t**5/150 - 3*t**4/20 + 8*t**3/15 + 5*t**2/2 + 1. Let f(n) be the second derivative of v(n). Factor f(j).
2*(j - 8)*(j - 1)/5
Let p(c) be the second derivative of 0*c**2 + 0 - 8/9*c**3 - 33*c + 1/18*c**4. What is n in p(n) = 0?
0, 8
Let p = 274 + -270. Let u(v) be the second derivative of -1/2*v**2 + 7/12*v**4 + 0 - 1/5*v**5 - 1/3*v**3 + p*v. Factor u(y).
-(y - 1)**2*(4*y + 1)
Factor -311*q**2 + 618*q**2 - 311*q**2 - 392*q - 9604.
-4*(q + 49)**2
Let k(s) be the first derivative of -s**6/6 - s**5/4 + 5*s**4/6 + 37*s + 45. Let q(i) be the first derivative of k(i). Factor q(w).
-5*w**2*(w - 1)*(w + 2)
Let p be (0/(3 - 1))/1. What is z in -2*z**2 - 5*z + 0*z**3 + 6*z + p*z**3 + z**3 = 0?
0, 1
Suppose 67 = 3*k + 55. Let a(s) be the second derivative of 0 + 5*s + 1/60*s**k + 1/30*s**3 - 1/5*s**2. Find y, given that a(y) = 0.
-2, 1
Let r(x) be the third derivative of -1/84*x**4 + 0 - 2/315*x**5 - 24*x**2 + 4/63*x**3 + 1/420*x**6 + 0*x. Factor r(a).
2*(a - 1)*(a + 1)*(3*a - 4)/21
Suppose 2178 + 44*y + 2/9*y**2 = 0. What is y?
-99
Suppose -103*l = 106*l - 222*l + 65. Solve -112/3*i**2 - 9*i**l + 0*i + 36*i**3 + 16/3 + 9*i**4 = 0 for i.
-2, -1/3, 2/3, 2
Let a = 1120 - 1120. Let c be 2/(-4)*-4 - 0. Factor -2/5*u**c - 1/5*u**3 + 0 + a*u.
-u**2*(u + 2)/5
Factor -168/5*x**2 - 2/15*x**3 - 395136/5 - 14112/5*x.
-2*(x + 84)**3/15
Suppose -6/17*t + 0 - 14/17*t**2 - 2/17*t**4 - 10/17*t**3 = 0. What is t?
-3, -1, 0
Let l(s) be the second derivative of 7/15*s**6 + 165/2*s**4 + 103/10*s**5 + 725/3*s**3 - 250*s**2 + 38*s + 0. Suppose l(j) = 0. Calculate j.
-5, 2/7
Let t(z) be the third derivative of -z**7/14 + z**6/40 + 7*z**5/4 - 37*z**4/8 + 3*z**3 + 301*z**2. Find d such that t(d) = 0.
-3, 1/5, 1, 2
Let l(g) be the second derivative of -g**4/24 + 19*g**3/6 - 361*g**2/4 - 2*g + 8. Determine p so that l(p) = 0.
19
Let z = 114 - 172. Let j = z - -58. Suppose -1/2*p**2 + 1/4*p**4 + 0*p**3 + j*p + 1/4 = 0. What is p?
-1, 1
Let x(k) be the first derivative of -2*k**3/21 + 24*k**2/7 + 104*k/7 + 100. Determine w, given that x(w) = 0.
-2, 26
Let y(k) be the second derivative of k**4/6 + 52*k**3 + 12*k - 15. Factor y(w).
2*w*(w + 156)
Suppose 7*l = -4 + 102. What is f in 10*f - 6*f**3 - l*f + 9*f**2 + 10*f = 0?
-1/2, 0, 2
Let d(k) be the third derivative of k**7/105 - 7*k**6/60 + 13*k**5/30 + k**4/4 - 6*k**3 - 63*k**2. Factor d(z).
2*(z - 3)**2*(z - 2)*(z + 1)
Let z(n) be the first derivative of -1/60*n**5 - 2/3*n**2 - 5/36*n**4 - 4/9*n**3 - 2 - 8*n. Let l(v) be the first derivative of z(v). Factor l(q).
-(q + 1)*(q + 2)**2/3
Let j(t) = -71*t**3 - 9*t**2 - 32*t + 8. Let x(f) = -47*f**3 - 6*f**2 - 20*f + 5. Let w(q) = -5*j(q) + 8*x(q). Factor w(g).
-3*g**2*(7*g + 1)
Solve -18/5 + 12/5*w**2 - 3/5*w**3 - 3/5*w = 0.
-1, 2, 3
Suppose 15*t = 13*t + 78. Let -t - 2*y**2 - 1 - 33*y**2 + 150*y = 0. Calculate y.
2/7, 4
Let h(q) be the first derivative of q**5/60 + q**4/18 - 7*q**3/18 + 2*q**2/3 + 6*q - 4. Let g(c) be the first derivative of h(c). Suppose g(n) = 0. What is n?
-4, 1
Let x(n) = 8*n**3 - 60*n - 14. Let z(t) = -3*t**3 + 20*t + 4. Let u(f) = -2*x(f) - 7*z(f). Factor u(p).
5*p*(p - 2)*(p + 2)
Let h(j) be the second derivative of 17*j**5 - 212*j**4 - 232*j**3 - 64*j**2 + 12*j - 2. Solve h(u) = 0.
-2/5, -2/17, 8
Let q = -8 + 13. Suppose 3*g + 3*p - q = -2, -4*g - p = -7. Suppose -g*k**4 + 10 - 6*k + 2*k**3 - 4*k + 6*k**2 - 6 = 0. What is k?
-2, 1
Let z(q) be the third derivative of 0*q**4 + 0 - 15*q**2 + 1/3*q**3 + 0*q - 1/30*q**5. Solve z(a) = 0.
-1, 1
Let n(w) be the first derivative of w**5 - 5*w**4 + 5*w**3 + 10*w**2 - 20*w - 60. Factor n(s).
5*(s - 2)**2*(s - 1)*(s + 1)
Let n(z) be the first derivative of -z**3/12 - 5*z**2/8 + 20. Suppose n(s) = 0. What is s?
-5, 0
Factor -4/3*j + 0 + 74/3*j**2 - 70/3*j**3.
-2*j*(j - 1)*(35*j - 2)/3
Let h = 98 + -94. Solve 16*c**2 - 12*c**3 + 41*c - 25*c - 8*c**h + 14*c**5 - 10*c**5 = 0.
-1, 0, 2
Let d(r) be the second derivative of -243*r**5/20 + 279*r**4/4 - 56*r**3 + 18*r**2 + 2*r - 304. Factor d(z).
-3*(z - 3)*(9*z - 2)**2
Let v(q) be the second derivative of 0 - q**4 + 0*q**2 - 3/5*q**5 - 42*q + 0*q**3 + 1/14*q**7 + 1/10*q**6. What is n in v(n) = 0?
-2, -1, 0, 2
Let b(w) be the second derivative of 0*w**3 + 1/165*w**6 + 0*w**4 + 0 - 3/110*w**5 + 0*w**2 + 14*w. What is i in b(i) = 0?
0, 3
Let -128/5*d + 22/5*d**4 + 2/5*d**5 + 0 + 72/5*d**3 + 32/5*d**2 = 0. Calculate d.
-4, 0, 1
Factor 7/9*m**2 + 1/9*m**3 + 4/3 + 16/9*m.
(m + 2)**2*(m + 3)/9
Let d(n) be the second derivative of -n**6/10 - 3*n**5/5 + 5*n**4/4 + 20*n + 13. Let d(z) = 0. What is z?
-5, 0, 1
Let d be 5*(-6)/((-18)/1). Factor 10/3*a + 0*a**3 + 0 - d*a**4 + 5*a**2.
-5*a*(a - 2)*(a + 1)**2/3
Suppose -10*d + 17*d = -4*d. Let c(l) be the third derivative of 0*l**3 + 0*l + d + 4*l**2 - 1/28*l**4 + 2/105*l**5. Solve c(a) = 0.
0, 3/4
Let l(h) be the first derivative of -6*h**5/5 + 9*h**4/4 + 5*h**3 - 9*h**2 + 39. Factor l(f).
-3*f*(f - 2)*(f - 1)*(2*f + 3)
Suppose 3*u - 2*q = 14, -6*u + 5*q = -2*u - 28. Factor 3*k**u + 2*k - 22 - 23 + 45.
k*(3*k + 2)
Let o(t) be the third derivative of -7*t**6/300 - 163*t**5/150 - 17*t**4/3 - 28*t**3/5 - 64*t**2 + t. Solve o(l) = 0 for l.
-21, -2, -2/7
Let s(n) = -52*n**2 - 84*n + 220. Let u(c) = -4*c**2 + c + 1. Let k(r) = s(r) - 12*u(r). Factor k(b).
-4*(b - 2)*(b + 26)
Let a(g) be the first derivative of -21/8*g**2 + 27 + 3/16*g**4 + 0*g + 3/2*g**3. Factor a(w).
3*w*(w - 1)*(w + 7)/4
Suppose 0 = 5*i + 4*z - 22, z + 3 + 2 = 4*i. Determine j so that i*j - 2*j**3 - 1 - 60*j**2 + 0 + 61*j**2 = 0.
-1, 1/2, 1
Suppose 0 = -9*z - 2*z + 66. Let y(j) be the second derivative of 1/18*j**4 + 0*j**3 + 0*j**2 + 0 + 1/63*j**7 - 1/30*j**5 - 1/45*j**6 + z*j. Factor y(g).
2*g**2*(g - 1)**2*(g + 1)/3
Suppose -4 = x - 2*x. Suppose -a + 0*a = -x. Solve 6*y - 2*y**2 - 13*y**3 - a*y**3 + 11*y**3 + 2 + 0 = 0 for y.
-1, -1/3, 1
Factor -232*u**2 - 100*u**2 - 68*u**3 - 7*u**4 + 80*u**2 + 3*u**4 + 324*u.
-4*u*(u - 1)*(u + 9)**2
Let c(z) be the second derivative of z**4/48 - 79*z**3/12 + 87*z + 2. Factor c(r).
r*(r - 158)/4
Let q(x) be the first derivative of -x**6/12 - x**5/5 + x**4 - x**3/3 - 7*x**2/4 + 2*x - 59. Suppose q(f) = 0. What is f?
-4, -1, 1
Determine x so that 4/15 + 2/15*x**2 - 2/3*x**3 - 2/5*x**4 + 2/3*x = 0.
-1, -2/3, 1
Let v(l) be the first derivative of 0*l**3 + 3 + 0*l**2 + 3/20*l**5 + 2*l - 1/2*l**4. Let w(y) be th