n be b(-3). Factor -12 - 22*p**3 - 96*p**2 - 12*p**3 + 61*p**n - 70*p - 9*p**3.
2*(p - 6)*(3*p + 1)**2
Suppose -9 = 5*r - 34. Let a be (-117)/78*(-2 + 0/(-1)). Suppose 4*x**2 + 4*x**4 - 3*x**2 - r*x**4 + 2*x + x**a - 3*x = 0. Calculate x.
-1, 0, 1
What is v in 8*v**2 + 17*v - 3*v - 8*v**2 + 5*v**2 - 7*v**2 = 0?
0, 7
Suppose 62*k - 21 = 55*k. Let n = 15 + -13. What is d in -1/2*d**k + 0*d + d**4 - d**n + 0 + 1/2*d**5 = 0?
-2, -1, 0, 1
Factor 30*s**2 - 16*s**4 - 5 + 31*s**4 - 20*s**3 - 20*s**3.
5*(s - 1)**3*(3*s + 1)
Let y(o) be the third derivative of 0 + 1/60*o**5 + 1/24*o**4 + 0*o - o**2 - 1/6*o**3 - 1/120*o**6. Factor y(q).
-(q - 1)**2*(q + 1)
Suppose 0 = 16*h - 12*h + 32. Let l(j) = -14*j**3 + 58*j**2 - 202*j + 142. Let i(t) = 5*t**3 - 19*t**2 + 67*t - 47. Let z(y) = h*i(y) - 3*l(y). Factor z(k).
2*(k - 5)**2*(k - 1)
Let q(a) = 55*a**3 + 60*a**2 + 60*a - 100. Let p(m) = -2*m**3 - m**2 - m + 1. Let f(t) = 25*p(t) + q(t). Solve f(n) = 0.
-5, -3, 1
Let x be 6/(-4) + 174/116. Suppose -2*s + 5 = 1. Find n such that 0*n**s + 0 + 4/3*n**4 + x*n + 1/3*n**3 = 0.
-1/4, 0
Let t(m) be the first derivative of 5/7*m**3 + 3/14*m**2 + 9/35*m**5 + 3/4*m**4 + 24 + 0*m. Factor t(x).
3*x*(x + 1)**2*(3*x + 1)/7
Let u = -8633/3 + 2878. Let -u*d + 1 - d**2 + 1/3*d**3 = 0. What is d?
-1, 1, 3
Let o(j) be the second derivative of 0 + 9*j + 20/3*j**3 + 5/12*j**4 + 0*j**2. Solve o(x) = 0.
-8, 0
Factor 1/2*x**3 + 5*x**2 + 14*x + 12.
(x + 2)**2*(x + 6)/2
Let w be 125 - (-12)/3 - 4. Let p = 251/2 - w. Factor 1/3*c + p - 1/6*c**2.
-(c - 3)*(c + 1)/6
Factor 0 - 4*d**3 - d**4 + 0*d + 1/2*d**5 + 0*d**2.
d**3*(d - 4)*(d + 2)/2
Let m = -3/182 - -561/910. Factor m*q**2 + 3/5 + 6/5*q.
3*(q + 1)**2/5
Let t(s) be the second derivative of -s**6/360 - s**5/120 + s**4/18 - s**3/12 - 21*s**2/2 - 7*s. Let c(k) be the first derivative of t(k). Factor c(g).
-(g - 1)*(g + 3)*(2*g - 1)/6
Let v = 258/35 - 146/35. Find m, given that v*m - 4/5*m**3 - 8/5 + 2/5*m**4 - 6/5*m**2 = 0.
-2, 1, 2
Let d(k) be the first derivative of 8*k + 0*k**2 - 2*k**3 - 4 - 1/2*k**4. Solve d(s) = 0 for s.
-2, 1
Let r = 1279 - 1276. Factor -10/11*q + 4/11 + 6/11*q**2 + 2/11*q**r - 2/11*q**4.
-2*(q - 1)**3*(q + 2)/11
Suppose 19*p + 3*p = -17*p. Factor 0 + p*d - 1/5*d**2 - 3/5*d**3 - 3/5*d**4 - 1/5*d**5.
-d**2*(d + 1)**3/5
Let f be 1 - (121/385 + (-4)/(-10)). Let r(q) be the first derivative of -9 - f*q**2 - 1/14*q**4 + 0*q + 2/7*q**3. Factor r(z).
-2*z*(z - 2)*(z - 1)/7
Let j(w) be the first derivative of 3*w**4 + 0*w**2 + 6/5*w**5 + 2/15*w**6 - 11 + 0*w**3 + 9*w. Let n(p) be the first derivative of j(p). Factor n(v).
4*v**2*(v + 3)**2
Let o(h) be the second derivative of -6*h - 9/4*h**2 + 25/8*h**3 + 0 + 9/16*h**4. Determine n so that o(n) = 0.
-3, 2/9
Suppose 0 = 4*h - 1 - 19. Suppose h*s + 0 = 3*q - 2, 0 = 3*q - s - 10. Factor -6 - d**2 + q - 5*d + 0 - 2*d**2.
-(d + 1)*(3*d + 2)
Let z = 235/4016 - -1/251. Let g(w) be the second derivative of 1/2*w**3 + 0 + 3/2*w**2 + 3*w + z*w**4. Determine p so that g(p) = 0.
-2
Let b(r) = -14*r - 3*r - 35*r**2 + 30 - 8*r + 25*r**3. Let i(w) = -w**4 - 24*w**3 + 34*w**2 + 24*w - 29. Let f(q) = -4*b(q) - 5*i(q). Factor f(o).
5*(o - 1)**2*(o + 1)*(o + 5)
Factor -234 + 60*n - 1/2*n**3 - 1/2*n**2.
-(n - 6)**2*(n + 13)/2
Let g(s) be the second derivative of 32/3*s**2 - 31*s - 64/9*s**3 + 0 + 7/3*s**4 - 11/30*s**5 + 1/45*s**6. Factor g(y).
2*(y - 4)**2*(y - 2)*(y - 1)/3
Let o(b) be the third derivative of -b**6/280 - 3*b**5/140 + 58*b**2. Factor o(y).
-3*y**2*(y + 3)/7
Factor -7*l**2 - 17/6*l**3 + 2/3*l - 1/6*l**4 + 28/3.
-(l - 1)*(l + 2)**2*(l + 14)/6
Let w(l) be the third derivative of 0*l - 1/420*l**7 + 0 - 1/2016*l**8 - 1/360*l**6 - 38*l**2 + 0*l**3 + 0*l**4 + 0*l**5. Suppose w(z) = 0. What is z?
-2, -1, 0
Let g(q) be the second derivative of -9*q + 117/50*q**6 + 1 + 4/5*q**3 + 0*q**2 - 17/5*q**4 + 183/50*q**5 - 81/70*q**7. Let g(s) = 0. Calculate s.
-1, 0, 2/9, 2
Let f be -4 - ((-5 - -2) + -6). Suppose 0 = -f*l + l + 5*g + 9, 2*l + g - 1 = 0. Factor 2*k**2 + l - 1 - 2*k + 0*k**2.
2*k*(k - 1)
Let s be 0 + (-4)/(-10) + (-264)/(-990). Let n(i) be the first derivative of -1/4*i**4 + s*i**3 - 6 - 2*i + 1/2*i**2. Find y, given that n(y) = 0.
-1, 1, 2
Let u(k) = 71*k**3 + 2*k**2 + k. Let v be u(-1). Let l = -70 - v. Determine b, given that l*b**3 + 0 - 1/3*b**5 + 0*b + 0*b**2 - 2/3*b**4 = 0.
-2, 0
Let m(v) = v**3 + 6*v**2 - 5*v - 48. Let g be m(-5). Solve -2/5*y - 7/5*y**g + 0 = 0 for y.
-2/7, 0
Let l(p) be the third derivative of 0*p**4 - 5/6*p**3 + 0*p - 2*p**2 - 1/1440*p**6 - 1/240*p**5 + 0. Let z(a) be the first derivative of l(a). Factor z(b).
-b*(b + 2)/4
Let n(f) = -f**2. Let h(z) be the second derivative of -z**4/12 + z**3 + 5*z**2/2 + 45*z. Let r(b) = -h(b) + 2*n(b). Factor r(a).
-(a + 1)*(a + 5)
Let c = 83 - 80. Factor -46*b + 0*b + 126*b**2 - 29*b - 17*b**c - 10*b**3 + 12.
-3*(b - 4)*(3*b - 1)**2
Let n be (3/(-43))/((-30)/(-219)). Let x = -2/215 - n. Let 27/2 + 27/2*d + x*d**3 + 9/2*d**2 = 0. What is d?
-3
Let o(u) be the first derivative of 0*u + 0*u**2 + 1 + 1/720*u**6 - 4/3*u**3 + 1/120*u**5 - 1/16*u**4. Let a(h) be the third derivative of o(h). Factor a(c).
(c - 1)*(c + 3)/2
Suppose -2*s = 10*s - 48. Suppose s*x - 2 = 14. What is a in 0 + 3/2*a**3 + 0*a**2 + 0*a - 9/4*a**x + 3/4*a**5 = 0?
0, 1, 2
Suppose 76729/8 + 1/8*x**2 + 277/4*x = 0. What is x?
-277
Let t = -74 - -79. Let n(l) be the second derivative of 0 + 4/15*l**4 - 4/15*l**3 - 1/10*l**t + 0*l**2 + 2*l + 1/75*l**6. Factor n(m).
2*m*(m - 2)**2*(m - 1)/5
Let z(o) be the third derivative of -o**6/360 - 2*o**5/45 - 13*o**4/72 - o**3/3 + 28*o**2 + 2. Let z(i) = 0. Calculate i.
-6, -1
Let f(i) be the second derivative of 0*i**3 + 0 - 2*i + 0*i**2 - 1/135*i**6 - 1/90*i**5 + 0*i**4. Factor f(a).
-2*a**3*(a + 1)/9
Let p(m) be the third derivative of m**7/105 - 29*m**6/60 + 112*m**5/15 - 49*m**4/3 - 30*m**2. Find j such that p(j) = 0.
0, 1, 14
Let c(u) be the second derivative of -u**6/150 - u**5/50 + u**3/15 + u**2/10 - 118*u. Factor c(w).
-(w - 1)*(w + 1)**3/5
Let j be (-1 - -1) + (-1395)/(-217) + -5. Suppose -6/7*m**2 - 8/7 + 24/7*m - j*m**3 = 0. What is m?
-2, 2/5, 1
Let v(t) be the third derivative of -t**7/105 + t**6/10 - t**5/30 - 2*t**4 - 16*t**3/3 + 65*t**2 + 2*t. Suppose v(c) = 0. Calculate c.
-1, 4
Let x(f) = 280*f**3 - 2832*f**2 - 6012*f + 1936. Let l(g) = 51*g**3 - 515*g**2 - 1093*g + 352. Let y(r) = 28*l(r) - 5*x(r). Factor y(h).
4*(h - 11)*(h + 2)*(7*h - 2)
Let o(a) = a**2 - 6*a - 16. Let d be o(9). Let u = d - 10. Suppose -t**2 + t**2 - u + 2*t - t**2 = 0. What is t?
1
Let r(u) be the second derivative of -1/15*u**4 + 2/5*u**2 + 1/5*u**3 - 3/50*u**5 + 0 + 19*u. Factor r(c).
-2*(c - 1)*(c + 1)*(3*c + 2)/5
Let n(k) be the first derivative of -k**6/2 - 24*k**5/5 - 15*k**4 - 10*k**3 + 63*k**2/2 + 54*k - 199. Find m, given that n(m) = 0.
-3, -2, -1, 1
Let d(i) = -3*i**2 + 23*i - 28. Let q(j) = -16*j**2 + 91*j - 111. Let u(a) = -9*d(a) + 2*q(a). Factor u(n).
-5*(n - 1)*(n + 6)
Suppose 19 = -3*a - 4*y - y, 15 = -3*a - 3*y. Let s(n) = n**2 + n - 6. Let o(q) = -6. Let b(u) = a*s(u) + 2*o(u). Solve b(i) = 0 for i.
-2, 1
Let -36 - 4*y**3 + 10*y + 4*y - 44*y**2 - 90*y = 0. What is y?
-9, -1
Let i be -7*(-36)/63 - 0. Let v(a) be the third derivative of -5*a**2 + 0 + 1/36*a**i + 0*a + 0*a**3 + 1/90*a**5. Determine g, given that v(g) = 0.
-1, 0
Suppose -l + 2*o = -3, -l = 3*l + 2*o - 52. Let -5 - l*m - 20*m**2 - 3 + 39*m = 0. What is m?
2/5, 1
Solve 0*n + 4/7*n**3 + 0 + 2/7*n**4 - 48/7*n**2 = 0 for n.
-6, 0, 4
Let a be 1440/140 + -10 - 5/42. Let q(g) be the first derivative of -a*g**2 + 4 - 1/18*g**3 + 1/24*g**4 + 0*g. Factor q(z).
z*(z - 2)*(z + 1)/6
Let u(y) be the first derivative of 3*y**4/28 - y**3/7 - 51*y**2/7 - 24*y + 49. Factor u(f).
3*(f - 7)*(f + 2)*(f + 4)/7
Suppose 4*k = 2*b + 14, 4*k + 9*b = 5*b - 4. Let 4/13 + 0*w**k - 2/13*w**3 + 6/13*w = 0. Calculate w.
-1, 2
Let i be 8/12*(265/(-35) + 8). Factor 0*m - 2/7*m**5 + 0*m**2 + 4/7*m**3 + 0 + i*m**4.
-2*m**3*(m - 2)*(m + 1)/7
Let g be ((-26)/8 + (-6)/8)/(-14). What is h in -2*h**3 - 4/7*h**2 - 8/7*h**4 + 0 + g*h = 0?
-1, 0, 1/4
Let w be 8/30 + (-7168)/(-1920). Let -2 - 2*f**w + 28/3*f**2 + 8/3*f**3 + 8/3*f = 0. What is f?
-1, 1/3, 3
Let m(l) be the first de