
-3, -1/5, 1
Let o(c) = -38*c - 186. Let z be o(-5). Suppose -16/5*d**5 + 52/5*d + 8/5 + 44/5*d**3 - 4*d**z + 92/5*d**2 = 0. What is d?
-1, -1/4, 2
Let h(t) = -t**3 - 6*t**2 - t - 4. Let w be ((-5)/5)/(2/12). Let i be h(w). Factor -3*b**3 + 4 + 3*b - b**2 - 1 + 0*b - i*b**2.
-3*(b - 1)*(b + 1)**2
What is u in 1/6*u**5 + 7/6*u**2 + 3*u - 1/2*u**4 - 7/6*u**3 + 4/3 = 0?
-1, 2, 4
Let f(i) be the second derivative of -i**5/50 - 4*i**4/5 - 48*i**3/5 - 58*i. Factor f(x).
-2*x*(x + 12)**2/5
Suppose -4*l = 3*l - 119. Suppose -3*i - 9 = 0, -3*i = 3*z + z - 51. Factor 6*g**2 + 10*g**3 + l - 3*g**3 + 3*g**5 + 5*g**3 - z*g - 11 - 12*g**4.
3*(g - 2)*(g - 1)**3*(g + 1)
Let w be 0 + (-6)/(-9)*(-3)/(-1). Factor -1/6*v**4 + 1/6*v**5 + 0 + 1/6*v**w + 0*v - 1/6*v**3.
v**2*(v - 1)**2*(v + 1)/6
Let h(k) be the second derivative of 1/14*k**7 + 0*k**2 + k**4 - 3/10*k**6 + 0 + 0*k**5 + 0*k**3 + 21*k. Factor h(p).
3*p**2*(p - 2)**2*(p + 1)
Factor 0 + 24*m**2 - 3/2*m**4 + 3/2*m**3 - 24*m.
-3*m*(m - 4)*(m - 1)*(m + 4)/2
Let n be 1457/(-2115) - 6/15*(-1 + -1). Factor -n*j**4 + 0*j - 1/9*j**3 + 0*j**2 + 0.
-j**3*(j + 1)/9
Suppose -2*b - 5 = -4*h + b, -3*b = 3*h - 9. Determine x, given that 4*x**h - 40 - 60 + 76 - 4*x = 0.
-2, 3
Let b(d) = -d**3 + 16*d**2 + 28*d - 187. Let n be b(17). Factor n - 3/7*k**3 + 0*k - 3/7*k**2.
-3*k**2*(k + 1)/7
Let a(w) be the second derivative of -4/3*w**3 - 1/3*w**4 + 0*w**2 + 0 - 19*w. Determine u, given that a(u) = 0.
-2, 0
Suppose 129/2*a**2 - 27/2*a**3 + 18 + 96*a = 0. What is a?
-1, -2/9, 6
Let d = -73 + 87. Suppose d*t - t = 39. Factor -2/13*r**t - 6/13*r + 2/13 + 6/13*r**2.
-2*(r - 1)**3/13
Solve -2/7*j**2 - 108/7*j - 1458/7 = 0.
-27
Let u = -46512/7 + 6645. Solve 0 - 9/7*n**3 + 6/7*n**2 + u*n**5 + 0*n**4 + 0*n = 0 for n.
-2, 0, 1
Let v(y) be the second derivative of -y**4/12 + y**3/6 + y**2 - 748*y. Suppose v(r) = 0. What is r?
-1, 2
Let z = -19 - -14. Let b be (10/z)/12 + (-22)/(-24). Factor 3/2*g - b - 3/4*g**2.
-3*(g - 1)**2/4
Let v be 4 - (0 + 1 - 180/2). Let l = v - 90. Factor -1/7*s**2 + 0 + 0*s**l + 1/7*s**4 + 0*s.
s**2*(s - 1)*(s + 1)/7
Let n = 23651/200 + -473/4. Let q(i) be the third derivative of 3/10*i**4 - 3*i**2 + 3/50*i**5 + 0 + 0*i + 4/5*i**3 + n*i**6. Find z, given that q(z) = 0.
-2
Let r(i) = 397*i**3 - 3355*i**2 + 1839*i - 256. Let v(q) = 992*q**3 - 8388*q**2 + 4596*q - 640. Let p(l) = 12*r(l) - 5*v(l). Let p(h) = 0. Calculate h.
2/7, 8
Let s(w) = -9*w**2 + 4*w - 3. Let t be s(1). Let v = -6 - t. What is j in 9 - 2*j**v - 8*j - 13 - 2*j**2 = 0?
-1
Suppose -18*q + 15 = -17*q. Let o = 18 - q. Factor -76*x**4 + 16*x**3 - 9*x + 44*x**o - 4*x**2 + 28*x**5 + x.
4*x*(x - 1)**3*(7*x + 2)
Let w(p) = 5*p**4 + 195*p**3 - 2941*p**2 + 957*p. Let k(l) = -8*l**4 - 388*l**3 + 5883*l**2 - 1915*l. Let b(s) = 8*k(s) + 14*w(s). Factor b(g).
2*g*(g - 31)**2*(3*g - 1)
Let c(g) = -1 + 4 + 2*g + 1 + 6. Let o be c(-5). Factor 1/2*n**3 + o + 0*n + 0*n**2 + n**4 + 1/2*n**5.
n**3*(n + 1)**2/2
Let l(w) = 7*w**2 + 22*w + 21. Let z(f) be the first derivative of -3*f**3 - 21*f**2/2 - 21*f + 19. Let x(d) = 3*l(d) + 2*z(d). Factor x(g).
3*(g + 1)*(g + 7)
Let c(x) = x**3 - x**2 + x + 1. Let o(d) = d**4 + 6*d**3 - d**2 + 3*d + 3. Let b(p) = 3*c(p) - o(p). Factor b(i).
-i**2*(i + 1)*(i + 2)
Factor -13/3 - 61*q - 49/3*q**3 - 217*q**2.
-(q + 13)*(7*q + 1)**2/3
Let p be 7 - 30*(-9)/(-108). Factor 27/4 + 3/4*d**2 - p*d.
3*(d - 3)**2/4
Suppose -4*z = -4*j - 17 - 3, 5*j + 4*z + 7 = 0. Let t = 5 + j. Suppose 2*u**t + 2 + 4*u + 0 - 3*u - u**3 - 4 = 0. Calculate u.
-1, 1, 2
Suppose 1/3*l**5 - 20/3*l**2 + 2*l**4 + 3*l + 14/3 - 10/3*l**3 = 0. Calculate l.
-7, -1, 1, 2
Let g(n) = n**3 + 9*n**2 + 19*n - 2. Let h be g(-5). Let a(i) be the third derivative of 0*i + 1/240*i**5 + i**2 + 3/8*i**h + 0 - 1/16*i**4. Solve a(s) = 0.
3
Factor 5241 + 306 + 5*h**2 + 258*h - 2*h**2.
3*(h + 43)**2
Let l be 2 + -3 - (-22 + 14). Let m(t) be the third derivative of 1/1050*t**l + 0*t + 0*t**5 + 0*t**3 + 0*t**6 + 0 + t**2 + 0*t**4. Factor m(z).
z**4/5
Let o(m) = -5*m**2 + 7*m + 199. Let w be o(7). Let 12/5*f**2 + 9/5*f + 3/5*f**w + 0 = 0. Calculate f.
-3, -1, 0
Let g(u) be the third derivative of -u**5/100 - 29*u**4/40 - 27*u**3/5 + 281*u**2. Factor g(s).
-3*(s + 2)*(s + 27)/5
Suppose -21*k = -45*k + 48. Factor 0 + 3/4*t - 1/4*t**k.
-t*(t - 3)/4
Suppose 0 = 3*f - 31 + 19. Find c, given that 0*c**3 - 8*c**2 - 2*c**3 - 2*c**3 + 32 + 24*c - f*c**2 = 0.
-4, -1, 2
Let y(f) be the second derivative of -f**6/24 - f**5/12 + 5*f**4/6 + 10*f**3/3 - 10*f**2 - 22*f. Let o(x) be the first derivative of y(x). Factor o(i).
-5*(i - 2)*(i + 1)*(i + 2)
Determine t, given that -5315*t**4 + 4 - 48*t**3 + 18*t**5 + 5276*t**4 + 8 + 153*t**2 - 96*t = 0.
-2, 1/6, 1, 2
Find u, given that 0 - 16/9*u**2 + 4/9*u**3 - 10/9*u**5 + 16/9*u**4 + 2/3*u = 0.
-1, 0, 3/5, 1
Suppose -2*a - 14*y = -11*y - 9, -1 = a - 4*y. Let o(c) be the first derivative of -6*c**2 + 18*c + 7 + 2/3*c**a. Solve o(p) = 0 for p.
3
Suppose -2*k + 5*m = 20, 0 = -3*m - 8 - 4. Let l be (k/(-14))/2 + 9/(-21). Factor -16/7 + l*d**3 - 8/7*d + 4/7*d**2.
2*(d - 2)*(d + 2)**2/7
Let r(a) = -2*a**4 - a**3 + a - 1. Let o(z) = z**4 - 9*z**3 - 21*z**2 + 3*z + 29. Let h(u) = -2*o(u) - 2*r(u). Factor h(n).
2*(n - 1)*(n + 2)**2*(n + 7)
Let g be 825/(-1197) - (-5)/15*2. Let m = g - -571/1729. Find x, given that -2/13*x**2 + 0 + m*x = 0.
0, 2
Let u(g) = 6*g**3 - 240*g**2 - 3840*g - 20502. Let z(t) = -t**3 + 48*t**2 + 768*t + 4100. Let f(h) = -2*u(h) - 11*z(h). Solve f(v) = 0.
-16
Let b = 1684 + -1679. Let c(d) be the first derivative of 0*d**2 + 0*d + 3 - 9/20*d**4 + 3/25*d**b + 2/5*d**3. Factor c(w).
3*w**2*(w - 2)*(w - 1)/5
Let x be 5/(-1) + 1 + 4. Factor 6/13*s**2 - 8/13 + x*s + 2/13*s**3.
2*(s - 1)*(s + 2)**2/13
Let s(l) be the second derivative of -l**7/14 - 13*l**6/10 - 12*l**5/5 + 47*l**4 - 32*l**3 - 384*l**2 - 21*l. What is g in s(g) = 0?
-8, -1, 2
Let q be (-1*1/3)/(0 + (-221)/102). Factor 0 + 0*a**2 + 2/13*a**5 + 0*a**4 - 4/13*a**3 + q*a.
2*a*(a - 1)**2*(a + 1)**2/13
Suppose 47*s = -51*s + 234 + 60. Factor -1/2 - 1/4*o**s - o**2 - 5/4*o.
-(o + 1)**2*(o + 2)/4
Let d(a) be the third derivative of a**8/100800 + a**7/5040 + a**6/900 - a**5/4 - a**2. Let m(f) be the third derivative of d(f). Factor m(w).
(w + 1)*(w + 4)/5
Let p = -116/1275 - -2/17. Let w(l) be the second derivative of -2/15*l**3 + p*l**6 + 0*l**2 - 7*l + 1/25*l**5 - 1/15*l**4 + 0. Let w(m) = 0. Calculate m.
-1, 0, 1
Let u(v) be the first derivative of 2*v**3 + 1/2*v**6 - 6/5*v**5 + 0*v + 9/2*v**2 + 6 - 3*v**4. Factor u(y).
3*y*(y - 3)*(y - 1)*(y + 1)**2
Let l be 90/(-20)*(-10)/3. Determine m so that 0 + 45*m + l*m**2 - 12*m**3 + 3*m**4 - 51*m + 0 = 0.
0, 1, 2
Let m(r) = 2*r**2 + 58*r + 48. Let o(p) = 3*p**2 + 117*p + 94. Let f(s) = -5*m(s) + 2*o(s). Let f(l) = 0. Calculate l.
-13, -1
Suppose -4*r = 4*w - 36, w + 17 = r + 4*w. Suppose -3*q = -0*v - v - 2, -r*q - 3*v - 6 = 0. Factor 2/7*d**2 + 2/7*d + q.
2*d*(d + 1)/7
Let d(l) be the second derivative of -l**4/48 - l**3/3 - 2*l**2 + 23*l + 5. Factor d(s).
-(s + 4)**2/4
Let q(l) = -2*l**3 - 8*l**2 + 26*l + 14. Let w be q(-6). Suppose -2/5 - 13/5*g - 11/5*g**w = 0. What is g?
-1, -2/11
Factor -31 - 38*z + 8*z + 39*z**2 + 31*z**2 - 69*z**2.
(z - 31)*(z + 1)
Solve 48228544/11*m + 397488/11*m**2 + 2/11*m**4 + 2194398752/11 + 1456/11*m**3 = 0 for m.
-182
Let f(w) be the third derivative of -w**5/75 - w**4/30 + 141*w**2. Suppose f(z) = 0. What is z?
-1, 0
Solve 25 + 6*f**4 - 33*f**5 + 5*f**4 - 2*f**4 - 15*f + 7*f**3 + 34*f**5 + 7*f**3 - 34*f**2 = 0 for f.
-5, -1, 1
Let p(j) be the third derivative of j**5/360 + j**4/72 - j**3/12 - 22*j**2 - j. Factor p(r).
(r - 1)*(r + 3)/6
Let z = -139940/57 + 2455. Let i = 193/399 - z. Find l such that -4/7 - 4/7*l**3 + 4/7*l + i*l**2 = 0.
-1, 1
Let v(b) be the first derivative of 7*b**3/3 - 17*b**2/2 + 6*b - 79. Factor v(a).
(a - 2)*(7*a - 3)
Let r be (-5 - 0) + 35*9/63. Let p(a) be the second derivative of r*a**3 - 1/40*a**5 + 3*a + 1/8*a**4 - a**2 + 0. Factor p(v).
-(v - 2)**2*(v + 1)/2
Let j(q) = -q**3 - 25*q**2 + 30*q + 91. Let b be j(-26). Let a be b/(-5) + (0 - 2). What is f in 3/5*f + 0*f**2 + 0 - a*f**3 = 0?
-1, 0, 1
Let j be 11 + (-65)/(-104)*-14. Let x(g) be the second derivative of -1/40*g**5 + 27