47
Let p(y) = y**3 - 4255*y**2 + 2013553*y - 317471455. Let l(j) = j**3 - j**2 + 4*j + 2. Let q(x) = 2*l(x) + p(x). Suppose q(v) = 0. What is v?
473
Let k(o) be the first derivative of -o**6/24 + 11*o**5/20 - 21*o**4/8 + 16*o**3/3 - 4*o**2 - 1016. Determine g, given that k(g) = 0.
0, 1, 2, 4
Let m(y) be the second derivative of -5*y**7/42 + 19*y**6/6 - 28*y**5 + 235*y**4/3 + 160*y**3/3 - 640*y**2 + 3059*y. Solve m(d) = 0 for d.
-1, 2, 8
Suppose 120*t + 7 = 119*t, -q + 2*t = -17. Let a(i) be the first derivative of q*i**2 - 6/5*i**5 - 20*i + 14*i**3 + 42 - 11/2*i**4. Let a(f) = 0. What is f?
-5, -2/3, 1
Suppose -14*s = -16*s - 6, 2*o = -2*s - 8. Let k(t) = -1. Let f(w) = -3*w**3 - 27*w**2 - 72*w - 43. Let h(c) = o*f(c) - 5*k(c). Factor h(d).
3*(d + 1)*(d + 4)**2
Suppose -44*x = -18*x - 260. Let y be x/(-2) - 54/(-10). Factor 2/5*g**3 - 2/5*g**2 - 2/5*g + y.
2*(g - 1)**2*(g + 1)/5
Let s(n) be the third derivative of 0*n + 0*n**4 - 1/105*n**7 + 0*n**3 - 5*n**2 - 1/30*n**6 + 3 + 4/15*n**5. Suppose s(g) = 0. What is g?
-4, 0, 2
Let g(q) = 286*q**3 + 15451*q**2 + 2465*q - 538. Let s(b) = -287*b**3 - 15452*b**2 - 2465*b + 536. Let x(l) = 7*g(l) + 6*s(l). Suppose x(h) = 0. Calculate h.
-55, -2/7, 1/8
Let r be (1 - -6) + (-6 - -2) + 0. Let g(j) be the second derivative of 7/48*j**r + 0 - 10*j + 1/4*j**2 - 1/48*j**4. Factor g(z).
-(z - 4)*(2*z + 1)/8
Find k, given that 16*k + 8/3*k**3 + 58/3*k**2 + 0 - 2/3*k**4 = 0.
-3, -1, 0, 8
Let 3*a**4 + 13/4*a**2 + 51/8*a**3 + 0*a + 0 - 1/8*a**5 = 0. What is a?
-1, 0, 26
Let u(n) be the second derivative of 13*n**5/160 - 245*n**4/96 + 49*n**3/12 + 9*n**2/4 - 695*n. Factor u(t).
(t - 18)*(t - 1)*(13*t + 2)/8
Suppose 0 = 6*b - 10*b. Let o(v) = v + 1. Let n be o(3). Suppose -3*u**5 + 6*u**2 + b*u**5 - u**3 + n*u**3 - 6*u**4 = 0. What is u?
-2, -1, 0, 1
Let m be -5 - (-1 + (-47 - 1)). Factor -9*t**2 + 22*t**2 + m*t - 9*t**2.
4*t*(t + 11)
Let f(a) = a**3 - 12*a**2 + 3*a - 9. Let z be f(12). Let j = -24 + z. Let 1 + 836*h**3 - h - 4*h**2 - 835*h**3 + j*h**2 = 0. Calculate h.
-1, 1
Suppose 16*o = 15*o - 5*r - 293, 3*r + 1104 = -4*o. Let g be 7*(-143)/o + 2/(-3). Factor 0*l + 0*l**2 - 8/3*l**g + 20/3*l**5 + 0 + 4*l**4.
4*l**3*(l + 1)*(5*l - 2)/3
Suppose 528*t + 387*t**3 + 149*t**3 + 1060*t**2 + 1559*t**4 - 779*t**4 - 776*t**4 = 0. Calculate t.
-132, -1, 0
Let q(o) = o**5 + 6*o**4 + 5*o**3 - 4. Suppose -192 = -25*v - 23*v. Let p(t) = -3*t**5 - 17*t**4 - 14*t**3 + 11. Let l(h) = v*p(h) + 11*q(h). Factor l(d).
-d**3*(d + 1)**2
Let d(b) be the first derivative of -841*b**4 - 2088*b**3 + 456*b**2 - 32*b + 3365. Solve d(f) = 0.
-2, 2/29
Let -2/3*h**2 - 34/15*h + 14/5 + 2/15*h**3 = 0. What is h?
-3, 1, 7
Factor -24*n**2 + 1288/3 - 4/3*n**3 + 172*n.
-4*(n - 7)*(n + 2)*(n + 23)/3
Let l be (-3 - (-80)/25) + 9/5. Let c = 21 + -18. What is i in -c + 19*i**2 + 30*i - 15 - 24*i**l - 7 = 0?
1, 5
Let h(c) = -c**3 - 59*c**2 + 27*c + 1614. Let k be h(-59). Suppose -5*b - 10 = 0, 2*b = a - 0*b - 40. Factor 45*l + 6 + 0 - a*l + k*l**3 - 36*l**2.
3*(l - 1)**2*(7*l + 2)
Let q(r) = 3*r**2 - 82*r + 25. Let a(f) be the third derivative of -f**4/24 + f**3/6 - 189*f**2. Let k(z) = 15*a(z) + 5*q(z). Factor k(t).
5*(t - 28)*(3*t - 1)
Let c(x) be the first derivative of x**4/2 - 18*x**3/5 + 6*x**2 - 16*x/5 - 4533. Let c(j) = 0. What is j?
2/5, 1, 4
Let i be -4 + 848/120 + (6/(-5))/3. Let k(g) be the first derivative of 18 + i*g**2 + 32/3*g + 2/9*g**3. What is f in k(f) = 0?
-4
Let t be (10402/(-525))/((-48)/(-160)). Let a = 724/9 + t. Find c, given that -24/5*c + a + 2/5*c**2 = 0.
6
Let t(o) be the second derivative of o**4/42 + 8254*o**3/21 + 17032129*o**2/7 + o - 628. Factor t(k).
2*(k + 4127)**2/7
Let t(a) = -5*a**5 - 9*a**4 + 2*a**3 + 10*a**2 + 19*a - 17. Let w(j) = -2*j**5 - 3*j**4 + j**3 + 3*j**2 + 7*j - 6. Let h(i) = 3*t(i) - 8*w(i). Factor h(c).
(c - 3)*(c - 1)**2*(c + 1)**2
Let n be -4 + (104/4 - 4). Let q be (15/n)/((-90)/(-54)). Factor -5/4*m - q - m**2 - 1/4*m**3.
-(m + 1)**2*(m + 2)/4
Let x(w) be the third derivative of 6/35*w**7 + 0 - 3/5*w**5 + 0*w**3 - 25*w + 2*w**2 + 1/2*w**4 - 5/112*w**8 + 1/40*w**6. Suppose x(g) = 0. What is g?
-1, 0, 2/5, 1, 2
Let t = 181919 + -181919. Factor t*p**2 + 3/8*p**3 + 0*p + 0.
3*p**3/8
Let v be 217/4185*63 - 80/50. Let x be (-4)/6*(-12)/2. Let -v*m - 1/3*m**x + 1/3*m**3 + 2/3 + m**2 = 0. Calculate m.
-2, 1
Let f(i) be the third derivative of -17*i**4/6 + 147*i**2. Let q be f(0). Find g, given that -3/2 + q*g + 3/2*g**2 = 0.
-1, 1
Let l(c) be the first derivative of -20/9*c**3 + 8/15*c**5 - 59 - 8/3*c**2 + 0*c - 1/9*c**6 + 1/2*c**4. Let l(i) = 0. What is i?
-1, 0, 2, 4
Let c be 19/(2356/8) - (362/(-155) - 32/(-80)). Find x, given that 2 - 1/3*x**c - 1/3*x = 0.
-3, 2
Let h = -92 + 94. What is f in 11*f**h - 6*f**2 + 15*f**2 - 17 - 32*f + 1 = 0?
-2/5, 2
Let w = 867325/7 + -123901. Factor 18/7 - 33/7*y + w*y**2 - 3/7*y**3.
-3*(y - 3)*(y - 2)*(y - 1)/7
Let l = 52 + -50. Suppose 0 = -3*j - 4*j + 35. Let -l*h**j + 12*h**4 - 4*h**4 + 0*h**4 = 0. Calculate h.
0, 4
Let s = 34696 - 34692. Determine y, given that 0 - 7/5*y**s - 36/5*y**2 - 8/5*y - 6*y**3 = 0.
-2, -2/7, 0
Suppose -44*k + 42*k + 18 = 0. Let h = 11 - k. Factor 10*r**2 - 4*r - 7*r**2 - h*r.
3*r*(r - 2)
Let r(m) be the second derivative of 0*m**3 + 0*m**4 + 5/2*m**2 - 1/120*m**5 - 14*m + 0. Let t(w) be the first derivative of r(w). Suppose t(z) = 0. What is z?
0
Factor 1/2*x**2 + 134689/2 + 367*x.
(x + 367)**2/2
Let s = 66 + -64. Let h(m) = -m**4 - m**3 - m**2 - m. Let l(p) = 13*p**4 + 13*p**3 + p**2 + 17*p. Let c(z) = s*l(z) + 22*h(z). Factor c(b).
4*b*(b - 1)**2*(b + 3)
Let l(x) = -20*x**2 + 5*x - 9. Let k(o) = o**3 + 10*o**2 + 6*o - 10. Let a be k(-9). Let b(v) = -7*v**2 + 2*v - 3. Let q(i) = a*b(i) - 6*l(i). Factor q(n).
(n + 1)*(n + 3)
Let f be 2977/1170 + -26 + 23360/900. Factor 1/4*r**2 - f + 3/4*r.
(r - 2)*(r + 5)/4
Let i = -2/563001 - -1501342/1689003. Suppose -i*l**3 + 32/9*l + 32/9 - 2/9*l**4 + 0*l**2 = 0. What is l?
-2, 2
Let f(u) be the third derivative of -u**5/30 - 35*u**4/12 - 124*u**3/3 + 449*u**2. Factor f(i).
-2*(i + 4)*(i + 31)
Let f(g) be the first derivative of g**6/6 + g**5/5 - 211*g**4/4 - 1093*g**3/3 + 855*g**2 + 2592*g - 6006. Determine z so that f(z) = 0.
-9, -1, 2, 16
Let p be -5 - 1 - (-25272)/3936. Let v = -7/41 + p. Factor v*h**4 + 5/4*h**3 + 7/4*h + 9/4*h**2 + 1/2.
(h + 1)**3*(h + 2)/4
Let z(a) be the second derivative of -a**5/100 - 17*a**4/20 - 5*a**3/3 + 64*a. Factor z(f).
-f*(f + 1)*(f + 50)/5
Let y(s) be the first derivative of -6*s**2 - 15 - 16*s - 9/4*s**4 + 6*s**3. Let v(l) be the first derivative of y(l). Suppose v(h) = 0. What is h?
2/3
Let z(y) be the second derivative of -1/25*y**6 + 0*y**2 - 1/5*y**4 - 1/210*y**7 + 0 - 2/15*y**3 - 13/100*y**5 + 14*y. Solve z(d) = 0 for d.
-2, -1, 0
Factor 69*b**2 + 105*b + 2*b**3 - 149 + 61 - 164 + 97*b - 21*b**2.
2*(b - 1)*(b + 7)*(b + 18)
Let q be -6 + 3 + 306/(-21)*(-88)/176. Determine f, given that -9 - 3/7*f**2 + q*f = 0.
3, 7
Suppose b - 7 + 3 = 0, -4*v - 2*b + 108 = 0. Suppose -v*q - 7*q = 0. Let 0*y + q*y**2 + 0 + 0*y**4 + 1/8*y**3 - 1/8*y**5 = 0. Calculate y.
-1, 0, 1
Let p be ((3 + 0)/6)/(17 - 3738/224). Suppose 0 - 2/5*o**3 - 8/5*o**2 - p*o = 0. What is o?
-2, 0
Let v(m) be the first derivative of -105*m**2 + 125/3*m**3 + 45/4*m**4 + 122 + 40*m. What is t in v(t) = 0?
-4, 2/9, 1
Let k be 38 + (-207)/115 + -35. Suppose -k*g**4 + 0*g**2 + 3/5*g**3 + 0 + 0*g - 9/5*g**5 = 0. Calculate g.
-1, 0, 1/3
Let k(i) be the second derivative of -i**6/252 + i**5/70 - i**4/84 + i**3/6 - 5*i**2/2 + 10*i + 2. Let j(x) be the second derivative of k(x). Factor j(l).
-2*(l - 1)*(5*l - 1)/7
Suppose 29*b = 24*b + 45. Suppose b*x = 44 - 8. Find g such that 3 + 4*g**3 + 1 - x*g - 363*g**2 + 359*g**2 = 0.
-1, 1
What is s in -168/5*s**2 - 368/5*s + 704/5 + 92/5*s**3 - 2/5*s**4 = 0?
-2, 2, 44
Let f be ((-1)/(-2) + 21/(-14))*-2. What is o in -13 + 3*o**2 + 10*o - 27 + 2*o**f = 0?
-4, 2
Suppose 0 = -17*i + 39 - 107. Let c be (i + (-198)/(-49))*7. Factor 1/7*k**4 + c*k + 0*k**2 - 1/7 - 2/7*k**3.
(k - 1)**3*(k + 1)/7
Let b = 444416/666615 + -2/222205. Factor -b*q**5 + 0*q + 2*q**4 - 4/3*q**3 + 0 + 0*q**2.
-2*q**3*(q - 2)*(q - 1)/3
Suppose -4*c = -5*s - 51, -2*c + s = -4*c + 29. Let t be c/2 - 