1
Let c(r) be the second derivative of -r**7/252 - r**6/60 - r**5/120 + r**4/24 + r**3/18 - 122*r. Let c(n) = 0. Calculate n.
-2, -1, 0, 1
Let g(a) = -4*a**2 + 206*a + 199. Let k(i) = i**2 - 41*i - 40. Let l(t) = 2*g(t) + 11*k(t). Factor l(s).
3*(s - 14)*(s + 1)
Let a(m) be the third derivative of -m**6/540 - m**5/9 - 16*m**4/9 + 512*m**3/27 + 7*m**2 + 6*m. Determine y, given that a(y) = 0.
-16, 2
Let y(f) be the second derivative of -f**4/4 + 60*f**3 - 5400*f**2 + 516*f. Solve y(v) = 0 for v.
60
Suppose n - 3*n = -3*i + 70, 0 = 4*i - 4*n - 92. Let d = 27 - i. What is w in 20*w**d + 4*w**2 - 24*w**3 + 4*w**2 = 0?
0, 2
Let b(i) be the first derivative of -i**3/4 + 543*i**2/4 - 98283*i/4 + 81. Factor b(m).
-3*(m - 181)**2/4
Let j(t) be the third derivative of t**6/420 + t**5/105 + t**4/84 + 87*t**2. Find n, given that j(n) = 0.
-1, 0
Let q(a) be the third derivative of -a**6/540 + a**4/12 + 69*a**2. Factor q(r).
-2*r*(r - 3)*(r + 3)/9
Let k(p) be the second derivative of p**4/24 + 5*p**3/12 + 3*p**2/2 - p - 10. Factor k(z).
(z + 2)*(z + 3)/2
Suppose 25 - 425 = -200*a. Let z be 2 - (2 - 2/15). Let -z*u**a + 4/15*u - 2/15 = 0. Calculate u.
1
What is u in -16*u + 180*u**2 + 3*u**5 - 30*u**4 + 128*u + 21*u**3 + 17*u**3 + u**3 - 4*u = 0?
-1, 0, 6
Suppose -5*p + 102 = p. Suppose 4*n - p = 11. Factor d**4 - 5*d**4 - 23 + n - 16*d + 12*d**2 + 8*d**3.
-4*(d - 2)**2*(d + 1)**2
Factor -7/3*v - 1/3*v**3 - 1 - 5/3*v**2.
-(v + 1)**2*(v + 3)/3
Let x(m) = -3*m**4 + 312*m**3 + 421*m**2 + 63*m - 108. Let v(t) = -t**4 + 155*t**3 + 211*t**2 + 31*t - 54. Let a(b) = -13*v(b) + 6*x(b). Factor a(d).
-(d + 1)**2*(d + 27)*(5*d - 2)
Let p be (16 - 5400/340) + 9/68. Let v(s) be the first derivative of -p*s**2 - 10 - 1/6*s**3 + s. Factor v(o).
-(o - 1)*(o + 2)/2
Let f(o) be the third derivative of o**7/14 + 25*o**6/12 - 71*o**5/12 + 15*o**4/4 + 3*o**2 - 180. Factor f(k).
5*k*(k - 1)*(k + 18)*(3*k - 1)
Let f be 1/((3/(-12))/((-2)/4)). Let 16*i**f - 45 + 9*i + 5 + 5*i**5 + 5*i**3 - 86*i**2 + 20*i**4 - 109*i = 0. Calculate i.
-2, -1, 2
Let x = -139 - 32. Let a = x - -175. Factor 1/2*c**3 - 3*c**2 - 9/4*c + 0 - 1/4*c**5 + c**a.
-c*(c - 3)**2*(c + 1)**2/4
Let y(c) be the third derivative of -c**6/120 + c**4/24 - c**3/6 - 19*c**2. Let s(a) = -4*a**3 + 4*a**2 + 2*a - 2. Let b(p) = -s(p) + 2*y(p). Factor b(v).
2*v**2*(v - 2)
Let w(n) be the second derivative of n**6/150 - 3*n**5/100 - n**4/15 - 17*n - 2. Factor w(j).
j**2*(j - 4)*(j + 1)/5
Let i be -4 - 1*(-372)/90. Let n(r) be the second derivative of r + i*r**5 + 0 - 4/45*r**6 + 1/9*r**4 - 5/9*r**3 + 2/3*r**2 + 1/63*r**7. Factor n(c).
2*(c - 2)*(c - 1)**3*(c + 1)/3
Let y = -10 - 32. Let x be (y/21)/(0 - 4). Factor 15/2*t + 9/2 + x*t**3 + 7/2*t**2.
(t + 1)*(t + 3)**2/2
Let v(x) = -x**3 + 12*x**2 + 2*x - 18. Let f be v(12). Let w be (11 + -2)*4/f. Factor -8*d - 20*d**2 + 3 + w + 3.
-4*(d + 1)*(5*d - 3)
Let l(b) be the second derivative of -b**6/18 - b**5/12 - 29*b + 1. Factor l(o).
-5*o**3*(o + 1)/3
Let a = -1290 + 1290. Determine i so that 0 + a*i**2 + 0*i**3 + 0*i + 1/2*i**4 + 1/2*i**5 = 0.
-1, 0
Factor 0 - 1/3*i**3 + 2*i**2 - 5/3*i.
-i*(i - 5)*(i - 1)/3
Let g(n) be the third derivative of -n**6/600 + n**5/75 + 3*n**2 + 17. Factor g(d).
-d**2*(d - 4)/5
Let l = -7/18 + 19/18. Let y(d) be the first derivative of -5/9*d**3 + l*d - 7 + 1/2*d**2. Determine z, given that y(z) = 0.
-2/5, 1
Let b be (-4)/(-8) - (-10)/4. Suppose -3*l = o + 1, -4*o - 6*l + l = -b. Find s, given that -22/5*s**o - 8/5 + 24/5*s + 6/5*s**3 = 0.
2/3, 1, 2
Let g(c) = 4*c**2 - 18*c + 20. Let h(j) = -j**2 - 1. Let i(f) = g(f) + 2*h(f). Let t be i(8). Let -8/5*m + 4/5*m**t - 12/5 = 0. What is m?
-1, 3
Let o = -1/113 + 461/1017. Determine k so that 2/9 + o*k + 2/9*k**2 = 0.
-1
Let k(c) be the first derivative of 5*c**3/3 + 25*c**2/2 - 70*c + 101. Suppose k(i) = 0. What is i?
-7, 2
Let w(x) be the second derivative of -15*x + 1/140*x**5 - 1/21*x**3 - 1/84*x**4 + 0*x**2 + 0. Factor w(v).
v*(v - 2)*(v + 1)/7
Let k be 11 + -12 + 0 + 53. Let d = 54 - k. What is v in d - 2*v + 1/2*v**2 = 0?
2
Factor -287496*l - 2371842 - 124*l**3 - 17710*l**2 - 140*l**3 - 2*l**4 + 4642*l**2.
-2*(l + 33)**4
Let o(i) be the third derivative of i**7/165 + i**6/220 - i**5/30 - i**4/44 + 4*i**3/33 - 2*i**2 + 2*i. Determine k so that o(k) = 0.
-1, 4/7, 1
Let s(x) = -3*x**2 - 2. Let o(h) = 51*h**2 + 105*h + 144. Let d(f) = o(f) + 18*s(f). Suppose d(r) = 0. Calculate r.
-1, 36
Let h(j) be the third derivative of -j**6/1260 + j**5/210 - 17*j**3/6 - 11*j**2. Let i(u) be the first derivative of h(u). Factor i(l).
-2*l*(l - 2)/7
Let a(f) be the second derivative of 3*f**5/10 + 17*f**4/24 + f**3/6 - 3*f**2/4 - 120*f. Factor a(y).
(y + 1)*(3*y - 1)*(4*y + 3)/2
Let w(c) be the third derivative of -2*c**2 + 0*c + 1/12*c**4 + 1/6*c**3 + 0 + 1/30*c**5 + 1/180*c**6. Let n(j) be the first derivative of w(j). Factor n(t).
2*(t + 1)**2
Let z = -7 + 39. Suppose 2 - z*m + 4*m**2 - 8 + 70 = 0. Calculate m.
4
Determine f, given that -1/2*f**4 + 7*f**3 - 16 + 33/2*f**2 - 7*f = 0.
-2, -1, 1, 16
Let m(k) = -2*k**2 + 222*k - 3638. Let x be m(20). Factor 3/2*s**4 - 15/2*s**x - 9/2*s - 3/2*s**3 + 0.
3*s*(s - 3)*(s + 1)**2/2
Let f(n) be the third derivative of n**7/3780 - n**6/270 + n**5/60 + n**4/3 - 19*n**2. Let t(b) be the second derivative of f(b). Solve t(l) = 0.
1, 3
Let f(j) be the third derivative of j**7/140 + j**6/40 - j**5/10 - j**4/8 + 3*j**3/4 + 11*j**2. Factor f(v).
3*(v - 1)**2*(v + 1)*(v + 3)/2
Let v(l) = 11*l**2 - 68*l + 284. Let x(j) = -4*j**2 + 23*j - 94. Let m(p) = 3*v(p) + 8*x(p). What is i in m(i) = 0?
10
Factor 5*m**5 - 5*m**3 - 983*m**4 + 983*m**4.
5*m**3*(m - 1)*(m + 1)
Suppose 213*t = 195*t. Find n, given that -4/7*n**2 + t - 12/7*n**3 + 0*n = 0.
-1/3, 0
Let i(m) be the first derivative of -m**6/12 + 3*m**5/5 - 3*m**4/2 + 5*m**3/3 - 3*m**2/4 + 9. Find z, given that i(z) = 0.
0, 1, 3
Let u be (3/12)/(4/(-16)). Let r be (0 - 15/(-6)) + u. Find l, given that -r + 1/2*l**2 - l = 0.
-1, 3
Let z = 405 + -402. Solve 0*r + 2/7*r**2 + 2/7*r**4 - 4/7*r**z + 0 = 0 for r.
0, 1
Let l = 181 - 178. Let v(r) be the third derivative of 5/3*r**4 + 0*r - 7/5*r**5 - 8/9*r**l + 0 + 3*r**2 + 49/180*r**6. Factor v(n).
2*(n - 2)*(7*n - 2)**2/3
Let g = -60 + 176/3. Let i = g + 2. Find q such that 4/3*q - 2 + i*q**2 = 0.
-3, 1
Let t = -1541/3 + 514. Let g(b) be the third derivative of -t*b**4 - 3*b**2 - 1/60*b**5 - 8/3*b**3 + 0*b + 0. Determine x, given that g(x) = 0.
-4
Suppose -2*b = -2*y + 4, -5*y - b - 3*b + 19 = 0. Factor 4*i**2 + 1/2*i - 1/2*i**y - 4.
-(i - 8)*(i - 1)*(i + 1)/2
Let g(d) = d**2 + 10*d - 6. Let u be g(-11). What is n in 5*n**3 + 15*n**u - 809 - 5*n**2 + 809 + 25*n**4 = 0?
-1, 0, 1/3
Let f be 53/3 + -80 + 63. Solve -8/9*b**4 - 2/9*b**5 - f*b**3 + 0 + 8/9*b + 8/9*b**2 = 0.
-2, -1, 0, 1
Let h = -14 - -19. Suppose 9 + 1 = h*a. Solve 16*f + 8 - f + 6*f**a - 2*f**2 - 3*f = 0 for f.
-2, -1
Suppose -74/7*a - 45/7*a**3 - 1/7*a**5 + 85/7*a**2 + 24/7 + 11/7*a**4 = 0. Calculate a.
1, 2, 3, 4
Let -2/9*d**2 + 8/9 - 2/9*d**3 + 8/9*d = 0. Calculate d.
-2, -1, 2
Let b be -16 + (-100)/36 + (-4)/18. Let d = b - -22. Determine g, given that -4/13*g**2 - 2/13*g**d - 2/13*g + 0 = 0.
-1, 0
Let v(o) = 77 + 329*o + 527*o**2 + 225*o**2 + 176*o - 85*o. Let b(d) = -251*d**2 - 140*d - 26. Let i(t) = 17*b(t) + 6*v(t). Determine f, given that i(f) = 0.
-2/7
Suppose 2*i + 3*r - 9 = 0, 2*i = 6*i + r - 23. Let l(u) be the first derivative of 0*u**4 + 1/9*u**i + 0*u**2 + 0*u**3 - 2/15*u**5 + 0*u + 2. Factor l(b).
2*b**4*(b - 1)/3
Let t(a) be the second derivative of -3*a**5/20 - 7*a**4/2 + 2*a**3 + 84*a**2 + 4*a + 95. Factor t(k).
-3*(k - 2)*(k + 2)*(k + 14)
Let c(p) = -26*p**3 - 67*p**2 + 521*p - 713. Let a(k) = 8*k**3 + 22*k**2 - 174*k + 238. Let w(m) = -7*a(m) - 2*c(m). Suppose w(j) = 0. Calculate j.
-10, 2, 3
Let g(f) be the third derivative of 0 - 8*f**2 + 1/280*f**6 + 0*f + 0*f**5 + 0*f**3 + 0*f**4. What is h in g(h) = 0?
0
Let s(h) be the third derivative of 1/7*h**7 - 9*h**2 - 1/16*h**8 - 4/7*h**3 + 101/280*h**6 - 13/14*h**4 + 0 - 31/70*h**5 + 0*h. Determine k so that s(k) = 0.
-1, -2/7, 1, 2
Let c(m) be the first derivative of -m**4/4 - m**3 - 3*m**2/2 + 15. Let l be c(-2). Determine n so that -4/3*n**l + 4/3 - 2/3*n + 2