
2
Let o(l) be the third derivative of -l**7/42 - 7*l**6/30 - 11*l**5/12 - 11*l**4/6 - 2*l**3 + 152*l**2 - l. Find u such that o(u) = 0.
-2, -1, -3/5
Factor 0*r**2 + 33 - 32*r + 44 + 0*r**2 + 19 + 2*r**2.
2*(r - 12)*(r - 4)
Let c = -16/47 + 269/376. Let h(v) be the first derivative of -c*v**4 + 1/2*v**3 + 0*v - 1/4*v**2 - 1 + 1/10*v**5. Factor h(k).
k*(k - 1)**3/2
Let k be -5 - -4 - (3 + 3). Let l be 4 - (1 - k/(-3))*-3. Factor 2/17*f**5 + 2/17*f**3 + 0*f - 4/17*f**4 + 0*f**2 + l.
2*f**3*(f - 1)**2/17
Suppose 0 = -3*y + y - 2. Let l(c) = c**3 - c**2. Let r(w) = 3*w**3 - 18*w**2 + 15*w. Let d(z) = y*r(z) + 6*l(z). Determine f so that d(f) = 0.
-5, 0, 1
Let i(a) be the third derivative of 8*a**2 + 0 + 0*a - 1/390*a**5 + 1/13*a**4 - 12/13*a**3. Factor i(n).
-2*(n - 6)**2/13
Let c(a) be the first derivative of 7/11*a**2 + 10/11*a**3 - 6 + 8/55*a**5 + 2/11*a + 13/22*a**4. What is q in c(q) = 0?
-1, -1/4
Let j(u) = 25*u**2 + 11015*u - 22680. Let t(w) = -w**2 - 408*w + 840. Let y(r) = -2*j(r) - 55*t(r). Factor y(f).
5*(f - 2)*(f + 84)
Let n(i) be the third derivative of -i**6/540 + 11*i**5/135 - 35*i**4/27 + 200*i**3/27 - 2*i**2 - 28. Find w, given that n(w) = 0.
2, 10
Let h(v) = 6*v**4 + 6*v**3 + 4*v**2 + 4*v + 2. Let p(l) = 2*l**4 - l**2 + l + 1. Let g(k) = 2*h(k) - 4*p(k). Suppose g(b) = 0. Calculate b.
-1, 0
Let y(c) be the first derivative of 8 + 1/2*c**3 - c**2 + 1/4*c**4 - 1/10*c**5 - 2*c. Factor y(d).
-(d - 2)**2*(d + 1)**2/2
Factor 12 + 40*w + 10*w**3 + 5*w**3 + 8 + 25*w**2 + w**3 - 11*w**3.
5*(w + 1)*(w + 2)**2
Let u(t) be the third derivative of 2/75*t**5 + 0*t**3 + 0*t**4 + 1/300*t**6 - 12*t**2 + 0 + 0*t. Factor u(k).
2*k**2*(k + 4)/5
Let j(s) be the first derivative of -2*s**5/5 + 15*s**4/2 - 26*s**3 + 37*s**2 - 24*s - 349. Factor j(o).
-2*(o - 12)*(o - 1)**3
Suppose 26*l - 3 - 101 = 0. Let b(w) be the first derivative of -1 + 0*w + 3/4*w**l + 2/3*w**3 + 1/5*w**5 + 0*w**2. Factor b(s).
s**2*(s + 1)*(s + 2)
Let q = 18 + -8. Suppose 0 = -0*l + 3*l - 3*j, 4*l = -j + q. Suppose -2*o**2 - l*o**2 - 15*o - 8*o**2 - 6 + 42*o = 0. Calculate o.
1/4, 2
Suppose -12*c = -41*c. Let l(k) be the first derivative of c*k**2 + 4/3*k**3 - k**4 + 4 + 0*k. Determine s so that l(s) = 0.
0, 1
Let w(l) be the third derivative of l**6/30 + 7*l**5/15 - 7*l**4/2 - 18*l**3 - 172*l**2. Factor w(b).
4*(b - 3)*(b + 1)*(b + 9)
Let x(p) be the third derivative of -p**8/9408 - p**7/2520 - p**6/2520 - 7*p**4/12 + 21*p**2. Let z(k) be the second derivative of x(k). Solve z(s) = 0 for s.
-1, -2/5, 0
Suppose 3*j = 14 - 5. Determine g so that 23*g**2 + 11 - 10*g**4 - 11 + 5*g**5 + 17*g**2 - 15*g**j - 20*g = 0.
-2, 0, 1, 2
Let a = 181 - 181. Let b(t) be the third derivative of -t**2 - 1/540*t**6 + a*t + 0*t**3 + 1/945*t**7 + 0 + 0*t**5 + 0*t**4. Factor b(d).
2*d**3*(d - 1)/9
Let q(y) = -780*y + 780. Let p be q(1). Factor p*t - 4/3*t**2 + 2/3*t**3 + 0.
2*t**2*(t - 2)/3
Let f(m) be the first derivative of 2*m**3/33 - 136*m**2/11 + 9248*m/11 + 111. Suppose f(g) = 0. What is g?
68
Suppose 3*t - 10 - 5 = 0. Let m(h) = -2*h**2 + 3*h. Let q(r) = 0*r**2 + 3*r**2 - 4*r**2 + 2*r**2. Let k(z) = t*q(z) + m(z). Factor k(o).
3*o*(o + 1)
Let y(c) be the third derivative of c**7/315 - c**6/36 + 4*c**5/45 - c**4/9 - 7*c**2. Factor y(h).
2*h*(h - 2)**2*(h - 1)/3
Let k(s) be the second derivative of 11*s**3 - 363/2*s**2 - 1/4*s**4 - 39*s + 0. Factor k(z).
-3*(z - 11)**2
Factor 15*r**2 - 123*r**2 + 39*r**2 - 64 + 48*r**3 - 79*r**2 + r**4 + 168*r - 5*r**4.
-4*(r - 8)*(r - 2)*(r - 1)**2
Let m(j) = 2*j**2. Let y(p) = 729*p**4 - 1944*p**3 + 1102*p**2 - 224*p + 16. Let o = 19 - 41. Let g(z) = o*m(z) + 2*y(z). Factor g(b).
2*(b - 2)*(9*b - 2)**3
Let n(h) = h**2 - 4*h - 1. Let r = -4 - -9. Let s be n(r). Factor 2*d**3 + s*d - 3*d**3 + d**2 - d - d.
-d*(d - 2)*(d + 1)
Let u(k) = -5*k**3 + 45*k**2 - 40*k. Let v(b) = b**2 - b. Let o(q) = -u(q) - 5*v(q). Let o(y) = 0. Calculate y.
0, 1, 9
Solve 385*z - 747*z - 21*z**2 + 377*z + 18 - 15*z**3 + 3*z**4 = 0 for z.
-1, 1, 6
Let g(k) be the first derivative of -k**6/30 - 3*k**5/25 - k**4/10 + 2*k**3/15 + 3*k**2/10 + k/5 - 209. Find n, given that g(n) = 0.
-1, 1
Let a = 31367 - 31364. Factor 16/19*s + 88/19*s**2 + 0 + 18/19*s**4 + 4*s**a.
2*s*(s + 2)**2*(9*s + 2)/19
Let s(f) = 3*f + 6 - 3*f - 2*f**2 + f**2. Let q be s(-2). Let -1/3 - 3*g**q + 2*g = 0. Calculate g.
1/3
Let i(p) be the second derivative of p**6/3 - 13*p**5/40 - 3*p**4/4 + 13*p**3/12 - p**2/2 - p - 8. Find d such that i(d) = 0.
-1, 1/4, 2/5, 1
Let 2*a**4 - 3*a**4 + 9*a**3 + 4*a**2 - 5*a**3 - 2*a**4 = 0. What is a?
-2/3, 0, 2
Let d(m) be the third derivative of 0 - 14*m**2 - 1/60*m**5 - 1/12*m**4 - 1/6*m**3 + 0*m. Factor d(s).
-(s + 1)**2
Let h(w) be the second derivative of w**4/27 + 127*w**3/54 - 16*w**2/9 + 17*w + 2. Find m such that h(m) = 0.
-32, 1/4
Let n = -39 - -49. Find w such that 4 - n*w**3 + 18*w**2 - 8*w + w + 2*w**4 - 3*w - 4*w = 0.
1, 2
Factor -138/7*z + 1587/7 + 3/7*z**2.
3*(z - 23)**2/7
Let b(q) be the third derivative of 0*q**4 + 0*q**5 + 1/12*q**6 + 0 - 5/336*q**8 - 1/42*q**7 + 4*q**2 + 0*q**3 + 0*q. Determine r so that b(r) = 0.
-2, 0, 1
Let y(q) be the first derivative of q**6/60 + q**5/8 + q**4/8 - 3*q**3/4 - 10*q - 4. Let l(z) be the first derivative of y(z). Suppose l(v) = 0. What is v?
-3, 0, 1
Suppose 4*x = 14*x + 450. Let c = 49 + x. Factor -2/3 + 4/3*k - 4/3*k**3 + 2/3*k**c + 0*k**2.
2*(k - 1)**3*(k + 1)/3
Factor -2/5*y**2 + 0 + 28/5*y.
-2*y*(y - 14)/5
Let c = -20 - -25. Let t(w) be the second derivative of -1/50*w**c - 1/5*w**2 + 1/30*w**4 + 1/15*w**3 + 4*w + 0. Solve t(d) = 0.
-1, 1
Let g(d) be the first derivative of -d**4/42 + 4*d**3/21 - 3*d**2/7 - 6*d + 9. Let t(z) be the first derivative of g(z). Determine w so that t(w) = 0.
1, 3
What is j in 2/13*j**3 + 378/13*j**2 + 500094/13 + 23814/13*j = 0?
-63
Let g = -2172 + 15210/7. Solve -2/7*y + 0 - 6/7*y**2 - g*y**3 - 2/7*y**4 = 0 for y.
-1, 0
Let k(l) be the second derivative of l**6/30 + 3*l**5/20 + l**4/12 - l**3/2 - l**2 + 76*l. Factor k(j).
(j - 1)*(j + 1)**2*(j + 2)
Let n(o) be the third derivative of o**5/12 + 65*o**4/12 + 40*o**3 + 51*o**2. Let n(t) = 0. What is t?
-24, -2
Let u(f) = -f**3 + 7*f**2 + 16*f - 12. Let v(w) = 3*w**2 + 9*w - 6. Let m(q) = -3*u(q) + 5*v(q). Suppose m(d) = 0. What is d?
-1, 1, 2
Let b(y) be the first derivative of -2*y**5/55 + y**4/22 + 10*y**3/33 + 3*y**2/11 - 82. Factor b(g).
-2*g*(g - 3)*(g + 1)**2/11
Suppose c - 78 + 72 = -w, 0 = w + 5*c - 22. Suppose 1/7*t**w + 5/7 + 6/7*t = 0. What is t?
-5, -1
Let z = 94 - 91. What is j in 3 + 21*j**3 + 35*j**2 - 41*j**2 - z = 0?
0, 2/7
Let j(h) be the second derivative of -128*h**6/5 - 576*h**5/5 - 216*h**4 - 216*h**3 - 243*h**2/2 + 160*h. Factor j(z).
-3*(4*z + 3)**4
Suppose -2*d + 6*d + 3*h = 18, 3*h = 3*d - 3. Let t(q) be the first derivative of 1/6*q**6 + 2/3*q**d - 1 + 0*q**2 - 3/4*q**4 + 0*q + 0*q**5. Factor t(o).
o**2*(o - 1)**2*(o + 2)
Suppose 8*p = 4*p - 24. Let v be (-3)/6*(1 - (-5 - p)). Factor -3/7*b**2 - 3/7*b + v.
-3*b*(b + 1)/7
Let y(z) be the second derivative of 1/36*z**4 - 14*z + 1/60*z**5 + 0*z**3 + 0*z**2 + 0. Let y(u) = 0. What is u?
-1, 0
Factor 233 - 2*u**2 - 4*u**2 + 71 - u**2 + 11*u**2 + 160*u.
4*(u + 2)*(u + 38)
Factor 389*m**2 - 18*m - 196*m**2 + 15 - 190*m**2.
3*(m - 5)*(m - 1)
Let 48/11 + 96/11*b**2 + 134/11*b + 10/11*b**3 = 0. Calculate b.
-8, -1, -3/5
Suppose 95*n - 97*n + 3*a = 6, -27 = -5*n - 3*a. Suppose -3*m + 0 - n*m**2 + 39/4*m**3 - 15/4*m**4 = 0. What is m?
-2/5, 0, 1, 2
Let p(w) be the second derivative of 3*w**5/80 - 13*w**4/16 + 5*w**3/4 + 9*w**2 - 5*w - 4. Find d, given that p(d) = 0.
-1, 2, 12
Let c be 87*(-3 + (-39)/(-9)). Factor 4*s**4 - 2*s**4 + c*s**3 - 114*s**3.
2*s**3*(s + 1)
Let l(c) = -84*c + 6052. Let s be l(72). Find f such that 0 - 4/3*f**s - 64/3*f + 21*f**3 - 80*f**2 = 0.
-1/4, 0, 8
Let k(v) = v**3 + v**2. Let a be k(0). Let f be 0*4/(-12) + a. Determine g so that -5*g**4 + 4*g**4 + f*g**3 + 7*g**3 - 3*g**2 - 2*g - 5*g**5 + 4*g**4 = 0.
-1, -2/5, 0, 1
Let t(c) be the first derivative of -147/5*c**5 + 127/3*c**3 - 16*c + 49 + 4*c**2 + 7*c**4. Let t(f) = 0. Calculate f.
-4/7, 1/3, 1
Let u(x) = -11*x + 0 + x**2 + 2 + 2*x + 10. Let b be u(8). Factor 0*i**3 - i**2 + 0 - 1/2*i**5 + i**b + 1/2*i