
-2, -1, 1
Let w(x) be the first derivative of 27/10*x**2 + 1/20*x**4 - 27/5*x - 3/5*x**3 - 68. Factor w(k).
(k - 3)**3/5
Let p be (0 + -2)*(-1 - (-7)/(-2)). Let d(q) = q**2 - 9*q + 3. Let m be d(p). Let -22*c**2 + m*c**3 + 7*c + 2*c + 3 + 31*c**2 = 0. Calculate c.
-1
Factor -2592000 + 31860*u**2 + 3/4*u**4 - 1231200*u - 537/2*u**3.
3*(u - 120)**3*(u + 2)/4
Let t(n) = 2*n**3 - 19*n**2 + 9*n + 4. Let r be t(9). Let q be 4 + 3 + (r - 9). Find h such that 17*h + 6*h**3 - 2*h**4 + 0*h**q + 2*h**2 - 41*h + 18*h = 0.
-1, 0, 1, 3
Let s(g) be the first derivative of -5*g**3/3 + 145*g**2/2 - 264*g + 197. Let t(j) = -20*j**2 + 580*j - 1055. Let a(l) = -25*s(l) + 6*t(l). Factor a(m).
5*(m - 27)*(m - 2)
Let p(m) be the third derivative of -m**8/2352 + m**7/147 - m**6/40 - 2*m**5/21 + 25*m**4/42 - 6*m**2 + 35. Let p(h) = 0. Calculate h.
-2, 0, 2, 5
Suppose -285*i**2 + 78*i - 118*i**2 - 1 - 45*i**3 + 33*i**2 - 33*i**3 + 374*i**4 - 3 = 0. Calculate i.
-1, 1/11, 2/17, 1
Let d = 178 + -90. Suppose -30 - d*k + 2 + 540*k**3 - 68*k**2 - 548*k**3 = 0. What is k?
-7, -1, -1/2
Let z(x) be the third derivative of 1/1470*x**7 + 0 + 1/420*x**6 - 38*x**2 + 0*x - 1/84*x**4 - 1/420*x**5 + 0*x**3. Suppose z(c) = 0. What is c?
-2, -1, 0, 1
Let b(c) = 44*c - 279. Let t be b(24). Let x = t + -777. Factor x + 3/2*z**3 - 1/3*z + 7/6*z**2.
z*(z + 1)*(9*z - 2)/6
Let a = -4988 - -4988. Let n(k) be the third derivative of a - 1/54*k**4 + 0*k + 1/270*k**5 - 1/9*k**3 - 14*k**2. Factor n(h).
2*(h - 3)*(h + 1)/9
Factor 96*j**2 + 22 - 45*j + 4*j**3 - 6 + 88 - 159*j.
4*(j - 1)**2*(j + 26)
Suppose 0 = -3*b + 6*b, -3*r = 4*b. Let d(a) be the second derivative of 0 + 8*a - 1/3*a**3 - 1/3*a**4 - 1/10*a**5 + r*a**2. Factor d(s).
-2*s*(s + 1)**2
Let -5*j + 16*j - 95*j**3 - 11*j - 33*j**2 + 50*j**3 - 6*j = 0. Calculate j.
-2/5, -1/3, 0
Let d(h) be the first derivative of -h**5/5 + 3*h**4 - 19*h**3/3 - 6*h**2 + 20*h + 861. Let d(l) = 0. Calculate l.
-1, 1, 2, 10
Let a be (3/(-4))/(49/(-196)). Solve 24*k - 21*k**3 + 17*k**2 - 3*k**a + 28 + 4*k**4 - 49*k**2 + 0*k**4 = 0 for k.
-1, 1, 7
Find d, given that 0 + 174/7*d**3 + 0*d + 176/7*d**2 - 2/7*d**4 = 0.
-1, 0, 88
Let b(s) = -s**2 + 22*s + 1. Let m(z) = -3*z**3 + 32*z**2 - 95*z - 86. Let p(w) = 2*b(w) + m(w). Let p(a) = 0. Calculate a.
-1, 4, 7
Let r(t) be the first derivative of -237 + 12*t**3 + 54*t + 87/2*t**2 + 3/4*t**4. Factor r(f).
3*(f + 1)*(f + 2)*(f + 9)
Let l(h) = -h**3 + 2*h**2 - h + 5. Let a(c) = -23*c**3 + 68*c**2 + 1055*c + 145. Let n(x) = 2*a(x) + 6*l(x). Factor n(d).
-4*(d - 8)*(d + 5)*(13*d + 2)
Let c be 150/10 + -8 - 4. Suppose c*m + 5*f = m + 19, 2*m = -3*f + 13. Suppose -14/3*b**m - 4/3*b**3 + 40/3*b + 2/3*b**4 - 8 = 0. Calculate b.
-3, 1, 2
Suppose -2*s - 2*s + 5*i + 6 = 0, 0 = 2*s - i - 6. Solve 204*c**3 - 1344*c**5 - 18*c - 1320*c**3 + 237*c**2 + 1230*c**4 + 930*c**s = 0 for c.
0, 1/4, 6/7
Let j(p) = -50*p**4 + 260*p**3 - 72*p**2 - 14*p + 14. Let l(n) = -2*n**4 + n**3 - 2*n**2 - n + 1. Let x(o) = -2*j(o) + 28*l(o). Factor x(m).
4*m**2*(m - 11)*(11*m - 2)
Let y(b) be the second derivative of -4*b**2 + 0 - 2/5*b**3 - b + 1/10*b**4 - 1/100*b**5. Let w(x) be the first derivative of y(x). Solve w(r) = 0 for r.
2
Let x = 1016081/812884 + 6/203221. Let 0 + 1/2*i**2 - x*i**3 + 2*i + 1/4*i**4 = 0. What is i?
-1, 0, 2, 4
Let r(u) be the third derivative of -u**6/660 - 13*u**5/330 - u**4/11 - 583*u**2. Factor r(p).
-2*p*(p + 1)*(p + 12)/11
Let h(a) be the second derivative of 1/48*a**4 + 2*a - 1/80*a**5 + 1/24*a**3 - 52 - 1/8*a**2. Let h(f) = 0. Calculate f.
-1, 1
Let x(r) be the second derivative of -r**7/3780 - r**6/540 - r**5/180 + 7*r**4/6 - r**2/2 + 42*r. Let d(u) be the third derivative of x(u). Factor d(w).
-2*(w + 1)**2/3
Factor -9/5*u**2 - 407/5*u - 18.
-(u + 45)*(9*u + 2)/5
Factor 1437/4*j**2 + 73/4*j**3 + 1225/2 + 3815/4*j + 1/4*j**4.
(j + 1)*(j + 2)*(j + 35)**2/4
Let u(i) be the second derivative of i**5/5 + 121*i**4/3 + 475*i**3/2 + 531*i**2 + 5782*i. Let u(h) = 0. What is h?
-118, -3/2
Let q(j) = -7*j**4 - 2*j**3 - 15*j**2 + 2*j + 4. Let m(x) = -x**4 - x**2. Suppose -7*i = 37 - 23. Let o(p) = i*q(p) + 18*m(p). Factor o(a).
-4*(a - 2)*(a - 1)*(a + 1)**2
Let h(c) be the third derivative of c**7/630 + c**6/90 - 73*c**5/180 - 55*c**4/18 + 16*c**3 + 29*c**2 + 3*c + 24. Determine g, given that h(g) = 0.
-9, -4, 1, 8
Let i(j) be the third derivative of 0 - 23/120*j**4 - 3*j**2 + 0*j - 7/15*j**3 - 1/30*j**5 - 1/600*j**6. Solve i(r) = 0.
-7, -2, -1
Let z(h) be the second derivative of -h**4/78 - 32*h**3/39 - 112*h**2/13 - 1156*h. Factor z(b).
-2*(b + 4)*(b + 28)/13
Let y = -947 - -1072. Suppose y*n = 123*n - 6, -n + 12 = 5*j. Factor -18/23*u - 2/23 - 48/23*u**2 - 32/23*u**j.
-2*(u + 1)*(4*u + 1)**2/23
Suppose 13 - 205 = -12*t. Factor 8 - 46*y + 93*y + t*y**3 + 2*y**4 + 16 + 9*y + 46*y**2.
2*(y + 1)*(y + 2)**2*(y + 3)
Let b(j) be the second derivative of j**4/18 - 79*j**3/9 - 65*j - 10. Factor b(q).
2*q*(q - 79)/3
Factor 810 - 5/2*z**2 + 385/2*z.
-5*(z - 81)*(z + 4)/2
Let o = -21 - -31. Suppose -o*i = -i - 36. Factor -4*z - 2*z - i*z**2 + z**2 + 6 + 3.
-3*(z - 1)*(z + 3)
Let t(u) = -754*u**3 - 2*u**2 + 5*u + 7. Let j be t(-1). Let g = j - 751. Factor 1/3*z**2 + 0*z - 1/6*z**g + 0.
-z**2*(z - 2)/6
Let b(z) be the first derivative of 1/4*z**4 + 24 - 1/6*z**6 + 2*z**3 + 0*z**2 - 6/5*z**5 + 0*z. Factor b(k).
-k**2*(k - 1)*(k + 1)*(k + 6)
Let a(g) be the second derivative of 1/6*g**4 - 41*g + 2 - 1/40*g**5 - 5/12*g**3 + 1/2*g**2. Factor a(v).
-(v - 2)*(v - 1)**2/2
Let o be (0 - -2*123) + 18/9. Determine v so that 244*v**2 - 544*v + 160*v - o*v**2 - 9216 = 0.
-48
Let b(d) be the first derivative of 3/10*d**5 - 15/8*d**4 + 0*d + 2*d**3 + 1 + 0*d**2. What is z in b(z) = 0?
0, 1, 4
Let u(b) be the second derivative of b**5/50 - 79*b**4/30 + 1247*b**3/15 + 12943*b**2/5 + b - 791. Factor u(z).
2*(z - 43)**2*(z + 7)/5
Let d(o) be the first derivative of -o**3/3 - o**2/2 + 5*o - 9. Let s be d(0). Solve -32*y**3 + 20*y**4 + 16*y**2 + 3*y**5 + 0*y**s - 3*y**5 - 4*y**5 = 0 for y.
0, 1, 2
Determine w so that -180 + 1/2*w**2 - 13*w = 0.
-10, 36
Let 13/3*b**2 - 11*b - 15 + 1/3*b**3 = 0. What is b?
-15, -1, 3
Let a = 405875 - 405873. Determine m, given that 1/5*m**a + 289/5 - 34/5*m = 0.
17
Let x(b) be the second derivative of b**5/4 - 25*b**4/12 - 70*b**3/3 + 80*b**2 + 5*b - 40. Factor x(k).
5*(k - 8)*(k - 1)*(k + 4)
Let f be (-36)/(-120) + 3377/10. Factor -226*s**2 - 5*s**4 - 316 + 149*s**2 + 38*s - 513*s**2 - 105*s**3 - f*s + 1316.
-5*(s - 1)*(s + 2)*(s + 10)**2
Suppose 3*r + h - 34 = -21, 0 = -2*h + 8. Factor 3*a + 12*a**3 - 10*a**r - 18*a**2 + 18 - 5*a**3.
-3*(a - 1)*(a + 1)*(a + 6)
Let q(r) be the third derivative of -r**7/840 - r**6/160 + 7*r**5/16 - 325*r**4/96 + 1070*r**2. Determine h so that q(h) = 0.
-13, 0, 5
Let k be (2260/100)/(3/(-75)). Let q = k + 1133/2. Factor q*t**2 + 12*t + 24.
3*(t + 4)**2/2
Suppose 0 = -4*x - 2*z, 0 = -2*x + 7*x + 3*z - 2. Let l be 3 + (-4 - x) + 3. Let -2*w**2 + w**3 + 15*w**l + 2*w**3 - 16*w**4 = 0. Calculate w.
0, 1, 2
Factor -898*p**2 + 320*p**2 + 5*p**3 - 652*p**2.
5*p**2*(p - 246)
Let 24*p**5 + 498428*p**2 + 492796*p**3 - 492800*p + 6619*p**4 - 495616 - 20*p**5 - 9431*p**4 = 0. Calculate p.
-1, 1, 352
Let l(o) be the first derivative of 5/3*o**3 - 7/8*o**2 + 54 - 1/2*o - 11/16*o**4. Solve l(n) = 0.
-2/11, 1
Suppose -5*n - w + 9 = -3*n, 0 = n - 3*w + 13. Let x(a) = 5*a**3 - 4*a**2 + 2*a + 1. Let s be x(n). Factor 14*f**2 - s*f**2 + 21*f**2 + 2 + 6*f + 2*f**3.
2*(f + 1)**3
Let g = -504800/13 - -38832. Solve -8/13*m**4 + g*m**2 + 4/13*m**3 - 2/13*m - 8/13 - 2/13*m**5 = 0.
-4, -1, 1
Let w = -227470/3 - -75827. What is n in 2/3*n**4 + 0 + 12*n - 4*n**2 + 1/3*n**5 - w*n**3 = 0?
-3, 0, 2
Suppose -2*v + 59 + 197 = -5*x, -3*v + 346 = 2*x. Let -77*h**3 - 8 - 312*h + 101*h**3 + v*h**2 + 97 + h**4 + 80 = 0. What is h?
-13, 1
Suppose -1302*f + 2655*f - 13461 = -3134*f. Factor -2401/6 + 97/6*j**2 + 2303/6*j + 1/6*j**f.
(j - 1)*(j + 49)**2/6
Let l(q) be the third derivative of q**6/40 - 201*q**5/20 + 195*q**4 - 1544*q**3 + 37*q**2 - 37*q + 1. Solve l(i) = 0 for i.
4, 193
Let g(l) be the second derivative of -l**4/48 + 89*l**3/24 - 87*l**2/4 - 1549*l - 2. Factor g(i).
-(i - 87)*(i - 2)/4
Let v be (-1)/(-1) - (-13 - -12