k + 3)*(k + 4)/2
Suppose 5*l + v = 1, -6*l + 4*v - 4 = -9*l. Suppose 94*q - 85*q = l. Determine n so that 24/5*n + 3/5*n**2 + q = 0.
-8, 0
Let u be (-1 - 1) + -8 + -4*(51 + -54). Factor -10 - 48/5*b + 2/5*b**u.
2*(b - 25)*(b + 1)/5
Suppose -5*p + 1 = 11. Let t be (-3 - p)/(-1) + -1 + 3. Factor -n**3 + 8*n + 2*n**4 - 7*n**3 - 8 + 0*n**t + 6*n**2.
2*(n - 2)**2*(n - 1)*(n + 1)
Let t = -179944 + 1619510/9. What is s in 0 - 2/9*s**4 + t*s**3 + 0*s**2 + 0*s = 0?
0, 7
Suppose 3*c = 47*c + 17468. Let k = c - -399. Factor 0*w - 147/4*w**k + 3.
-3*(7*w - 2)*(7*w + 2)/4
Let r(o) be the first derivative of -o**5/12 - o**4/16 + 2*o**3/9 - 729. Let r(m) = 0. What is m?
-8/5, 0, 1
Let t(c) be the second derivative of c**7/21 + 32*c**6/15 + 9*c**5 + 44*c**4/3 + 29*c**3/3 + 742*c. Factor t(p).
2*p*(p + 1)**3*(p + 29)
Let h(o) be the second derivative of o**7/42 - 4*o**6/15 - 13*o**5/20 + 8*o**4/3 + 6*o**3 + 1046*o. Suppose h(x) = 0. Calculate x.
-2, -1, 0, 2, 9
Suppose -4 = -7*f - 382. Let w be -2 + f/(-19) + 7 + -7. Factor 24/19*t + 2/19*t**3 + w + 12/19*t**2.
2*(t + 2)**3/19
Let v = 9008 - 8989. Let u(k) be the third derivative of 1/20*k**5 + 1/8*k**4 - 1/2*k**3 + 0*k + v*k**2 - 1/40*k**6 + 0. Let u(y) = 0. Calculate y.
-1, 1
Let w(h) be the third derivative of h**5/300 - 19*h**4/30 - 79*h**3/10 - 9*h**2 + 3*h - 56. Determine n, given that w(n) = 0.
-3, 79
Let f = 217 + -201. Let g(c) = 10*c**2 - 398*c. Let r(t) = -3*t**2 + 132*t. Let k(u) = f*r(u) + 5*g(u). Factor k(w).
2*w*(w + 61)
Let d(l) be the first derivative of l**9/13608 + l**8/1512 + l**7/1260 - l**6/180 - 59*l**3/3 - 16. Let a(c) be the third derivative of d(c). Factor a(n).
2*n**2*(n - 1)*(n + 3)**2/9
Let r(n) = -17588*n + 263839. Let f be r(15). Let f*s - 1/4*s**2 - 361 = 0. Calculate s.
38
Factor 4*a**5 + 3633430*a**4 - 2120*a**2 - 565 - 752*a**3 - 2068*a - 3633446*a**4 - 115.
4*(a - 17)*(a + 1)**3*(a + 10)
Let g(m) = -m**3 + 19*m**2 - 15*m - 52. Let i be g(18). Let y be (-10)/(-45) + (-50)/(-18). Factor 0 - 4/3*o - 2/3*o**i + 2/3*o**y.
2*o*(o - 2)*(o + 1)/3
Let d be (780/(-48) + 16)*-8. Let w(b) be the third derivative of 20*b**d + 1/30*b**5 + 0*b - b**4 + 12*b**3 + 0. Let w(j) = 0. What is j?
6
Let r be 6 - 135/21 - (-51)/21. Factor -197*t**2 + 8*t**4 + 193*t**2 - 4*t**4 + r*t**5 - 2*t.
2*t*(t - 1)*(t + 1)**3
Suppose -2/9*o**4 + 148/9*o - 8*o**3 + 0 + 26/3*o**2 = 0. Calculate o.
-37, -1, 0, 2
Let c = 285 - 301. Let g be (13 + (-23 - 8))/(30/c). Find l such that -32/5 + 40*l**2 - 48/5*l + 28/5*l**5 - g*l**4 - 20*l**3 = 0.
-2, -2/7, 1, 2
Let p(b) = 4*b - 27. Let i be p(5). Let x(m) = m**3 + 6*m**2 - 9*m + 1. Let a be x(i). Factor -a*u + 16 - 5*u + 351*u**2 - 347*u**2.
4*(u - 4)*(u - 1)
Let s = 449 + 625. Let z = -1074 + s. Factor -3/2*p - 15/4*p**2 - 9/4*p**3 + z + 3/4*p**5 + 3/4*p**4.
3*p*(p - 2)*(p + 1)**3/4
Factor -119*w**2 + 180*w + 5*w**4 + 168*w**2 + 70*w**3 - 540 + 236*w**2.
5*(w - 1)*(w + 3)*(w + 6)**2
What is i in 248/7 - 2/7*i**2 + 54/7*i = 0?
-4, 31
Let d(z) be the second derivative of -5*z**4/36 - 95*z**3/3 + 575*z**2/6 - 227*z. Solve d(p) = 0.
-115, 1
Let n be 130/14 - (37 + (-114 - -86)). Factor -2*f**3 + 20/7 - n*f**4 - 58/7*f + 54/7*f**2.
-2*(f - 1)**3*(f + 10)/7
Factor 64/15*y - 28/15*y**2 + 2/15*y**3 + 256/15.
2*(y - 8)**2*(y + 2)/15
Let r(p) be the first derivative of -23 - 20*p**4 + 85/2*p**2 + 8*p**5 - 5/6*p**6 - 50*p + 10/3*p**3. Find f such that r(f) = 0.
-1, 1, 2, 5
Let h(n) be the first derivative of 4*n**5/5 - 13*n**4 + 68*n**3 - 134*n**2 + 112*n - 2211. Determine l so that h(l) = 0.
1, 4, 7
Let j(t) be the third derivative of -t**5/75 + 173*t**4/5 - 179574*t**3/5 + 1645*t**2. Determine p, given that j(p) = 0.
519
Factor 1/2*m**2 + 1525225/2 - 1235*m.
(m - 1235)**2/2
Let w(x) = -102*x**2 + 1675*x - 410. Let c(u) = -715*u**2 + 11730*u - 2870. Let k(y) = 2*c(y) - 15*w(y). Factor k(f).
5*(4*f - 1)*(5*f - 82)
Suppose -10*s = -63 + 23. Factor -11*q**s - 15*q**4 + 42*q**4 - 13*q**4 - 9*q**3 + 12*q.
3*q*(q - 2)**2*(q + 1)
Factor 14010*j + 19*j**4 + 3*j**5 - 38*j**3 + 14002*j - 28004*j - 5*j**5 + 20*j**2 - 7.
-(j - 7)*(j - 1)**3*(2*j + 1)
Let n be (23574/(-8))/(-85 + 83). Let j = n - 1473. Factor 0 + j*m**5 - 3/4*m**2 + 0*m**3 + 3/4*m**4 - 3/8*m.
3*m*(m - 1)*(m + 1)**3/8
Suppose -2*v + 2 = 0, -1 + 36 = 13*u + v - 18. Factor -2/15*k**5 + 0 - 2*k**3 + 6/5*k**2 + 0*k + 14/15*k**u.
-2*k**2*(k - 3)**2*(k - 1)/15
Let z(w) be the second derivative of 5*w**7/42 + w**6 + w**5 - 5*w**4/2 - 25*w**3/6 + 3*w + 1084. Factor z(f).
5*f*(f - 1)*(f + 1)**2*(f + 5)
Let i(r) be the third derivative of 2*r**2 + 20*r + 1/1512*r**8 + 0*r**4 + 0 + 0*r**5 + 0*r**3 - 23/540*r**6 - 22/945*r**7. Determine j so that i(j) = 0.
-1, 0, 23
Let h(w) be the first derivative of -w**4/4 + 14*w**3 + 45*w**2 - 85*w + 422. Let r be h(44). Factor 5 + 6/5*c**2 - 8*c + 1/5*c**4 + 8/5*c**r.
(c - 1)**2*(c + 5)**2/5
Factor 584/5 + 2/5*w**2 - 296/5*w.
2*(w - 146)*(w - 2)/5
Let w(y) be the first derivative of 9/32*y**4 - 3/20*y**5 - 25 + 0*y + y**3 - 1/16*y**6 + 3/4*y**2. Let w(r) = 0. What is r?
-2, -1, 0, 2
Let y be 7/4*((-3)/35)/((-606)/1010). Let l(g) be the second derivative of -3*g - 5*g**2 + y*g**5 - 1/6*g**6 + 0 + 5/4*g**4 - 5/6*g**3. Factor l(n).
-5*(n - 2)*(n - 1)*(n + 1)**2
Let x(i) be the first derivative of i**3/6 + 87*i**2/2 + 173*i/2 - 1502. Suppose x(b) = 0. Calculate b.
-173, -1
Suppose 7*y - 630 = 2653. Factor -790 - 377*d - 1370 + y*d + 44 - d**2.
-(d - 46)**2
Suppose 15536*v + 2*w + 24 = 15537*v, 0 = -v - w - 9. Determine m, given that -69/4*m**4 + 0*m + 15/2*m**3 + 0 + 12*m**v - 9/4*m**5 = 0.
-8, -2/3, 0, 1
Let q(u) = -3*u**2 - 831*u + 1738. Let k(r) = -4*r**2 - 821*r + 1738. Let g(v) = -4*k(v) + 5*q(v). Solve g(f) = 0 for f.
2, 869
Factor -576/5 - 156/5*j**2 - 6/5*j**3 + 120*j + 3/5*j**4.
3*(j - 6)*(j - 2)**2*(j + 8)/5
Let o be (-11)/(-7) + 24/56. Determine a, given that -a**4 + a**4 - 3258*a**5 + o*a**3 + 3256*a**5 = 0.
-1, 0, 1
Suppose 5*w + 10*w = 795. Let h = w + -5. Determine v, given that 4*v**3 - v**5 + h*v**4 - 3*v**5 - 48*v**4 = 0.
-1, 0, 1
Let j be 248/20 + -1 - 9. Suppose b + 5 = 1, 0 = -5*p - 5*b - 5. Let -12*r - 24/5*r**5 + j - 12*r**4 + 6*r**p + 15*r**2 = 0. Calculate r.
-2, 1/2
Let p be (0 + 32)*746636/15774. Factor p*g**2 + 36*g**4 + 4096/3 + 2560*g + 1064/3*g**3 + 4/3*g**5.
4*(g + 1)*(g + 2)*(g + 8)**3/3
Factor -36063*u + 3*u**3 + 36048*u + 18 - 17*u**2 + 11*u**2.
3*(u - 3)*(u - 1)*(u + 2)
Suppose -5*h - 25 = -42*x + 41*x, -5*x - 3*h + 97 = 0. Suppose 0 = 44*m - 112 - x. Find r such that -1/5*r**4 + 1/10*r**5 - 7/10*r**m + 0*r - 2/5*r**2 + 0 = 0.
-1, 0, 4
Solve -1060*k - 369*k**2 - 344*k**2 - 1065 + 718*k**2 = 0 for k.
-1, 213
Suppose 3*r + 9*x = 8*x + 14, r - 4*x = 9. Let b(c) be the first derivative of 0*c + 13 + 1/5*c**r - 5/6*c**4 - 1/3*c**2 + c**3. Factor b(l).
l*(l - 2)*(l - 1)*(3*l - 1)/3
Let i(b) be the first derivative of -b**4 - 160*b**3/3 + 54*b**2 + 40824*b - 660. Factor i(w).
-4*(w - 14)*(w + 27)**2
Let r(g) be the second derivative of g**4/48 + 161*g**3/3 + 1287*g**2/8 - 5726*g. Factor r(x).
(x + 1)*(x + 1287)/4
Let c = 2378/13 - 237761/1300. Let f(t) be the second derivative of 6*t + 0*t**2 + 0*t**3 + 0*t**4 - 1/150*t**6 + 0 + c*t**5. Factor f(l).
-l**3*(l - 3)/5
Let r(i) be the first derivative of -3*i**5/5 - 81*i**4 - 2326*i**3 + 47790*i**2 - 261075*i - 1854. Factor r(h).
-3*(h - 5)**2*(h + 59)**2
Determine j so that 13356*j + 642*j**3 + 443*j**3 - 889*j**3 + 2964*j**2 + 10584 + 4*j**4 = 0.
-21, -6, -1
Let v = 1751522/15 - 116768. Suppose 0 - 2/3*k + v*k**3 + 8/15*k**2 = 0. Calculate k.
-5, 0, 1
Let x(g) be the first derivative of g**3/3 - 747*g**2 + 558009*g + 3157. Factor x(z).
(z - 747)**2
Let h(j) be the third derivative of -j**7/3360 - 19*j**6/480 - 37*j**5/160 - 263*j**4/24 - 2*j**2 + 4*j. Let f(b) be the second derivative of h(b). Factor f(v).
-3*(v + 1)*(v + 37)/4
Factor -8*i**3 + 16*i**3 + 552*i + 0*i**3 + 441*i**2 + 19*i**3 + 180.
3*(i + 15)*(3*i + 2)**2
Let j = -8863625/7 + 1268312. Let v = j + -2076. Solve 12/7*c - 26/7*c**4 + 34/7*c**2 - v*c**3 + 15/7*c**5 - 8/7 = 0.
-1, -2/3, 2/5, 1, 2
Determine d, given that 5/3*d**3 + 7/3*d - 2/3 - 3*d**2 - 1/3*d**4 = 0.
1, 2
Let r be (-34)/(-20) + ((105/(-14))/15)/1. Find l such that 8/5*l**2 - r*l**4 + 0*l**3 + 0