2, 13
Let b(x) be the third derivative of 1/30*x**6 - 1/6*x**4 + 0*x**3 + 0*x + 0*x**5 + 36*x**2 + 0. Factor b(o).
4*o*(o - 1)*(o + 1)
Let t(b) = 2*b**4 + 54*b**3 + 198*b**2 + 18*b. Let m(u) = 3*u**4 + 53*u**3 + 195*u**2 + 21*u. Let v(q) = -6*m(q) + 7*t(q). Factor v(x).
-4*x**2*(x - 18)*(x + 3)
Let n(p) = p**3 - 1. Let x(m) be the first derivative of -m**4/2 - 11*m**3/3 + 16*m**2 - 25*m - 87. Let b(h) = 12*n(h) + 4*x(h). Factor b(f).
4*(f - 7)*(f - 2)**2
Solve 1/3*l**3 + 2288/3*l + 10816/3 - 100/3*l**2 = 0.
-4, 52
Let b(n) be the first derivative of 16*n**5/5 + 13*n**4 - 4*n**3 - 80*n**2 - 112*n - 621. Factor b(y).
4*(y + 1)*(y + 2)**2*(4*y - 7)
Let m(n) be the second derivative of -7*n**6/180 + 13*n**5/30 + 11*n**4/4 + 53*n**3/9 + 73*n**2/12 + 503*n. Solve m(c) = 0 for c.
-1, 73/7
Let -19887*j**4 + 10020*j**4 + 3960*j**3 + 3*j**5 + 10068*j**4 + 18900*j**2 = 0. What is j?
-30, -7, 0
Suppose -148*y**3 - 739*y**4 - 45011 - 3744*y**2 - 10285 + 737*y**4 - 34560*y = 0. What is y?
-24, -2
Let n(u) be the third derivative of 1/26*u**4 + 0*u + 0 + 1/390*u**5 + 3/13*u**3 - 4*u**2. Factor n(b).
2*(b + 3)**2/13
Let g(y) be the second derivative of -1 + 81*y + 0*y**2 + 30*y**4 - 63/20*y**5 - 50*y**3 + 1/10*y**6. Find i, given that g(i) = 0.
0, 1, 10
Suppose m = -3*o - 3*m + 723, 1240 = 5*o - 5*m. Let u be 28/o - (-4)/42*3. Let 0*v**2 - u*v**3 + 2/5*v + 0 = 0. Calculate v.
-1, 0, 1
Let u be 314/(-120) + (-1947)/(-708). Let n(c) be the second derivative of 1/15*c**4 + 0 + 0*c**2 + 6/25*c**5 + u*c**6 - c + 0*c**3. Factor n(o).
4*o**2*(o + 1)*(5*o + 1)/5
Let r(o) = 7*o**4 - 39*o**3 + 100*o**2 + 80*o. Let u(s) = -51*s**4 + 274*s**3 - 700*s**2 - 558*s. Let w(f) = 15*r(f) + 2*u(f). Suppose w(b) = 0. What is b?
-2/3, 0, 6, 7
Suppose -3*n + 2*n + 2 = 0. Let q = -116 - -119. Suppose 5*a - 2*a**2 + a**n - 2 + 0*a**2 + a**3 - q*a**2 = 0. What is a?
1, 2
Let t(i) be the first derivative of 2*i**6/21 - 8*i**5/5 + 5*i**4 - 88*i**3/21 + 74. Determine a so that t(a) = 0.
0, 1, 2, 11
Suppose -572*b - 52 = -1147*b + 549*b. Factor -10 + 5/2*w**3 - 25/2*w**b + 20*w.
5*(w - 2)**2*(w - 1)/2
Factor 100/7 + 2/7*s**2 + 54/7*s.
2*(s + 2)*(s + 25)/7
Let q(j) = -11*j**2 - 352*j - 737. Let t(m) = -6*m**2 - 176*m - 372. Let o(c) = -4*q(c) + 7*t(c). Determine p so that o(p) = 0.
-86, -2
Let w(r) be the first derivative of -r**5 + 5*r**4/4 + 5*r**3/3 - 5*r**2/2 - 186. Determine o, given that w(o) = 0.
-1, 0, 1
Suppose -40662 = -189*o - 39906. Suppose 0*f**3 - 1/4*f + 0 + 1/2*f**o - 1/2*f**2 + 1/4*f**5 = 0. Calculate f.
-1, 0, 1
Let f(p) be the first derivative of 35 - 7/2*p + 3/2*p**2 + 1/6*p**3. Let f(i) = 0. Calculate i.
-7, 1
Let k be ((-234)/182)/(366/(-4697)). Solve -33/8*j**3 + 3/8*j**5 - 3/4*j**4 - k*j + 15*j**2 + 6 = 0.
-4, 1, 2
Let k(j) = 12 - 32*j - 12*j**2 - 5*j + 30*j + 4*j**3. Let x(b) = 12*b**3 - 36*b**2 - 20*b + 36. Let m = 3 - 11. Let u(a) = m*k(a) + 3*x(a). Factor u(r).
4*(r - 3)*(r - 1)*(r + 1)
Let y = -744/2453 + 62592/12265. Factor y*v**2 - 46/5*v**3 + 2/5*v**5 + 0 + 4*v**4 + 0*v.
2*v**2*(v - 1)**2*(v + 12)/5
Let g(u) = u**4 + 2*u**2 - u. Let x(w) = 12*w**4 + 20*w**3 + 40*w**2 - 24*w - 32. Let p(k) = -8*g(k) + x(k). Factor p(o).
4*(o - 1)*(o + 2)**3
Suppose 0 = 13*j - 2166 - 1331. Suppose -4*o + j = -3*r, -2*o - 3*r + 139 = -0*r. Solve -62*n - 249*n**4 - 252*n**2 + 245*n**4 + 386*n - o*n**3 = 0 for n.
-9, 0, 1
Determine t so that -1083*t + 619*t - 766*t - 3270 + 5*t**2 - 1730 = 0.
-4, 250
Suppose 570*p + 126 = 591*p. Let k(u) be the first derivative of -1/2*u**3 + p*u + 14 + 9/4*u**2. Factor k(s).
-3*(s - 4)*(s + 1)/2
Let u(m) be the third derivative of -289*m**7/70 + 11237*m**6/20 - 434269*m**5/20 - 25779*m**4/2 - 3042*m**3 - 2096*m**2. What is p in u(p) = 0?
-2/17, 39
Suppose -165/4 - 261/8*q + 45/8*q**3 + 3/8*q**4 + 111/8*q**2 = 0. What is q?
-11, -5, -1, 2
Let s be (1 + 5/(-1))/2. Let v(q) = q**2 - 92*q**3 - 2 - 99*q**3 + 188*q**3. Let d(h) = -4*h**3 + h**2 - h - 3. Let m(c) = s*d(c) + 3*v(c). Factor m(k).
-k*(k - 2)*(k + 1)
Let z(w) be the first derivative of w**6/60 - 9*w**5/140 + w**4/14 + w**3/42 + 81*w**2/2 - 23. Let s(l) be the second derivative of z(l). What is k in s(k) = 0?
-1/14, 1
Let w(h) be the third derivative of h**5/120 + 7*h**4/24 - 275*h**3/12 + 214*h**2 - 3*h. Find z such that w(z) = 0.
-25, 11
Suppose -2*i + 25 + 75 = 0. Let l = i + -42. Solve 3 - 4*q**2 + 9*q + 3*q**3 - 5*q**2 + l*q**2 + 10*q**2 = 0 for q.
-1
Let j = 919 - 1837/2. Let g = -732 - -732. Solve -j*h**3 + 0 - 1/2*h**2 + g*h = 0.
-1, 0
Let b(j) be the third derivative of -j**6/300 - 68*j**5/25 + 137*j**4/5 - 1648*j**3/15 + 3*j**2 + 108. Let b(c) = 0. Calculate c.
-412, 2
Factor 62*s - 1922 - 1/2*s**2.
-(s - 62)**2/2
Let t(h) be the second derivative of 2*h**6/105 - 443*h**5/70 + 23971*h**4/42 + 8864*h**3/3 + 5376*h**2 + 2359*h. Solve t(r) = 0.
-3/2, -1, 112
Let m be (-8240474)/(-214385) + ((-526)/(-106) - 5). Factor -1/5*f**3 + m - 16/5*f - 13/5*f**2.
-(f - 3)*(f + 8)**2/5
Let a(f) be the first derivative of -40*f**6/3 - 136*f**5 - 805*f**4/4 + 365*f**3/3 + 885*f**2/2 + 315*f + 3597. Find t such that a(t) = 0.
-7, -1, -3/4, 1
Solve 1/5*r**2 - 511/5*r + 102 = 0 for r.
1, 510
Factor 15*l + 1/2*l**2 - 3*l**3 - 1/2*l**4 + 0.
-l*(l - 2)*(l + 3)*(l + 5)/2
Suppose 0 = -37*r - 20*r + 24*r + 66. Solve 4/9*b**3 + 0 - 2/9*b**r - 4/9*b + 2/9*b**4 = 0 for b.
-2, -1, 0, 1
Let q(y) be the first derivative of y**6/10 + 9*y**5/20 + 60*y + 13. Let m(s) be the first derivative of q(s). Let m(i) = 0. What is i?
-3, 0
What is r in -1/2*r**2 + 36 + 71/2*r = 0?
-1, 72
Let 436 - 418 - 336 - 6*m**2 + 4*m**2 + 320*m = 0. What is m?
1, 159
Let h(i) = -i**3 - 2352*i**2 + 170433*i + 350473. Let k(f) = 588*f**2 - 42610*f - 87618. Let d(o) = -4*h(o) - 18*k(o). Let d(n) = 0. What is n?
-2, 148
Let z(s) be the third derivative of s**5/750 - s**4/15 + 17*s**3/25 - 2*s**2 - 212*s. What is r in z(r) = 0?
3, 17
Let k(p) = -2*p + 15. Suppose -11*c - 15 = -14*c. Let f be k(c). Find r such that 16*r**3 + 16*r**4 - 473*r + 473*r + 4*r**f = 0.
-2, 0
Determine v, given that -88*v - 4/3*v**2 + 0 = 0.
-66, 0
Let -4/5*a**3 + 0 + 44/5*a**2 + 0*a = 0. What is a?
0, 11
Let l(w) = -w**2 - 8*w - 7. Let u be l(-6). Suppose 15 = 5*v - u. Factor -v*k + 2*k**3 + 2*k**3 - k**2 - 5*k**2 + 2*k**5 + 6*k**4 - 2*k**3.
2*k*(k - 1)*(k + 1)**2*(k + 2)
Solve -5/2*k**2 + 1095/2*k - 545 = 0 for k.
1, 218
Factor -1250/11*o**2 + 8/11 + 0*o.
-2*(25*o - 2)*(25*o + 2)/11
Let z(j) be the third derivative of -j**6/900 - 43*j**5/450 - 37*j**4/90 + 328*j**3/45 + 3064*j**2. Factor z(m).
-2*(m - 2)*(m + 4)*(m + 41)/15
Let c(q) be the third derivative of 3*q**2 + 9/40*q**4 + 1/75*q**5 - 7/30*q**3 + 0 - 13*q. Suppose c(j) = 0. Calculate j.
-7, 1/4
Let v = 10565 - 95077/9. Let o(i) be the first derivative of 18 - 5/36*i**4 - v*i + 17/27*i**3 + 7/9*i**2. Factor o(k).
-(k - 4)*(k + 1)*(5*k - 2)/9
Let x(c) = c**2 - 39. Let y be x(-7). Suppose -109 + 95*i**3 + y*i**5 - 161*i - 51 - 290*i**2 + 75*i**4 - 319*i = 0. What is i?
-4, -1, -1/2, 2
Let h(a) be the second derivative of -a**7/357 + 2*a**6/255 + 2*a**5/85 - a**4/51 - a**3/17 - 6101*a. Find m, given that h(m) = 0.
-1, 0, 1, 3
Suppose -4*f - r + 832 = 0, 0*r = f - 4*r - 208. Let j = f - 206. Let -2*x**4 + 0 + 2/7*x + 2*x**j - 24/7*x**5 + 22/7*x**3 = 0. What is x?
-1, -1/3, -1/4, 0, 1
Factor 245*g**4 - 45141*g**3 - 1/3*g**5 + 0 + 0*g + 134689/3*g**2.
-g**2*(g - 367)**2*(g - 1)/3
Let m be (-11)/((-3)/(11 + -2)). Suppose 35 = n + m. Determine s so that 1 - 16 - 162*s**n + 184*s - 17 - 40*s = 0.
4/9
Let m(b) = -26*b**2 + b + b + 4*b + 21*b**2 + 11*b**3. Let q(g) = 23*g**3 - 10*g**2 + 13*g. Let z(d) = 13*m(d) - 6*q(d). Find k, given that z(k) = 0.
0, 1
Let a(r) be the second derivative of r**5/80 + 5*r**4/48 - 11*r**3/12 + 2*r**2 - 503*r. Factor a(u).
(u - 2)*(u - 1)*(u + 8)/4
Factor 1/3*i**4 - 32*i + 0 - 32/3*i**2 + 2/3*i**3.
i*(i - 6)*(i + 4)**2/3
Let v = 8299/2 + -4147. Let i(u) be the second derivative of v*u**3 - 1/4*u**4 + 0 - 3/20*u**5 - 5*u - 9/2*u**2. Factor i(p).
-3*(p - 1)**2*(p + 3)
Let j(x) be the second derivative of 30*x - 1/39*x**6 - 67/78*x**4 - 12/13*x**2 + 16/65*x**5 + 4/3*x**3 + 1. Determine q so that j(q) = 0.
2/5, 1, 2, 3
Let x be (2/1)/(8/16). Let c = 8 - 5. Factor 2*f**5 - 30*f + 14*f**3 +