*(k - 1)**2
Solve -93339/4*y**3 + 6160050 - 3016845*y - 279*y**4 - 3/4*y**5 + 963819/2*y**2 = 0.
-195, 6
Suppose 65*b + 45 = 80*b. Let s(k) be the first derivative of -16/27*k**b + 0*k + 27 + 4/9*k**2 + 1/6*k**4. Suppose s(j) = 0. What is j?
0, 2/3, 2
Let f(n) be the third derivative of n**9/3024 - n**7/252 + n**5/24 - 13*n**4/24 - 130*n**2 - 2*n. Let j(k) be the second derivative of f(k). Factor j(h).
5*(h - 1)**2*(h + 1)**2
Solve 142*u**3 - 19600688/3 + 90308/3*u**2 + 18776360/9*u + 2/9*u**4 = 0.
-214, 3
Let s(w) be the first derivative of -5*w**4/4 + 95*w**3/3 - 125*w**2 + 160*w - 678. Factor s(g).
-5*(g - 16)*(g - 2)*(g - 1)
Let p be (0 + (-60)/50)/(1 + (-39)/30). Let f(l) be the third derivative of 0*l - 1/60*l**5 + 0*l**3 + 9*l**2 + 1/12*l**p + 0. Suppose f(s) = 0. What is s?
0, 2
Suppose 3*t = 3*z - 21, -3*t = 13 + 2. Suppose -5*i**z + 210*i - 1330 - 653 - 222 = 0. Calculate i.
21
Find c such that 346*c + 0*c**2 - 1316*c - 3*c**2 - 785*c = 0.
-585, 0
Let s be 2810/(-3) + (-3)/9 - -6. Let n = s - -935. Let 3/4*a**2 + 1/2*a**3 + 0 + 0*a - 1/4*a**n = 0. Calculate a.
-1, 0, 3
Suppose -109299*f**2 - 144052*f - 358568*f - 3*f**4 - 1607472 - 33705*f - 1122*f**3 - 154698*f - 130281*f = 0. What is f?
-183, -4
Let k = 38 + -18. Let q(v) = 6 - 10*v + v - k*v + 44 - 7*v**2. Let w(g) = 3*g**2 + 14*g - 25. Let d(n) = -4*q(n) - 9*w(n). Factor d(j).
(j - 5)**2
Let y(w) be the second derivative of -45/7*w**2 - 6 - 17/14*w**3 - 1/28*w**4 + 3*w. Suppose y(p) = 0. What is p?
-15, -2
Let x be (-336)/(-260) - 792/(-2574). Let 0 + x*h + 2/5*h**3 + 2*h**2 = 0. Calculate h.
-4, -1, 0
Factor 0*b**2 + 0*b**3 + 1/2*b**5 + 0*b - 49/2*b**4 + 0.
b**4*(b - 49)/2
Let j(s) be the second derivative of -3*s**5/140 + 25*s**4/7 - 1250*s**3/7 + 21*s - 25. Factor j(i).
-3*i*(i - 50)**2/7
Let c = -258121 + 4905181/19. Suppose -c - 84/19*b - 2/19*b**2 = 0. Calculate b.
-21
Suppose -14*j = -27*j + 30*j. Let x(a) be the third derivative of 1/36*a**5 + 1/360*a**6 + 0*a - 15*a**2 + 1/18*a**4 + j*a**3 + 0. Factor x(z).
z*(z + 1)*(z + 4)/3
Let m be ((-17284)/(-1218) - 14)/(12/19166). Let -148/9*k + 2/9*k**2 + m = 0. What is k?
37
Let x(h) be the second derivative of h**6/10 + 42*h**5/5 + 81*h**4/2 + 80*h**3 + 159*h**2/2 + 1394*h. Factor x(w).
3*(w + 1)**3*(w + 53)
Factor -20*i**2 - 220*i**2 - 788*i + 238*i**2.
-2*i*(i + 394)
Let o(u) be the second derivative of u**6/1080 + 19*u**5/180 + 59*u**3/3 - 106*u. Let k(h) be the second derivative of o(h). Suppose k(m) = 0. Calculate m.
-38, 0
Factor -3*l**2 - 18 - 5*l**2 + 69 + 10*l**2 + 39 + 92*l.
2*(l + 1)*(l + 45)
Suppose -10304*w + 10427*w - 492 = 0. Determine h so that -16/5*h**4 + 0*h - 8/5*h**2 + 0 - w*h**3 - 4/5*h**5 = 0.
-2, -1, 0
Let l(k) = 8*k**4 - 78*k**3 + 54*k**2 + 393*k. Let y(j) = 4*j**4 - 40*j**3 + 28*j**2 + 196*j. Let s(n) = 4*l(n) - 7*y(n). Factor s(z).
4*z*(z - 5)**2*(z + 2)
Let g(w) = 5*w**2 - 38*w - 207. Let o be g(-5). Let m = 64/3 + -20. Let -m*k**2 + 24*k - o = 0. What is k?
9
Let n(k) be the third derivative of 0*k + 1/24*k**6 + 58 - 35/6*k**4 - k**5 + 0*k**3 + k**2. Determine w, given that n(w) = 0.
-2, 0, 14
Let w be 48/112*56/3744. Let m(z) be the third derivative of w*z**4 + 1/260*z**6 - 1/130*z**5 + 0*z**3 + 0 - 9*z**2 - 1/1365*z**7 + 0*z. Solve m(r) = 0 for r.
0, 1
Let k(l) = -4*l - 53*l**2 + 5 + l**3 - 1 + 56*l**2. Let i be k(-4). Suppose i*z**2 + 2*z + 13*z + 0*z**2 - 7*z = 0. Calculate z.
-2, 0
Suppose x - 60 = 4*x. Let m = x + 24. Determine v, given that -4*v**2 + m*v**4 - 12*v**2 - 223*v - 4*v**3 + 239*v = 0.
-2, 0, 1, 2
Let t(h) be the third derivative of h**7/35 - 17*h**6/12 + 127*h**5/15 - 23*h**4/3 - 200*h**3/3 + 2173*h**2. Let t(d) = 0. Calculate d.
-2/3, 2, 25
Let u = -209 + 140. Let w be (-5)/(-3)*u/(-460). Let 0 - 1/4*j**3 - w*j**2 + 0*j = 0. What is j?
-1, 0
Let q be ((-3)/24)/((-63)/(-56)) - 232/(-144). Let -6 - q*o**2 - 15/2*o = 0. Calculate o.
-4, -1
Find f, given that -225 - 12*f**3 + 153*f - 97*f + 154*f + 27*f**2 = 0.
-15/4, 1, 5
Let s(a) = -21*a + 6*a**2 + 11 - 4 - 9 - 5. Let i be s(12). Find c such that i*c**3 + c**2 + 134*c**2 + 141*c**2 + 20*c - 56*c**2 = 0.
-2/11, 0
Suppose -8*c - 99 = -41*c. Find v, given that -28*v - 12*v**3 + 36*v**2 - 24 + 4*v**c + 0*v**3 = 0.
-1/2, 2, 3
Let w = -191 + 291. Solve -w*c + 26 - 59*c**2 + 28 - 35*c**3 - 71*c**2 - 14 = 0.
-2, 2/7
Let i(g) be the third derivative of g**5/180 + 83*g**4/24 + 964*g**3/9 + 3143*g**2. Factor i(c).
(c + 8)*(c + 241)/3
Let a(g) be the first derivative of 0*g - 28/13*g**2 - 24/65*g**5 - 43/26*g**4 - 1/39*g**6 - 40/13*g**3 + 155. Find h, given that a(h) = 0.
-7, -2, -1, 0
Factor 224/9 + 2/9*x**2 + 116/9*x.
2*(x + 2)*(x + 56)/9
Solve 2/5*b**4 + 18/5*b**3 + 28 + 2/5*b**2 - 162/5*b = 0 for b.
-7, -5, 1, 2
Let s(t) be the first derivative of -t**3/18 - 21*t**2/2 + 980*t/3 - 9421. Factor s(q).
-(q - 14)*(q + 140)/6
Let r(s) = -s**3 + 11*s**2 - 4*s + 38. Let v be r(11). Let u be (-56)/v*21/28. Find g such that 17/3*g**3 + 11/3*g - u*g**2 - 5/3*g**4 - 2/3 = 0.
2/5, 1
Factor 1362 - 1362 + 22*v**2 + 180*v - 13*v**2 - 11*v**2.
-2*v*(v - 90)
Let y(z) be the second derivative of -z**5/2 + 9*z**4/4 - 9*z**2/2 + 3*z. Let f(k) = -7*k**3 + 18*k**2 - 6. Let s(p) = -8*f(p) + 5*y(p). Factor s(q).
3*(q - 1)**2*(2*q + 1)
Factor -2/7*r**2 - 52/7 + 30/7*r.
-2*(r - 13)*(r - 2)/7
Solve 64*t**2 - 32 + 132*t**3 + 8*t**3 + 25*t**4 + 10 + 61*t**2 - 170*t - 98 = 0.
-4, -2, -3/5, 1
Factor 56 + 4/5*s**3 + 8/5*s**2 - 292/5*s.
4*(s - 7)*(s - 1)*(s + 10)/5
Let k(s) be the second derivative of s**4/30 - 1508*s**3/5 + 5116644*s**2/5 + 964*s. Factor k(j).
2*(j - 2262)**2/5
Let n(h) = h**2 + 6*h. Let m(r) = -r**2 - 5 + 5 - 7*r. Suppose -2*b - 8 = -5*o, -3*b + 4*o = 5*o - 22. Let t(d) = b*m(d) + 7*n(d). Factor t(u).
u**2
Let l(x) be the third derivative of -x**5/210 - 11*x**4/4 + 232*x**3/21 + 3*x**2 + 69. Factor l(d).
-2*(d - 1)*(d + 232)/7
Let b(q) = 22*q + 158. Let o be b(-7). Suppose 55*r**o + 13*r**2 - 65*r**4 + 11*r**2 - 34*r**3 = 0. What is r?
-4, 0, 3/5
Let q(g) be the third derivative of g**8/168 - g**7/21 - 2*g**6/15 + 2*g**5/5 - 2*g**2 - 74. Find r such that q(r) = 0.
-2, 0, 1, 6
Determine t so that -4/5*t**5 + 0 - 14/5*t**2 + 12/5*t**3 + 14/5*t**4 - 8/5*t = 0.
-1, -1/2, 0, 1, 4
Suppose 5*u + 6*h - 8*h = 10, u - 20 = 4*h. Suppose -12*o + 97 - 49 = u. Let -1/2*n**2 - o + 3*n = 0. Calculate n.
2, 4
Let n(r) be the first derivative of 1/3*r**3 + 0*r + 26 + 1/24*r**6 + 1/2*r**4 + 1/4*r**5 + 0*r**2. Factor n(i).
i**2*(i + 1)*(i + 2)**2/4
Let z(m) = -25 - 3*m - 2*m**4 + 4 - 4*m**4 + 0*m**3 - 15*m**3. Let q(i) = -3*i**4 - 7*i**3 + i**2 - i - 10. Let r(t) = 9*q(t) - 4*z(t). Factor r(l).
-3*(l - 1)**2*(l + 1)*(l + 2)
Let c(n) be the first derivative of -1/60*n**4 + 0*n + 1/150*n**5 - 2 - 4*n**2 - 2/15*n**3. Let t(d) be the second derivative of c(d). Factor t(v).
2*(v - 2)*(v + 1)/5
Let b(c) be the third derivative of -c**7/105 - c**6/20 + 32*c**5/15 + 19*c**4 - 96*c**3 - 2533*c**2. Determine s so that b(s) = 0.
-6, 1, 8
Find g, given that -32/3*g**5 - 272/3*g**4 + 28 - 54*g**3 + 1312/3*g**2 + 670/3*g = 0.
-7, -3, -1/4, 2
Suppose -280 = -5*o + 4*y, 2*y - 15 = 5*o - 295. Suppose -32*k = -8 - o. What is t in 22/5*t - 2*t**k - 4/5 = 0?
1/5, 2
Determine l so that -8897*l**2 + 1868*l**2 - 1429138623 + 5739240*l - 249591*l - 90*l**3 + 93*l**3 = 0.
781
Let c(q) be the first derivative of -338*q**3/45 + 2548*q**2/5 - 57624*q/5 - 477. Factor c(f).
-2*(13*f - 294)**2/15
Let n(l) be the third derivative of 13*l**7/2940 + l**6/2520 - l**4/24 - 3*l**3 - 10*l**2 + 11*l. Let q(x) be the second derivative of n(x). Factor q(b).
2*b*(39*b + 1)/7
Factor 1303*u - 4566*u**2 + 4555*u + 4562*u**2 + 2014*u + 7876.
-4*(u - 1969)*(u + 1)
Let n(z) be the first derivative of -1/5*z**2 - 64 - 1/25*z**5 + 0*z - 3/20*z**4 + 1/30*z**6 + 1/3*z**3. Let n(q) = 0. What is q?
-2, 0, 1
Let s(j) = -820*j**3 - 265*j**2 - 320*j - 155. Let i(n) = -73*n**3 - 24*n**2 - 29*n - 14. Let k(o) = 45*i(o) - 4*s(o). Factor k(c).
-5*(c + 1)**2*(c + 2)
Find h, given that 452*h - 47040*h**2 - 5 + 878080*h**3 + 621*h - 233*h = 0.
1/56
Suppose -2*i + 3*y - 7 = -0*y, 0 = -3*i - y + 17. Let q(g) be the second derivative of 1/12*g**i + 2/9*g**3 + 8*g - 2/3*g**2 + 0. Let q(b) = 0. What is b?
-2, 2/3
Let r(j) be the second 