*n**4 + 3962770432/7 + 3972235648/7*n = 0. Calculate n.
-1256, -1
Let h = 123196 - 123194. Determine n, given that -3/5*n**h + 18/5 + 3*n = 0.
-1, 6
Suppose -183184 + 33*i**2 - 1712*i + 33*i**2 - 70*i**2 = 0. What is i?
-214
Let i(c) = c**3 - 22*c**2 - 11*c - 31. Let a be i(22). Let m = 273 + a. What is y in -4/21*y + 0 + m*y**3 + 2/21*y**4 - 2/7*y**2 = 0?
-1, 0, 2
Solve 5*a**5 + 11246*a**4 - 204*a**2 - 11302*a**4 - 259*a**3 - 6*a**5 = 0 for a.
-51, -4, -1, 0
Let v(l) be the first derivative of 2/3*l**3 + 94 + 0*l**2 - 32*l. Factor v(h).
2*(h - 4)*(h + 4)
Let q(l) be the third derivative of -l**6/840 - 19*l**5/140 + l**4/168 + 19*l**3/14 + 5*l**2 - 178*l. Factor q(n).
-(n - 1)*(n + 1)*(n + 57)/7
Let a(h) be the third derivative of h**8/20160 - h**7/630 + 7*h**6/720 - h**5/30 + h**4/6 + h**2. Let b(j) be the third derivative of a(j). Factor b(y).
(y - 7)*(y - 1)
Suppose -5*o = 2*a - 22, 7*a + 2*o - 16 = 5*a. Factor -5*i**4 + 0*i**4 - 785*i**3 - 3*i**5 + a*i**5 + 18*i**2 - 7*i**4 + 788*i**3.
3*i**2*(i - 3)*(i - 2)*(i + 1)
Let q be (196/168)/((-7)/(-4)) + (3 - 6270/(-72)). Factor -q*k**2 + 99*k - 27.
-3*(11*k - 6)**2/4
Factor -87616 - 7908*a**2 - 48544*a + 737*a**4 - 1430*a**4 - 328*a**3 + 689*a**4.
-4*(a + 4)**2*(a + 37)**2
Let j**2 - 5277 - 3*j**2 + 2700 + 2709 + 62*j = 0. What is j?
-2, 33
Let y(r) be the second derivative of -r**4/126 + 2*r**3/9 + 145*r**2/7 - 405*r - 3. Factor y(t).
-2*(t - 29)*(t + 15)/21
Let v(h) be the third derivative of 5*h**8/1008 + 181*h**7/63 - 727*h**6/72 + 91*h**5/9 - 2*h**2 - 265*h. Factor v(l).
5*l**2*(l - 1)**2*(l + 364)/3
Let b(r) = 4*r - 18. Let g be b(12). Let m = g + -29. Factor -17*w**2 + 0 + 14*w**2 - m - 5*w**3 + 4*w**4 + 5*w.
(w - 1)**2*(w + 1)*(4*w - 1)
Factor -4 - 1/6*k**2 - 5/3*k.
-(k + 4)*(k + 6)/6
Let w(t) = 11*t**2 + 68*t - 95. Let x(i) = 3*i**2 - 8*i + 1. Let n(p) = -3*w(p) + 12*x(p). Factor n(l).
3*(l - 99)*(l - 1)
Let t(p) be the first derivative of 15/2*p**2 - 25/3*p**3 + p**5 - 15/4*p**4 + 58 + 20*p. Solve t(d) = 0.
-1, 1, 4
Suppose -50*g = -38*g - 468. Determine t, given that 13*t - 135*t**2 + g*t - 4 + 15*t**2 = 0.
1/10, 1/3
Let w be ((-3)/21 - -1)/(3*(-4)/(-42)). Let 0 + 2/5*j**w - 6/5*j**2 + 0*j = 0. What is j?
0, 3
Suppose -3*g + 27 = 5*f + 2, 2*f + 6 = 2*g. Let b be f/6 - (-22)/6. Determine m, given that -b*m - 2*m**2 + 2 + 0*m + 4*m**2 = 0.
1
Solve -23*l**4 - 1458 + 91*l**4 + 178*l**2 - 567*l - 65*l**4 - 7*l**2 + 51*l**3 = 0 for l.
-9, -2, 3
Let s = 1377303/56 + -172162/7. Factor 27/8*j - 7/4 - 3/2*j**2 - s*j**3.
-(j - 1)**2*(j + 14)/8
Factor 8/5*r**3 + 96/5 - 26/5*r**2 + 2/5*r**4 - 16*r.
2*(r - 3)*(r - 1)*(r + 4)**2/5
Let n = 254896/1401807 + -2/127437. Factor 0*w - n*w**2 + 8/11.
-2*(w - 2)*(w + 2)/11
Suppose -50 = -48*c + 46*c. Suppose 168 = -c*x + 218. What is y in -1/2*y**3 + y**x - 1/2*y + 0 = 0?
0, 1
Factor -134*z**4 - 40*z**3 + 260*z**2 + 64*z + 248*z**3 + 79*z**4 + 67*z**4.
4*z*(z + 1)*(z + 16)*(3*z + 1)
Let x(d) = 3*d + 18. Let b be x(-6). Suppose -4 = -3*k + 5, b = -3*t + 2*k. Factor -3*v + 2*v + 118*v**2 - 119*v**2 + t.
-(v - 1)*(v + 2)
Let s(u) be the third derivative of -u**5/12 + 715*u**4/8 + 2155*u**3/3 + 1161*u**2. Let s(j) = 0. Calculate j.
-2, 431
Let c = -8414 + 8417. Let d = 4 + 0. What is k in -2*k**c - d*k**2 - 3 - 2*k**2 + 13 - 2 = 0?
-2, 1
Factor 23*x**2 - 172*x + 168*x - 89*x**2 - 2*x**4 + 669*x + 303*x - 36*x**3.
-2*x*(x - 4)*(x + 11)**2
Let d be (-3)/(((-165)/(-10))/(-11)) - 2183/1110. Let w(z) be the second derivative of 0 + 26*z - d*z**6 + 0*z**2 + 0*z**3 - 1/10*z**5 - 1/12*z**4. Factor w(s).
-s**2*(s + 1)**2
Let a = 92 - 88. Suppose z - 5*z = -c - 5, -a*c + 6 = -3*z. Suppose 0*k - 2*k**3 + 2*k + 4*k**2 - 4*k**z = 0. Calculate k.
-1, 0, 1
Suppose 6*a + 1 - 2 - 11 = 0. Let t(g) be the third derivative of -1/3*g**4 + 1/15*g**5 + 2/3*g**3 + 10*g**a + 0*g + 0. Find m such that t(m) = 0.
1
Let s(q) = -q**2 - 570*q - 40819. Let h be s(-84). Let 0*r + 0 + 5/7*r**h - 12/7*r**3 - 3/7*r**4 - 4/7*r**2 = 0. What is r?
-1, -2/5, 0, 2
Determine x so that 151*x**2 + 209093*x**3 - 208981*x**3 - 514*x**2 + 277*x - 62 + 4*x**4 = 0.
-31, 1/2, 2
Let w(z) be the second derivative of 8/3*z**3 + 72*z + 0 - 1/6*z**4 - 16*z**2. Solve w(n) = 0.
4
Factor -32*t**2 - 170 + 60*t**2 + 217 - 46*t - 29*t**2.
-(t - 1)*(t + 47)
Let d(h) = 40*h**2 - 49*h - 125. Let o(l) = -840*l**2 + 1030*l + 2635. Let x(s) = -85*d(s) - 4*o(s). Find m such that x(m) = 0.
-1, 17/8
Let m(v) be the third derivative of 49*v**6/300 + 2926*v**5/25 + 1671*v**4/20 + 358*v**3/15 + 1897*v**2 + 3*v. Factor m(a).
2*(a + 358)*(7*a + 1)**2/5
Let t(q) = -6*q**4 - 2*q**3 + 2*q**2 + 6*q - 4. Let g(r) = -2*r**4 + 0*r**3 + r**4 - r**2 + 26*r - 25*r + 0*r**3. Let h(i) = -4*g(i) + t(i). Factor h(p).
-2*(p - 1)**2*(p + 1)*(p + 2)
Let h(g) = 2*g**3 - 6874*g**2 - 27454*g - 27348. Let o(f) = 3*f**3 - 13747*f**2 - 54903*f - 54706. Let m(a) = 11*h(a) - 6*o(a). Solve m(b) = 0 for b.
-1713, -2
Let t = -37/54582 + 35410021/60313110. Let c = t - -3/221. Factor 3/5*n - c*n**2 + 0.
-3*n*(n - 1)/5
Let g = -48/439 - -2291/878. Let w(n) be the second derivative of -1/6*n**6 + g*n**3 + 25/12*n**4 + 0*n**2 + 1/4*n**5 + 2*n + 0. Factor w(l).
-5*l*(l - 3)*(l + 1)**2
Factor -51516 - 7308*v + 1585988 + 2*v**2 + 5141386.
2*(v - 1827)**2
Let z(j) = j**2 + 17*j - 26. Let o(s) = -2*s + 1. Let d(a) = 4*a**3 + 2*a**2 + 2*a - 3. Let y be d(1). Let b(q) = y*z(q) + 20*o(q). Factor b(x).
5*(x - 2)*(x + 11)
Let j(h) be the third derivative of -h**6/40 + 31*h**5/30 - 31*h**4/8 - 19*h**3/3 + 56*h**2 - 13. Find q, given that j(q) = 0.
-1/3, 2, 19
Suppose 5*t - 18*x + 85 = -15*x, 4*x = 5*t + 90. Let c be -7*(15/t)/15. Find g such that -c*g**3 - 5/2*g**2 + 0 + 0*g = 0.
-5, 0
Let n(g) be the first derivative of 0*g - 4/3*g**2 + 32/27*g**3 + 2/45*g**5 - 7/18*g**4 - 52. Factor n(j).
2*j*(j - 3)*(j - 2)**2/9
Determine t so that 281*t**2 - 64*t - 481*t**2 - 53 - 10*t**4 + 53 - 104*t**3 = 0.
-8, -2, -2/5, 0
Let a(x) = -5*x**2 - 4720*x - 1113923. Let n(v) = 90*v**2 + 84960*v + 20050615. Let m(z) = 55*a(z) + 3*n(z). Find g such that m(g) = 0.
-472
Let k(m) be the first derivative of -m**6/12 + 82*m**5/5 - 9073*m**4/8 + 29187*m**3 - 80919*m**2 + 78732*m - 3599. Find y, given that k(y) = 0.
1, 54
Suppose -114 = 211*k - 268*k. Factor -k*p**3 - 3/2*p**4 - 1/2*p**2 + 0*p + 0.
-p**2*(p + 1)*(3*p + 1)/2
Factor -3100/3*q + 1/3*q**2 - 3101/3.
(q - 3101)*(q + 1)/3
Suppose 232*b + 57 = 235*b. Suppose -30*m = -b*m - 22. Determine z, given that 0 + 2/11*z**4 - 2/11*z**m + 4/11*z - 4/11*z**3 = 0.
-1, 0, 1, 2
Let u = -39301/10 - -19653/5. Factor -2/5*d - u*d**2 + 33/10.
-(d + 3)*(5*d - 11)/10
Let d be 6/(-57) + 17/((-4199)/(-767)). Let q(r) be the first derivative of 17 + 3/7*r**2 - 3/7*r - 1/7*r**d. Find n, given that q(n) = 0.
1
Let p(g) be the first derivative of -16/7*g**2 - 64/7*g + 32 - 4/21*g**3. Factor p(u).
-4*(u + 4)**2/7
Let y(g) = -g**3 - 7*g**2 - 10*g + 5. Let q = 84 + -89. Let v be y(q). Factor 23*a**4 - v*a**4 - 2 - 12*a**2 - 12*a - 5*a**2 + 12*a**3 + a**2.
2*(a - 1)*(a + 1)*(3*a + 1)**2
Let h(o) be the first derivative of -o**6/24 + 11*o**5/5 - 83*o**4/16 - 11*o**3/3 + 21*o**2/2 - 559. Suppose h(n) = 0. Calculate n.
-1, 0, 1, 2, 42
Let s = -14463 + 86779/6. Let b(o) be the second derivative of 2/3*o**3 + s*o**4 - 3*o**2 + 0 - 22*o. Find x such that b(x) = 0.
-3, 1
Let i be (1*(-3 - -2))/((-1)/(-24)*-6). Let m(a) be the third derivative of 19*a**2 + 0*a + a**i + 8*a**3 + 1/20*a**5 + 0. Determine b, given that m(b) = 0.
-4
Factor -820*r - 132*r**2 + 132 + 1656*r - r**3 - 835*r.
-(r - 1)*(r + 1)*(r + 132)
Let k(q) be the second derivative of 60*q**4 - 5 + 2*q + 2000*q**2 - 1600/3*q**3 + 1/15*q**6 - 16/5*q**5. Factor k(g).
2*(g - 10)**3*(g - 2)
Let d(o) be the third derivative of -o**6/40 + 2*o**5/5 - 7*o**4/8 - o**2 + 368. Factor d(b).
-3*b*(b - 7)*(b - 1)
Let v(b) = -b + 1. Let x(r) = r**2 - 3. Let t(i) = -2*v(i) - x(i). Let s(y) = -4*y**2 + 16*y - 8. Let h(l) = -s(l) + 2*t(l). What is j in h(j) = 0?
1, 5
Factor 0*y + 0 - 20/9*y**4 + 52/9*y**3 - 4/9*y**5 - 28/9*y**2.
-4*y**2*(y - 1)**2*(y + 7)/9
Let p be 10*3/432*262/1310. Let l(o) be the third derivative of -2/45*o**6 + 2/45*o**5 - 23*o**2 + 0 + 0*o**3 + 0*o - p*o**4. Factor l(s).
-s*(4*s - 1)**2/3
Let i(d) be the seco