 1
Suppose -1411*o = -1666*o. Let y(w) be the second derivative of 0 + 0*w**4 + 1/225*w**6 + 25*w - 1/150*w**5 + o*w**2 + 0*w**3. Factor y(j).
2*j**3*(j - 1)/15
Solve 0 + 21/2*z - z**2 = 0.
0, 21/2
Let u(w) be the second derivative of -w**4/126 + 50*w**3/63 - 32*w**2/7 + 7*w - 35. Determine d so that u(d) = 0.
2, 48
Solve -6/5*t**3 - 21/5*t**2 + 24/5*t + 36/5 + 3/5*t**4 = 0 for t.
-2, -1, 2, 3
Let a(q) be the first derivative of -5*q**4/4 + 1075*q**3 - 693375*q**2/2 + 49691875*q - 525. Factor a(r).
-5*(r - 215)**3
Factor 10*p**2 + 22*p**2 - 3*p - 6 + 14*p**2 - 43*p**2.
3*(p - 2)*(p + 1)
Let c(o) be the second derivative of -o**5/25 - 136*o**4/15 - 266*o**3/5 + 2812*o. Factor c(u).
-4*u*(u + 3)*(u + 133)/5
Let n(s) be the second derivative of s**6/360 + s**5/20 + s**4/3 - 2*s**3/3 - s**2 + 10*s + 2. Let p(c) be the second derivative of n(c). Factor p(f).
(f + 2)*(f + 4)
Let m(d) be the second derivative of 1/10*d**2 + 50 - 1/15*d**3 - 2*d + 1/60*d**4. Factor m(c).
(c - 1)**2/5
Suppose 2*l - 2*f + 0 = -2, 2*l = -f + 13. Determine q so that 51*q**2 + 5*q**l - 133*q**2 + 62*q**2 = 0.
-2, 0, 2
Let n = 63 - 59. Suppose 2*y - 10 = -3*x + 75, -2*x - 194 = -n*y. Factor 37*s + y*s + 44*s**2 + 13*s - s - 144 + 4*s**3.
4*(s - 1)*(s + 6)**2
Let k(u) = 152*u + 19306. Let t be k(-127). Let -6/5*y**t + 1/5*y**3 + y + 0 = 0. What is y?
0, 1, 5
Let k(x) be the first derivative of -3/8*x**4 - 3/10*x**5 - 67 + 0*x + 1/2*x**3 + 3/4*x**2. Find v, given that k(v) = 0.
-1, 0, 1
Let b(q) = -3*q**2 + 21*q + 3. Let l be b(7). Suppose -5*j + 7 = -l. Suppose 2*y**j + 11*y - 4*y**3 - 7*y - 2*y**2 = 0. Calculate y.
-1, 0, 1
Let s(n) be the third derivative of 0 - 2*n - 64*n**2 - 25/12*n**4 - 15/2*n**3 - 1/12*n**5. Factor s(q).
-5*(q + 1)*(q + 9)
Factor 2*i**2 + 3852*i + 2105 - 4436 + 2378 + 3803.
2*(i + 1)*(i + 1925)
Let q(k) be the third derivative of k**7/525 - 41*k**6/300 + 79*k**5/150 - 13*k**4/20 + 5*k**2 - 44*k - 5. Factor q(m).
2*m*(m - 39)*(m - 1)**2/5
Suppose 103 = 4*d - 22*u + 23*u, 0 = -3*d - u + 77. Let k(t) = -2*t**2 + 52*t + 2. Let y be k(d). Factor -2/3*x**y + 0 - 6*x.
-2*x*(x + 9)/3
Factor 1/3*z**5 + 0*z + 8/3*z**2 + 0 + 2/3*z**3 - 5/3*z**4.
z**2*(z - 4)*(z - 2)*(z + 1)/3
Let c(l) be the first derivative of 36*l**5/5 + 31*l**4 + 16*l**3 - 10730. Factor c(h).
4*h**2*(h + 3)*(9*h + 4)
Let o be ((-158)/790)/(26/24 - 5/4). Factor 3/5*h**2 - 9/5*h + o.
3*(h - 2)*(h - 1)/5
What is m in 19*m**4 - 252*m**2 - 3*m**3 - 113*m**2 - 116*m**2 + 1690*m + m**5 - 401*m**2 - 41*m**2 = 0?
-13, 0, 2, 5
Let q(d) be the first derivative of 36*d**5/5 + 98*d**4 + 1136*d**3/3 + 496*d**2 - 553. Suppose q(x) = 0. What is x?
-62/9, -2, 0
Let l(o) be the third derivative of o**5/120 - 47*o**4/8 + 281*o**3/12 + 48*o**2 - o. Factor l(k).
(k - 281)*(k - 1)/2
Factor 2/11*h**2 - 110 - 232/11*h.
2*(h - 121)*(h + 5)/11
Let q = -71 + 80. Solve q*g**3 - 3*g**5 + 21*g**2 - 31*g**2 + 16*g**2 = 0.
-1, 0, 2
Let d(n) be the third derivative of 0*n - 7*n**2 + 0 - 1/40*n**5 + 27/4*n**4 - 729*n**3. Determine j, given that d(j) = 0.
54
Find b such that -39*b**3 + 3*b**5 - 204*b**3 + 6*b**4 + 71*b**2 + 49*b**2 + 114*b**3 = 0.
-8, 0, 1, 5
Suppose -5*j + 4*j = 0. Let o = j + 4. Let -9*x**2 + 3*x**3 + 4*x**2 + o*x**2 = 0. Calculate x.
0, 1/3
Suppose -9*u + 5*u - o = -13, 1 = -2*u - 3*o. Factor 6*q**3 - 19*q**4 - 8*q**3 - 2*q**5 + 12*q**4 + 11*q**u.
-2*q**3*(q - 1)**2
Let b(c) be the first derivative of -c**4/20 + 23*c**3/5 - 315*c**2/2 + 2375*c - 854. Factor b(s).
-(s - 25)**2*(s - 19)/5
What is r in -843*r**4 - 22*r**2 + 410*r**4 + 423*r**4 + 6*r - 38*r**3 = 0?
-3, -1, 0, 1/5
Factor 25/4 + 2*c**3 + 1/4*c**4 - 10*c + 3/2*c**2.
(c - 1)**2*(c + 5)**2/4
Let m(a) be the second derivative of -1/30*a**5 - 4*a + 2*a**2 - 13/9*a**3 + 16 + 4/9*a**4. Solve m(d) = 0 for d.
1, 6
Let r(k) = -k**3 + 38*k**2 + 57*k + 37. Let l be r(35). Factor -1 - 15*x**2 + 7 + 5716*x - l*x.
-3*(x - 1)*(5*x + 2)
Suppose -56 = -20*n + 4. Let 6*o**4 - 9*o**n + 8*o**5 - 3*o + 6*o**3 - 6*o**2 - 5*o**5 + 3*o**3 = 0. Calculate o.
-1, 0, 1
Let d(t) be the third derivative of 5*t**8/112 - 7*t**7/6 + 103*t**6/24 - 71*t**5/12 + 35*t**4/12 - 1152*t**2. Suppose d(i) = 0. Calculate i.
0, 1/3, 1, 14
Let p(f) be the third derivative of f**11/83160 - f**10/9450 + f**9/3780 + 3*f**5/20 + f**3/6 - 58*f**2. Let t(v) be the third derivative of p(v). Factor t(w).
4*w**3*(w - 2)**2
Suppose -96 + 104*g - 6*g**3 - 3/2*g**2 - 1/2*g**4 = 0. Calculate g.
-8, 1, 3
Let o(w) be the third derivative of -5/18*w**3 - 1/60*w**6 + 7/180*w**5 + 71*w**2 + 0 + 1/18*w**4 + 0*w. What is f in o(f) = 0?
-5/6, 1
Let w(t) be the first derivative of 3*t**2 - 11 - 81*t**3 - 249/4*t**4 + 0*t. Factor w(s).
-3*s*(s + 1)*(83*s - 2)
Let r(u) be the third derivative of u**5/270 + 25*u**4/12 - 916*u**3/27 + 2*u**2 - 2*u - 18. Factor r(g).
2*(g - 4)*(g + 229)/9
Let x = 116173 + -580861/5. Let f be -1 - (1 + 6/(-3)). Find t such that 4/5*t**2 + f*t - x = 0.
-1, 1
Solve -132*l + 2/3 + 6534*l**2 = 0 for l.
1/99
Let z(k) be the third derivative of -1/24*k**4 + 1/1050*k**7 + 1/600*k**6 - 1/100*k**5 - 1/15*k**3 + 198*k**2 + 0 + 0*k. Determine r so that z(r) = 0.
-1, 2
Let g(p) = -2*p**3 - 30*p**2 + 26*p - 69. Let r be g(-16). Let b(l) be the first derivative of 0*l + 4/3*l**3 - 5*l**4 + 0*l**2 + r + 5*l**5. Factor b(d).
d**2*(5*d - 2)**2
Let n(r) = 14*r**2 - 5*r + 6. Let h be -2*(-1)/2*(-28 - -29). Let c(x) = -3*x**2 + x - 1. Let q(j) = h*n(j) + 5*c(j). Solve q(m) = 0.
-1, 1
Let 167*w**2 - 114*w**2 + 2979 + 181*w - 99 - 48*w**2 + 69*w = 0. Calculate w.
-32, -18
Let j be 2*1/(-6) + 1/3. Let a = 7 - j. Factor 0*k**2 + 4*k + 3*k**2 - a*k.
3*k*(k - 1)
Factor -6441 - 6328 + 12961 + 22224*b + 643107*b**2.
3*(463*b + 8)**2
Let k = -65 - -67. Factor -8*a**3 - 27*a**2 - 4*a + 4*a**3 + 7*a**2 + 12*a**k.
-4*a*(a + 1)**2
Solve 160*f**2 + 10*f**3 - 104*f**4 + 24*f**4 - 3290*f**5 - 80 + 3285*f**5 - 5*f = 0.
-16, -1, 1
Let k(g) = -31 + 7*g + 12*g - 48 - 10*g. Let u be k(9). Factor -2/7*r**u + 24/7*r - 72/7.
-2*(r - 6)**2/7
Let j(p) be the first derivative of p**4/66 + 4*p**3/33 - 88*p - 199. Let z(y) be the first derivative of j(y). Factor z(h).
2*h*(h + 4)/11
Let w = 186567/5 + -37313. Let 4/5*y**3 + 0 - 9/5*y**2 + w*y = 0. What is y?
0, 1/4, 2
Solve 17*z**2 + 37*z**3 - 28*z**4 + 5*z**2 + 2*z + 4*z**5 + 29*z + 10 - 68*z = 0 for z.
-1, 1/2, 2, 5
Suppose -q + 7 = -4*d + 52, -2*d - 4*q = -36. Suppose -4*n = -2*n - 36. Factor -d*u - 1 + 6 - 7 - n*u**2.
-2*(3*u + 1)**2
Let z(q) = 41*q**3 - 805*q**2 + 181*q - 15. Let b(c) = 20*c**3 - 402*c**2 + 90*c - 6. Let h(w) = 5*b(w) - 2*z(w). Factor h(o).
2*o*(o - 22)*(9*o - 2)
Let q = 31870005 - 8031224669/252. Let h = q + -313/36. Determine o, given that -4/7*o**2 - 80/7*o - h = 0.
-10
Let y = 143345/215031 - -3/71677. Factor 0 + y*n**2 - 40/3*n.
2*n*(n - 20)/3
Let w(h) = h**2 - 4. Suppose -n - 8 = -9*r + 5*r, -2*r - n + 10 = 0. Let y be w(r). Factor -y*o**2 + 6*o**2 + o**2 - 3*o**3 + 7*o**2.
-3*o**2*(o - 3)
Let f(q) be the second derivative of q**4/78 + 8*q**3/39 - 20*q**2/13 + 1911*q. Factor f(o).
2*(o - 2)*(o + 10)/13
Let f(r) be the second derivative of r**8/840 + r**7/60 + r**6/18 - 2*r**3/3 - r**2 + 55*r. Let v(d) be the second derivative of f(d). Factor v(l).
2*l**2*(l + 2)*(l + 5)
Let d be ((-6)/(-7))/(1328/8199072). Factor -1555848 + 84*y**3 + 148176*y - 1/2*y**4 - d*y**2.
-(y - 42)**4/2
Solve 2/11*v**2 + 54/11*v + 304/11 = 0 for v.
-19, -8
Let f = 821621/547750 + 2/273875. Determine d so that 3/2*d**3 - f*d - 21/2 + 21/2*d**2 = 0.
-7, -1, 1
Let b = -5561 + 200197/36. Let q(c) be the second derivative of -1/18*c**3 - c**2 + 0 + b*c**4 - 9*c. Let q(s) = 0. Calculate s.
-2, 3
What is x in 45/4*x**2 + 0*x + 0 + 3/2*x**4 - 33/4*x**3 = 0?
0, 5/2, 3
Let h(b) = -2*b**4 + 27*b**3 + 9*b**2 - 27*b + 14. Let j(c) = c**4 - 13*c**3 - 4*c**2 + 13*c - 6. Let y(s) = -3*h(s) - 7*j(s). Factor y(t).
-t*(t - 10)*(t - 1)*(t + 1)
Factor 2*n**2 - 43*n**2 + 2*n**2 - 18*n + 2*n**3 + n**2 + 106*n + 128.
2*(n - 16)*(n - 4)*(n + 1)
Suppose -13*a - 1217 = -5416. Find k, given that 657*k**3 - 432 + a*k**4 + 3*k**5 - 1515*k**2 + 2253*k - 404*k**4 - 885*k = 0.
1, 12
Let b(m) = 224*m + 8736. Let s be b(-39). Factor 0 + 4/19*t**2 + 2/19*t**4 + 6/19*t**3 + s*t.
2*t**2*(t + 1)*(t + 2)/19
Let w(x) 