19
Suppose -9 = -2*h - 1. Let d(w) = -2*w**2 - 38*w - 176. Let l be d(-9). Factor 4*v**3 + 1 + l*v + 2*v**4 + 3*v**2 + 4*v**2 - v**2 - v**h.
(v + 1)**4
Let f(g) = 20*g - 20*g + 4*g + 266 + 10*g + 8*g. Let l be f(-12). Factor -l*t + 8/5*t**2 - 2/5*t**3 + 4/5.
-2*(t - 2)*(t - 1)**2/5
Let f(u) be the first derivative of -2/5*u**5 - u**4 + 0*u**3 + 0*u + 0*u**2 - 6. Let f(z) = 0. What is z?
-2, 0
Suppose -64*w + 2*k - 18 = -68*w, -4*w + 5*k = 3. Let m(i) be the first derivative of -1/15*i**w - 1/5*i - 1/5*i**2 - 4. Determine p so that m(p) = 0.
-1
Let j be 92/230*54/12*4. Let w(f) be the first derivative of 0*f**2 - 6*f**3 + 7/2*f**6 - 32 - 75/4*f**4 + 0*f - j*f**5. Determine a, given that w(a) = 0.
-1, -2/7, 0, 3
Let l = -3/360034 - -7259725585/1080102. Let -l*b**3 - 50823362/3*b - 1431644/3*b**2 - 3608458702/15 - 2/15*b**5 - 142/3*b**4 = 0. Calculate b.
-71
Factor -218/5*n - 43 - 3/5*n**2.
-(n + 1)*(3*n + 215)/5
Let x = 24777 + -24773. Let v(z) be the first derivative of x*z**2 + 4*z**3 + 4/3*z - 41. Factor v(f).
4*(3*f + 1)**2/3
Let s = 88 - 86. Factor 4*x**2 + 30*x**s + 34*x**2 - 76*x**3 + 8*x.
-4*x*(x - 1)*(19*x + 2)
Let k be (-76)/(-266)*(-14)/(-2). Suppose 4*y + 2 = 5*l, 3*l = 6*y - 4*y + 2. Factor -y*i**2 + 5*i**2 + 0*i**k + 3*i**4 - 190*i**3 + 196*i**3.
3*i**2*(i + 1)**2
Let k be (6144/(-3328))/(12/(-39)). Factor -52/9*y + 2/9*y**2 - k.
2*(y - 27)*(y + 1)/9
Let m(l) be the second derivative of -l**5/90 + l**4/2 + 40*l**3/9 + 49*l**2 + 101*l. Let g(v) be the first derivative of m(v). Solve g(f) = 0 for f.
-2, 20
Suppose -168*q - 9408 - 3/4*q**2 = 0. What is q?
-112
Let a(w) = -3*w**2 + 157*w - 752. Let u(t) = 14*t**2 - 776*t + 3761. Let v(x) = -11*a(x) - 2*u(x). Factor v(s).
5*(s - 30)*(s - 5)
Find h such that -456/5*h**2 - 156/5*h - 426/5*h**4 + 0 + 27/5*h**5 + 1011/5*h**3 = 0.
-2/9, 0, 1, 2, 13
Suppose 11 = 6*a - l, 1248*l + 25 = 3*a + 1249*l. Solve -4/3*n**5 - 8/3*n**2 + 28/3*n**a + 44/3*n - 20/3 - 40/3*n**3 = 0 for n.
-1, 1, 5
Factor -6101*i**4 - 5*i**3 + 60*i - 6095*i**4 + 12201*i**4 - 40*i**2.
5*i*(i - 2)**2*(i + 3)
Suppose -16*x + 5*q + 1281 = -15*x, 4*q = -x + 1281. Let o be (2*1)/2*x/1708. Let -3/4 - 3/2*w - o*w**2 = 0. Calculate w.
-1
Let -22 - 16/3*w + 68/3*w**2 - 2/3*w**4 + 16/3*w**3 = 0. What is w?
-3, -1, 1, 11
Let r(m) = -m**2 + 4*m + 16. Let w be r(8). Let u be (w/(-12))/4*3. Suppose 8*n**3 - 8*n**2 - 20*n**4 - 4*n - 4*n**5 + u + 24*n**4 + 3 = 0. Calculate n.
-1, 1
Let s = 346029001/219303 + -28/31329. Let v = s - 1577. Factor 0 + 2/7*g**4 - v*g**3 + 0*g + 0*g**2.
2*g**3*(g - 3)/7
Let x be (17/(-4) - -4)/(1164/(-144) - -8). Factor -2/5*y**x + 6/5*y**2 + 8/5*y + 0.
-2*y*(y - 4)*(y + 1)/5
Let j be (-15)/(-42)*-2*(6/(-138) - 810/5175). Determine b, given that -j*b - 2/7 + 78/7*b**2 = 0.
-2/13, 1/6
Let n(q) be the second derivative of q**7/630 + q**6/180 + q**4/12 + 27*q**2/2 - 130*q. Let d(u) be the third derivative of n(u). Find x such that d(x) = 0.
-1, 0
Let y(i) be the third derivative of i**7/2520 - i**6/144 - i**5/20 + i**4/24 - 151*i**3/6 + 59*i**2. Let d(f) be the second derivative of y(f). Factor d(h).
(h - 6)*(h + 1)
Let g(w) be the first derivative of 5/22*w**4 + 0*w + 2/55*w**5 + 0*w**2 - 38 + 4/11*w**3. Let g(s) = 0. Calculate s.
-3, -2, 0
Let j be 2/5 + 4189/(-885). Let y = 5 + j. Determine u so that 1/3*u**2 + u + y = 0.
-2, -1
Let l(t) = -13*t**2 + 38*t**2 - 26*t**2 - 2. Let v(c) = 7*c**2 + c + 10. Let b(u) = 6*l(u) + v(u). What is q in b(q) = 0?
-2, 1
Solve -8*j**2 + 10 - j**4 + 12*j**3 + 0*j**4 + 446*j - j**4 - 458*j = 0 for j.
-1, 1, 5
Let l = 1396021 - 1396017. Solve 25/2*z**5 - 88*z - 155/2*z**l - 24 - 4*z**2 + 132*z**3 = 0 for z.
-2/5, 2, 3
Let j be 305/240 + 34/544. Suppose 1/3*k**3 + j*k + 0 - 5/3*k**2 = 0. What is k?
0, 1, 4
Let f(d) = -38*d**2 - 33*d + 23. Let v(j) = -20*j**2 + 9*j - 16*j + 12 - 9*j. Let h(w) = -4*f(w) + 7*v(w). Suppose h(y) = 0. Calculate y.
-2, 1/3
Let n(g) = 21*g + 166. Let y be n(18). Factor -1034*b**2 - 881*b**2 - 5*b**3 + y + 25*b**3 + 543*b**2 + 808*b.
4*(b - 68)*(b - 1)*(5*b + 2)
Let w(j) be the first derivative of j**6/10 + 9*j**5/5 + 27*j**4/2 + 54*j**3 + 243*j**2/2 + 103*j - 18. Let y(q) be the first derivative of w(q). Factor y(m).
3*(m + 3)**4
Let o(i) = -i**3 + i + 1. Let d(c) = -c**3 - 20*c**2 + 35*c + 3. Let l(r) = -d(r) + 3*o(r). Factor l(k).
-2*k*(k - 8)*(k - 2)
Let k = -697/954 + 101/106. Solve 2/9*g**5 + 2/9*g**4 + 0 - 2/9*g**3 + 0*g - k*g**2 = 0 for g.
-1, 0, 1
Let f be (18/(-8))/(147/24 + -6). Let m be f/(-20) + (-45)/(-30). What is r in 12/5*r - 3/5*r**4 + 0 - 3/5*r**3 + m*r**2 = 0?
-2, -1, 0, 2
Factor -4/3*t**3 - 2/3 + 4/3*t**2 - 2/3*t**4 + 2/3*t + 2/3*t**5.
2*(t - 1)**3*(t + 1)**2/3
Let q(d) = d - 1. Let t(w) = -2*w**2 - 16*w + 18. Let v = -16 + 24. Suppose v*j + 38 = 22. Let g(a) = j*q(a) + t(a). Suppose g(k) = 0. Calculate k.
-10, 1
Suppose 68/13 + 70/13*x + 2/13*x**2 = 0. What is x?
-34, -1
Let n = 1033/1235 - -238/247. Let n*u + 3/5*u**2 + 0 = 0. What is u?
-3, 0
Let a = 409846/3 + -136615. Suppose a*x**2 + 0 + 14/3*x = 0. Calculate x.
-14, 0
Let t be 40/(-66) + 20/(-330) + (-512)/(-624). Find k, given that 0 + 16/13*k - t*k**2 = 0.
0, 8
Let l(n) be the first derivative of n**6/90 + n**5/6 + 11*n**4/12 + 22*n**3/9 + 10*n**2/3 + 76*n + 286. Let i(f) be the first derivative of l(f). Factor i(u).
(u + 1)*(u + 2)**2*(u + 5)/3
Suppose 0 = -2*n + 19 + 5. Suppose 62*u - 9*u**2 + 83*u - n*u**3 - 103*u - 24 + 3*u**4 = 0. What is u?
-2, 1, 4
Suppose 4*f = 3*f + 5. Suppose -3*a + f = -4. Factor -2*r**2 + 8*r**2 + 1 + r**4 + r - 2*r - 3*r - 4*r**a.
(r - 1)**4
Factor -32*o**2 - 4*o**3 + 64*o + 1/2*o**4 + 384.
(o - 12)*(o - 4)*(o + 4)**2/2
Let o(h) be the first derivative of -3/2*h**2 - 1/9*h**3 + 47 + 3*h + 1/12*h**4. Factor o(s).
(s - 3)*(s - 1)*(s + 3)/3
Factor 826/5*z + 54*z**3 + 822/5*z**2 + 276/5 - 2/5*z**4.
-2*(z - 138)*(z + 1)**3/5
Let t(a) be the second derivative of 61 - a - 40/7*a**2 + 3/7*a**4 + 8/7*a**3 - 1/35*a**5. Suppose t(v) = 0. Calculate v.
-2, 1, 10
Let g(o) be the third derivative of o**8/168 - o**7/105 - 23*o**6/20 - 191*o**5/30 - 46*o**4/3 - 20*o**3 + 2*o**2 + 2*o - 9. Solve g(z) = 0 for z.
-6, -1, 10
Let x(j) be the first derivative of j**4/28 - 45*j**3/7 + 327*j**2/7 - 520*j/7 - 3276. Solve x(y) = 0.
1, 4, 130
Let t(c) be the second derivative of -c**4/42 - 10*c**3 - 1575*c**2 - 961*c. Solve t(j) = 0.
-105
Factor -11316/5*t - 2/5*t**2 - 16006482/5.
-2*(t + 2829)**2/5
Let b(y) be the first derivative of -y**6/21 - 2*y**5/5 - 9*y**4/14 + 2*y**3/3 + 10*y**2/7 - 537. Find w such that b(w) = 0.
-5, -2, -1, 0, 1
Let o be (-338)/(-264) + (-79)/2607. Let c(w) be the third derivative of 0*w**3 + 0 + 25*w**2 - 1/12*w**5 + 0*w + o*w**4. Factor c(s).
-5*s*(s - 6)
Find x, given that -1/6*x**4 - 1357/3*x**3 - 1844161/6*x**2 - 613364*x - 306456 = 0.
-1356, -1
Let w = 1/218 + 490/109. Let o = 1223 - 1219. Factor 6*n - 9*n**3 + 0 - 15/2*n**o + w*n**2.
-3*n*(n + 1)**2*(5*n - 4)/2
Let y(l) be the third derivative of -l**6/540 - 7*l**5/90 - 5*l**4/27 + 2619*l**2. Find m such that y(m) = 0.
-20, -1, 0
Let h = -572237/42 + 81827/6. Suppose 4*s**4 - 88/7*s**2 + h*s**3 + 2/7*s**5 - 28 - 50*s = 0. Calculate s.
-7, -1, 2
Let p be ((-1120)/(-4200))/((-1)/2 + 1048/(-432) + 3). What is t in 0*t + 0 - 3/5*t**4 + 3*t**3 - p*t**2 = 0?
0, 2, 3
Let b(c) = -723*c - 72*c**2 + 57 + 795*c + 9*c**2. Let m = 33 + -66. Let w(i) = 8*i**2 - 9*i - 7. Let f(n) = m*w(n) - 4*b(n). Factor f(u).
-3*(u - 1)*(4*u + 1)
Let g(t) = -11*t**4 - 13*t**3 + 67*t**2 - 2*t - 13. Let s(m) = -6*m**4 - 7*m**3 + 37*m**2 - m - 7. Let j(c) = 4*g(c) - 7*s(c). Suppose j(r) = 0. Calculate r.
-3, -1/2, 1
Let h(q) be the second derivative of -q**6/180 + 4*q**5/15 + 53*q**4/36 - 8*q**3/9 - 35*q**2/4 + q - 3454. Find s such that h(s) = 0.
-3, -1, 1, 35
Let g be (183426/63)/((-21410)/(-70) - 8). Let q = g + 2/695. Solve 20/9*f**4 + 0 + 0*f + q*f**3 + 32/9*f**2 = 0.
-4, -2/5, 0
Determine b so that -132/7*b**3 + 6/7*b**5 + 270/7 + 6/7*b**4 + 414/7*b + 12/7*b**2 = 0.
-5, -1, 3
Let c(b) be the first derivative of 1/5*b**3 + 3 + 18*b + 4/5*b**2 + 1/60*b**4. Let v(p) be the first derivative of c(p). Let v(h) = 0. Calculate h.
-4, -2
Let x(s) be the first derivative of -s**4/7 + 8*s**3/21 + 6*s**2/7 - 924. Suppose x(f) =