) be the second derivative of j**5/170 + 7*j**4/34 + 45*j**3/17 + 275*j**2/17 - 32*j. What is o in w(o) = 0?
-11, -5
Let a = -292 - -189. Let c = 209/2 + a. Suppose 0 - c*l**5 + 3*l**4 - 3/2*l**3 + 0*l**2 + 0*l = 0. What is l?
0, 1
Let b(v) be the first derivative of -16*v - 1 - 32*v**2 + 56*v**4 + 28/3*v**6 + 212/5*v**5 + 20/3*v**3. Solve b(y) = 0.
-2, -1, -2/7, 1/2
Let o = 1068 + -1068. Let c(f) be the third derivative of 2*f**2 + 0*f + 1/30*f**5 - 1/12*f**4 + o*f**3 + 0. Determine z, given that c(z) = 0.
0, 1
Let n(k) be the first derivative of 3*k**5/5 - 9*k**4 + 27*k**3 + 365. Find y, given that n(y) = 0.
0, 3, 9
Let q be (-9)/2*8/(-12). Let o(c) be the first derivative of -2 + c**q + 5*c**2 - 3 - 2*c**2 - 8. Solve o(p) = 0 for p.
-2, 0
Let a(p) be the second derivative of 2*p**6/15 + p**5/5 - p**4 - 2*p**3/3 + 4*p**2 - 66*p. Factor a(d).
4*(d - 1)**2*(d + 1)*(d + 2)
Let b(h) be the second derivative of h**7/1260 + h**6/90 + h**5/15 + 5*h**4/6 + 18*h. Let v(w) be the third derivative of b(w). Factor v(f).
2*(f + 2)**2
Factor 4*p**4 + 26*p**2 - 6*p**4 - 38*p + 14*p.
-2*p*(p - 3)*(p - 1)*(p + 4)
Let y(z) be the second derivative of z**4/12 - 11*z**3/3 + 21*z**2/2 - 162*z. Factor y(b).
(b - 21)*(b - 1)
Let o(w) = -w**3 + 11*w - w + w**2 - 9*w + 1. Let h(m) = -9*m**3 + 5*m**2 + 6*m + 8. Let s(f) = 3*h(f) - 24*o(f). Solve s(n) = 0 for n.
-2, -1, 0
Let z(v) be the third derivative of 0 + 6/5*v**3 + 5/112*v**8 + 0*v - 4/5*v**4 + 5*v**2 + 79/200*v**6 + 3/10*v**7 - 9/20*v**5. Determine m, given that z(m) = 0.
-3, -1, 2/5
Let i(k) be the first derivative of 3*k**5/5 + 9*k**4/4 - k**3 - 9*k**2/2 + 91. Factor i(p).
3*p*(p - 1)*(p + 1)*(p + 3)
Let g(q) = q**3 - 4*q**2 - 12. Let z be g(6). Suppose -z*w**3 + 64*w**3 + 0*w**4 + w**4 + 5*w**2 + 2*w = 0. What is w?
-2, -1, 0
Let a(x) = 117*x**3 - 12*x**2 - 8*x - 9. Let y(p) = -29*p**3 + 3*p**2 + 2*p + 2. Let g(q) = -2*a(q) - 9*y(q). Let g(i) = 0. What is i?
-2/9, 0, 1/3
Let o(m) be the second derivative of m**7/42 + m**6/10 - m**5/5 + 245*m. Factor o(f).
f**3*(f - 1)*(f + 4)
Let w(n) be the first derivative of 0*n + 0*n**2 + 4*n**3 + 4/15*n**5 - 2 + 2*n**4. Let w(x) = 0. Calculate x.
-3, 0
Solve 0*t + 5/3*t**5 + 880*t**3 + 75*t**4 + 2420/3*t**2 + 0 = 0.
-22, -1, 0
Let n(z) = 3*z**2 + 16*z - 14. Let g be n(-8). Let u be 3/2*(-2 - g/(-24)). Factor 3/8*x - 1/8 - 3/8*x**2 + u*x**3.
(x - 1)**3/8
Factor 26*f**3 - 29*f**3 - 111*f**2 + 2*f + f + 20 + 91.
-3*(f - 1)*(f + 1)*(f + 37)
Let b(o) = o**3 + 3*o**2 - 8*o - 19. Let h be b(-3). Suppose 0 = -2*v + 3*n + 6 - 12, 3*v + h*n = 29. Factor -16/13*j**2 + 8/13*j**v - 2/13 + 10/13*j.
2*(j - 1)*(2*j - 1)**2/13
Factor 8*s + 2/3*s**3 + 0 - 14/3*s**2.
2*s*(s - 4)*(s - 3)/3
Let s(a) = -a**5 + a**4 - a**3 - 5*a**2 + 14*a + 4. Let f(i) = 3*i**5 - 2*i**4 + 4*i**3 + 14*i**2 - 41*i - 12. Let x(h) = -6*f(h) - 17*s(h). Factor x(o).
-(o - 1)*(o + 1)**2*(o + 2)**2
Let b(y) be the first derivative of 3*y**5/35 + 9*y**4/14 + 5*y**3/7 - 36*y**2/7 - 108*y/7 - 200. Factor b(r).
3*(r - 2)*(r + 2)*(r + 3)**2/7
Let l be -2 + (0 - -5) + -3. Suppose 2*w + 7*w = l. Factor 0 + w*r + 3/2*r**2 + 0*r**3 - 3/2*r**4.
-3*r**2*(r - 1)*(r + 1)/2
Find m, given that 4/7*m - 92/7*m**2 - 47/7*m**3 + 0 = 0.
-2, 0, 2/47
Suppose 6*d - 7 = 5. Determine k, given that -5 + k**3 + 11*k**3 + 5*k**4 - 10*k - d*k**3 + 0*k**3 = 0.
-1, 1
Suppose 3*m - a - 2 = 0, -4*a - 8 = 3*m - 4*m. Let o(b) be the second derivative of m + 0*b**2 - 2/15*b**3 - 1/10*b**4 - 5*b - 1/50*b**5. Factor o(d).
-2*d*(d + 1)*(d + 2)/5
Suppose -56 = 8*f - 22*f. Let j(p) be the third derivative of -1/120*p**6 + 0 + 2/3*p**3 + 0*p - 6*p**2 + 1/12*p**5 - 1/3*p**f. Determine r so that j(r) = 0.
1, 2
Let w(x) be the first derivative of -25*x**4/4 - 5*x**3/9 + 10*x**2 + 20*x/3 + 367. Solve w(p) = 0 for p.
-2/3, -2/5, 1
Factor 115*n - 4*n**2 - 32 - 154*n + 119 + 69 + 79*n.
-4*(n - 13)*(n + 3)
Let a = 2767/5 + -553. Let w(y) be the third derivative of 0*y + 1/70*y**7 + 0*y**3 + 0 + a*y**5 - 5*y**2 + 1/2*y**4 + 1/8*y**6. Factor w(r).
3*r*(r + 1)*(r + 2)**2
Let t be (-6)/(-27) - (-8)/18. Suppose -131*z + 113 = -411. Solve -4/9*y + 2/9*y**5 + 2/3*y**2 - t*y**z + 2/9*y**3 + 0 = 0 for y.
-1, 0, 1, 2
Let t(h) be the first derivative of 0*h**2 + 1/48*h**4 + 1 + 1/12*h**3 + 2*h. Let g(q) be the first derivative of t(q). Factor g(v).
v*(v + 2)/4
Let s(i) be the second derivative of i**6/42 - 11*i**5/35 + 37*i**4/28 - 38*i**3/21 - 10*i**2/7 + 4*i + 18. Factor s(z).
(z - 5)*(z - 2)**2*(5*z + 1)/7
Let b(q) = 28*q**2 - q - 1. Let n be b(-1). Let k = n - 25. Suppose -2*x**k - 17*x + 18*x + 3*x**5 - 2*x**5 = 0. What is x?
-1, 0, 1
Let q(l) = -l**2 + 1. Let r(h) be the third derivative of h**6/60 - 7*h**5/60 + 3*h**3/2 + 13*h**2. Let x(z) = 18*q(z) - 2*r(z). Suppose x(c) = 0. What is c?
-1, 0
Let r = -3/791 + 800/2373. Find b, given that 0*b - 1/3*b**3 - r*b**4 + 0 + 2/3*b**2 = 0.
-2, 0, 1
Let f(t) = -t + 9. Let x be f(14). Let i(g) = -13*g**2 - 67*g - 157. Let y(q) = -9*q**2 - 45*q - 105. Let h(m) = x*i(m) + 7*y(m). Factor h(b).
2*(b + 5)**2
Let n = -14 + 18. Factor n*x**3 - 43 + 0*x**3 - 2*x**4 - 2*x**2 + 43.
-2*x**2*(x - 1)**2
Suppose 200/7 - 2*z**2 - 696/7*z = 0. What is z?
-50, 2/7
Let x(c) be the first derivative of -2/9*c**3 + 5/6*c**4 - 5/3*c**2 + 0*c + 5 + 2/15*c**5. Factor x(g).
2*g*(g - 1)*(g + 1)*(g + 5)/3
Let t(x) be the third derivative of -x**5/30 - 23*x**4/6 - 529*x**3/3 - 5*x**2 - 7. What is y in t(y) = 0?
-23
Let j = 18054 + -126376/7. Factor -10/7 - 2*i**2 + j*i**3 + 22/7*i.
2*(i - 5)*(i - 1)**2/7
Let a(b) = -10*b**2 + 97*b + 30. Let w be a(10). Suppose n + 1/3*n**2 + w = 0. What is n?
-3, 0
Let x(f) be the first derivative of 2/5*f**5 + 16/9*f + 164/27*f**3 - 32 - 47/18*f**4 - 52/9*f**2. Suppose x(z) = 0. Calculate z.
2/9, 1, 2
Factor 45*r - 2025/2 - 1/2*r**2.
-(r - 45)**2/2
Factor 3/7*f**5 - 186/7*f**4 + 5952/7*f**2 + 2691/7*f**3 + 0 + 3072/7*f.
3*f*(f - 32)**2*(f + 1)**2/7
Let l(z) be the second derivative of -3*z**5/140 + 6*z**3/7 + 24*z**2/7 + 74*z + 2. Factor l(g).
-3*(g - 4)*(g + 2)**2/7
Suppose -3 - 2 = -59*n - 5. Factor n + 2/9*r**2 - 2/9*r.
2*r*(r - 1)/9
Let u be 0/2*4/16. Suppose -2*a + u = -4. Suppose 6 - 5*k**a - 9 - 20*k - 12 - 5 = 0. What is k?
-2
Let f(t) = t**3 - 4*t**2 + 2. Let w be f(4). Let y = -55 + 221/4. Let 0*s + y - 1/4*s**w = 0. Calculate s.
-1, 1
Factor 256 + 9*l**2 + 3*l**2 - 32*l + 4*l**2 - 15*l**2.
(l - 16)**2
Let j = 218 + -210. Let f(k) be the third derivative of 5/24*k**4 + 1/3*k**3 - 3/20*k**5 + 1/30*k**7 - 1/24*k**6 + 0 + 0*k + j*k**2. Factor f(a).
(a - 1)**2*(a + 1)*(7*a + 2)
Let x = -1843/20 - -462/5. Factor -x*l**2 + 0*l + 0.
-l**2/4
Factor -1/2*k**2 - 7*k + 0.
-k*(k + 14)/2
Let t be (-2)/(-13) + 1/(52/4360). Let i be 38/t - (-12)/(-72). Find j such that i*j + 0*j**2 - 2/7*j**3 + 0 = 0.
-1, 0, 1
What is b in 9/4*b + 9/2 + 1/4*b**2 = 0?
-6, -3
Let g(y) = y**3 + 9*y**2 + 12*y. Let x be g(-5). Factor -10*m**3 - 6*m**2 + 47*m - 63*m + x*m - 8.
-2*(m - 1)*(m + 2)*(5*m - 2)
Let h be (-1 - 0 - 0)*-3. Solve 5*a**4 + 33*a**3 - 11*a**h - 17*a**3 - 5*a**2 - 2*a**5 - 3*a**5 = 0.
-1, 0, 1
Let o(u) be the first derivative of -54*u**3/19 + 80*u**2/19 + 2*u/19 + 989. Factor o(b).
-2*(b - 1)*(81*b + 1)/19
Let v(t) be the first derivative of 3/20*t**4 + 72/5*t**2 - 13/5*t**3 - 108/5*t - 29. Factor v(s).
3*(s - 6)**2*(s - 1)/5
Let f(p) = 3*p**2 - 8*p + 9. Let y(m) = -25*m**2 + 65*m - 72. Let t be (4/3)/((-4)/(-18)). Let j(n) = t*y(n) + 51*f(n). Let j(a) = 0. Calculate a.
3
Suppose 5*h + 5*x = 5, -4*x = h - x + 1. Find l such that 3*l + 12 + h*l**2 - 13*l - 7*l + 3*l = 0.
1, 6
Suppose -198*o = -4*i - 201*o + 3, -15 = 5*o. Factor 1/3*s**2 + i - 2*s.
(s - 3)**2/3
Find u such that -76 + 76 - 54*u + 114*u - 4*u**2 = 0.
0, 15
Let b(a) = -3*a**3 + 13*a - 2 + a**4 + 9*a**4 - 7. Let x(o) = 51800*o**2 + 1 - o - o**4 - 51800*o**2. Let i(l) = 2*b(l) + 18*x(l). Find m such that i(m) = 0.
-1, 0, 2
Let w(l) = -5*l**4 + 25*l**3 - l**2 - 88*l + 78. Let r(n) = -n**4 + 6*n**3 - n**2 - 22*n + 20. Let z(h) = 9*r(h) - 2*w(h). Suppose z(o) = 0. What is o?
-4, -3, 1, 2
Factor -731*l**3 - 16*l**2 + 340*l**3 + 6*l**4 - 14*l**4 + 355*l**3.
-4*l**2*(l + 4)*(2*l + 1)
Let w be (42/56 - (-24)/(-33))/(1/8). Solve -8/11*x**2 - 4/11 - w*x**3 - 10/11*x = 0 for