4*m + 6 + 2*m. Let w be n(-6). Determine h, given that w*h**2 - 1/3*h**3 + 0*h + 0 = 0.
0
Let m(g) be the second derivative of -g**7/147 + g**6/35 - 3*g**5/70 + g**4/42 - 39*g. Determine n, given that m(n) = 0.
0, 1
Let d be 466/(-1680) + 14/49. Let r(g) be the third derivative of 1/24*g**4 - d*g**5 - g**2 - 1/12*g**3 + 0 + 0*g. Factor r(k).
-(k - 1)**2/2
Let z be (4/(1 - -7))/((-2)/(-8)). Let 2/9*x**z + 0 + 4/9*x = 0. Calculate x.
-2, 0
Determine v so that -4/3 - 4/3*v + 1/3*v**3 + 1/3*v**2 = 0.
-2, -1, 2
Suppose -13*h + 6*h**5 + 8*h**2 + 16*h**3 - 11*h**5 - 8*h**4 + h + h**5 = 0. Calculate h.
-3, -1, 0, 1
Let r(o) = -4*o**4 + 9*o**3 - 7*o**2 - 15*o + 11. Let n(u) = 20*u**4 - 44*u**3 + 36*u**2 + 76*u - 56. Let p(y) = 3*n(y) + 16*r(y). Factor p(m).
-4*(m - 2)*(m - 1)**2*(m + 1)
Let w(u) be the first derivative of 6/5*u**5 + 0*u + 1/2*u**6 + 0*u**3 - 4 + 3/4*u**4 + 0*u**2. Find r, given that w(r) = 0.
-1, 0
Let r(m) be the first derivative of 3 - 3/2*m**4 + 3/10*m**5 - 6*m + 3/2*m**3 + 3*m**2. Factor r(j).
3*(j - 2)**2*(j - 1)*(j + 1)/2
Let i(o) be the third derivative of o**6/320 + 3*o**5/160 - o**3/4 + 9*o**2. Factor i(u).
3*(u - 1)*(u + 2)**2/8
Suppose 2*j - 5*m + m = 12, 5*j = 4*m + 24. Find r, given that 1/2*r**2 - 1/2*r**5 - 3/2*r**3 + 0*r + 0 + 3/2*r**j = 0.
0, 1
Factor 2*w**3 + 4/9*w**2 - 4/9 - 2*w.
2*(w - 1)*(w + 1)*(9*w + 2)/9
Let i(u) = -2*u**3 + 6*u**2 + 20*u + 4. Let f(d) = 3*d**3 - 13*d**2 - 39*d - 9. Let o(k) = -4*f(k) - 7*i(k). Factor o(t).
2*(t + 1)*(t + 2)**2
Let s = 1001/3 - 333. Suppose -1/3*m + 0*m**3 + s*m**2 + 1/3*m**5 + 0 - 2/3*m**4 = 0. Calculate m.
-1, 0, 1
Suppose 2*u - 3*l + 7*l = -16, -3*u + l + 4 = 0. Let a(b) be the third derivative of -1/4*b**4 + 2/3*b**3 + 1/30*b**5 + 0 + 4*b**2 + u*b. Factor a(f).
2*(f - 2)*(f - 1)
Let h(r) be the third derivative of -r**8/28 + 16*r**7/105 + 3*r**6/5 - 4*r**5/15 - 5*r**4/2 - 8*r**3/3 + 30*r**2. Let h(c) = 0. Calculate c.
-1, -1/3, 1, 4
Let h(t) be the third derivative of -t**9/672 - t**8/224 - t**7/560 + t**6/240 - t**3/6 + t**2. Let o(b) be the first derivative of h(b). Factor o(p).
-3*p**2*(p + 1)**2*(3*p - 1)/2
Let c(h) = 10*h**4 + h**3 - 30*h**2 + 10*h + 20. Let w(z) = -2*z**4 + 6*z**2 - 2*z - 4. Let y(k) = -4*c(k) - 22*w(k). What is a in y(a) = 0?
-1, 1, 2
What is g in 2/7*g**3 + 0 - 6/7*g**4 + 2/7*g**5 + 6/7*g**2 - 4/7*g = 0?
-1, 0, 1, 2
Let u(c) = -4*c - 1. Let n be u(-3). Let t = n - 9. Let -1/5*z**t + 0 + 0*z - 1/5*z**3 = 0. What is z?
-1, 0
Let x(o) = o**2 - 4*o + 3. Let w(m) = m**3 - 9*m**2 + m - 6. Let v be w(9). Let z be x(v). Solve z*y + 1/2*y**2 + 0 = 0 for y.
0
Let s(u) be the second derivative of u**7/21 - 26*u**6/105 + 17*u**5/35 - 8*u**4/21 - u**3/21 + 2*u**2/7 - 22*u. Solve s(r) = 0 for r.
-2/7, 1
Let z(u) be the second derivative of 0*u**3 + 3/10*u**5 + 0*u**2 - 5*u + 0 - 1/3*u**4. Factor z(q).
2*q**2*(3*q - 2)
Let g(u) be the first derivative of -u**6/4 + 3*u**5/10 + 3*u**4/8 - u**3/2 - 13. Find a, given that g(a) = 0.
-1, 0, 1
Factor 12*m + 8*m**2 + 3*m**4 - 11*m**2 - 3*m**3 - 9*m**2.
3*m*(m - 2)*(m - 1)*(m + 2)
Let u = -19 - -21. Let c(a) be the second derivative of 0 - 1/40*a**5 - 4*a - 1/4*a**u - 1/4*a**3 - 1/8*a**4. Factor c(p).
-(p + 1)**3/2
Let i(u) be the first derivative of -2/21*u**3 + 2/7*u**2 + 2 + 0*u. Find j, given that i(j) = 0.
0, 2
Let m be (-6)/27 + 130/18. Suppose 9 + m = 4*f. Let 0*j**3 + 0 - 2/7*j + 4/7*j**f + 2/7*j**5 - 4/7*j**2 = 0. What is j?
-1, 0, 1
Let h = -153 + 463/3. Factor 2/3*k - 4/3 - 2/3*k**3 + h*k**2.
-2*(k - 2)*(k - 1)*(k + 1)/3
Suppose 34*p - 44*p + 20 = 0. Factor 0 + 2/15*l + 0*l**p - 2/15*l**3.
-2*l*(l - 1)*(l + 1)/15
Let b be (-3287)/779 + (-4)/(-1). Let l = 199/533 + b. Let -4/13*f**2 + 0*f + 0 - l*f**3 = 0. Calculate f.
-2, 0
Let b(s) be the first derivative of -s**4/4 - s**3 - 3*s**2/2 + 2*s - 4. Let h(n) be the first derivative of b(n). Factor h(r).
-3*(r + 1)**2
Let p be 2*2*(-3)/(-4). Factor 8*h + 8 + p*h**2 + 0*h - h**2.
2*(h + 2)**2
Let t(d) be the third derivative of -d**6/30 + d**4/2 + 4*d**3/3 + 5*d**2. Determine i, given that t(i) = 0.
-1, 2
Let v(z) be the third derivative of 0*z + z**2 + 0*z**4 + 1/480*z**5 + 1/1440*z**6 + 0 + 1/3*z**3. Let f(s) be the first derivative of v(s). Factor f(r).
r*(r + 1)/4
Let x be 2/(-7) - (3 + (-37)/7). Let b(c) be the second derivative of -3/2*c**x + 0 - 1/12*c**4 - 2/3*c**3 - 2*c. Let b(k) = 0. Calculate k.
-3, -1
Let i(k) be the third derivative of k**7/420 + k**6/20 + 9*k**5/20 + 9*k**4/4 + 27*k**3/4 + 19*k**2. Determine w so that i(w) = 0.
-3
Let c(v) be the second derivative of -3/2*v**3 + 3/4*v**4 + 3*v + 3/2*v**2 - 3/20*v**5 + 0. Factor c(o).
-3*(o - 1)**3
Let b(t) be the third derivative of t**6/60 - 3*t**5/10 + 2*t**4 - 16*t**3/3 - 5*t**2. Factor b(z).
2*(z - 4)**2*(z - 1)
Let n(x) be the first derivative of x**5/10 - x**4/4 - x**3/2 + x**2 + 2*x - 41. Find h such that n(h) = 0.
-1, 2
Let a(l) be the second derivative of l**6/720 + l**5/240 - l**3/2 - 2*l. Let x(g) be the second derivative of a(g). Factor x(q).
q*(q + 1)/2
Let y(s) = s**3 + s**2 + s. Let m(o) = 7*o**3 - o**2 + 9*o. Let i be ((-6)/15)/(2/40). Let k = -3 - i. Let u(z) = k*y(z) - m(z). Suppose u(t) = 0. Calculate t.
0, 1, 2
Suppose 4*m + 40 = -2*k, -88 = 4*k + k + 4*m. Let j be (-1)/(-4) + (-28)/k. Factor -j*u**2 - 3*u**4 + 2*u**2 + u**5 + 2*u**4.
u**4*(u - 1)
Suppose 1042*a**2 + 5*a - 3*a**4 - 10*a**3 + 4*a + 5 + a**5 - 1044*a**2 = 0. What is a?
-1, 1, 5
Let k be -2 + 7/4 + 22/24. Find a such that 8/3*a**3 + 8/3*a + k + 2/3*a**4 + 4*a**2 = 0.
-1
Suppose -3*y + 76 = 2*z, 0 = 2*z - 7*z + 10. Suppose 0*j + y = 2*j. Suppose -1 + k + 10*k - 4 + j*k**2 + 7 = 0. What is k?
-2/3, -1/4
Let z(u) be the first derivative of u**5/25 + u**4/2 + 32*u**3/15 + 16*u**2/5 - 13. What is b in z(b) = 0?
-4, -2, 0
Suppose -5*k**3 - k**5 + 2*k**3 + 7*k**2 - 2*k + 6*k**5 - 7*k**4 = 0. Calculate k.
-1, 0, 2/5, 1
Let t(r) = -4*r - 2. Let y be t(-3). Suppose -5*u + 22 = v, 0 = u + 4*u + 5*v - y. Let 0*k - 4*k**3 + 2*k**u - k + 3*k = 0. Calculate k.
-1, 0, 1
Let p(d) = 8*d**5 - 2*d**4 - 9*d**3 + 11*d**2 - 8*d. Suppose 0 = 2*o + 14 + 22. Let j(m) = m**5 - m**3 + m**2 - m. Let h(c) = o*j(c) + 2*p(c). Factor h(y).
-2*y*(y - 1)*(y + 1)**3
Let y(f) be the second derivative of 1/8*f**2 + 0 - 1/48*f**4 + 3*f + 0*f**3. Find o such that y(o) = 0.
-1, 1
Suppose 3*r + 0*x - 5*x = 40, 3*r - 4*x = 35. Suppose d - r = -3*c, 2 = 5*c - 2*d + 1. Factor c + z**2 - 6*z + 2 + 6.
(z - 3)**2
Let l = 7427/9 - 824. Let w(f) be the first derivative of 4/3*f - 1 - l*f**3 + 3/5*f**5 - 2/3*f**2 + 1/2*f**4. Find m such that w(m) = 0.
-1, 2/3
Let x(y) be the second derivative of y**9/3024 - y**8/840 + y**7/840 - y**3/3 - y. Let g(o) be the second derivative of x(o). Factor g(b).
b**3*(b - 1)**2
Factor -4/3*s**3 - 2/3*s + 0 + 2*s**2.
-2*s*(s - 1)*(2*s - 1)/3
Suppose 9 + 1 = 5*t. Let n = -34 + 104/3. Let -2/3*h**t - n*h + 0 = 0. What is h?
-1, 0
Suppose 3*t + 4 = -t. Let l(m) = -7*m**2 + 14*m - 4. Let j(z) = -z**2. Let s(a) = t*l(a) - 3*j(a). Factor s(p).
2*(p - 1)*(5*p - 2)
Let y(x) = -21*x + 23. Let r be y(1). Determine i, given that -8/5*i - 2/5*i**r - 6/5 = 0.
-3, -1
Let t(h) be the third derivative of -h**7/2100 + h**6/180 - 7*h**5/300 + h**4/20 - h**3/6 - 3*h**2. Let d(i) be the first derivative of t(i). Factor d(z).
-2*(z - 3)*(z - 1)**2/5
Let w(s) = -4*s**4 + 8*s**2 - 4. Let o(p) = 2*p**4 - 4*p**2 + 2. Let t(g) = -13*o(g) - 6*w(g). Solve t(y) = 0 for y.
-1, 1
Suppose -2*s + 8 = -12. Suppose -2*w = -s, -5*w + 25 = h - 2*h. Determine y so that -1/3*y + h - 1/6*y**2 = 0.
-2, 0
Let m(o) be the third derivative of -o**7/5880 - o**6/840 + o**4/12 - 5*o**2. Let s(u) be the second derivative of m(u). Find v, given that s(v) = 0.
-2, 0
Suppose 0 = -29*p + 28*p. Let c(a) be the second derivative of 0*a**2 + 0 + 0*a**4 - 2*a + p*a**3 + 1/60*a**6 - 1/40*a**5. Factor c(k).
k**3*(k - 1)/2
Let y(o) = -o**4 + 17*o**3 + o**2 + o. Let u be 13 - 2 - (1 + 1). Let v(n) = -4*n**3. Let h(g) = u*v(g) + 2*y(g). Factor h(s).
-2*s*(s - 1)*(s + 1)**2
Let b(y) = -y**4 - 114*y**3 - 605*y**2 - 4*y - 4. Let u(m) = 15*m**4 + 1595*m**3 + 8470*m**2 + 55*m + 55. Let r(p) = -55*b(p) - 4*u(p). Factor r(o).
-5*o**2*(o + 11)**2
Let q = 62 - 58. Let f(h) be the third derivative of 1/3