derivative of -17/60*m**6 + 0 + 0*m + 7/10*m**n + 2/3*m**3 - 11/12*m**4 + 2*m**2 + 1/21*m**7. Factor u(b).
2*(b - 1)**3*(5*b - 2)
Suppose 5*c - 12 + 5*c**2 + 27 - 15 = 0. Calculate c.
-1, 0
Find i, given that 8*i**4 + 2*i**5 - 8*i + 1 + 6*i**3 - 8*i**2 - 1 = 0.
-2, -1, 0, 1
Let w(c) = -c + 4. Let h be w(4). Let d be 0 - h - 12/(-27). Factor 2/9*u**4 + d*u**3 - 2/9*u**5 - 4/9*u**2 + 2/9 - 2/9*u.
-2*(u - 1)**3*(u + 1)**2/9
Factor 16/3*r - 2/3*r**2 - 32/3.
-2*(r - 4)**2/3
Factor -a**2 + 1 + 1/4*a - 1/4*a**3.
-(a - 1)*(a + 1)*(a + 4)/4
Let l(o) = 14*o**3 - 7*o**3 - 9*o**2 + 9*o**4 - 4*o**5 + 2*o**5. Let a(z) = z**5 - 4*z**4 - 3*z**3 + 4*z**2. Let d(m) = 5*a(m) + 2*l(m). Factor d(t).
t**2*(t - 2)*(t - 1)*(t + 1)
Suppose 3*m = -23*m + 104. Factor -25/3*q**2 - 1/3*q**5 - 16/3*q - 19/3*q**3 - 7/3*q**m - 4/3.
-(q + 1)**3*(q + 2)**2/3
Let j(z) be the first derivative of z**6/9 - 2*z**5/5 - 5*z**4/6 + 2*z**3/3 + 4*z**2/3 + 35. Let j(w) = 0. Calculate w.
-1, 0, 1, 4
Let c(f) be the second derivative of f**4/20 - f**3/5 + 7*f. Find m such that c(m) = 0.
0, 2
Let t(z) be the second derivative of z**6/240 - z**4/4 - z**3/6 + 3*z. Let b(a) be the second derivative of t(a). Factor b(r).
3*(r - 2)*(r + 2)/2
Let o(h) = 14*h**5 + 42*h**4 + 58*h**3 + 50*h**2 + 24*h - 2. Let g(r) = -r**5 - r**4 + r**3 + r**2 + 1. Let w(f) = -6*g(f) - o(f). Find t, given that w(t) = 0.
-1, -1/2
Suppose 4*k - 25 = -5*t - k, -8 = 2*t - 4*k. Find u such that 1/3*u**5 + 10/3*u**3 - 5/3*u**4 + 5/3*u - 10/3*u**t - 1/3 = 0.
1
Let m(x) be the third derivative of 0 + 1/24*x**4 + 1/210*x**7 - 3*x**2 - 1/1008*x**8 - 1/18*x**3 + 0*x - 1/180*x**6 - 1/90*x**5. What is k in m(k) = 0?
-1, 1
What is z in -18*z**2 - 4*z**3 - 37 + 3*z**5 + 82 - 36 + 9*z**4 + 3*z - 2*z**3 = 0?
-3, -1, 1
Solve -675/7 - 3/7*p**3 + 87/7*p**2 - 585/7*p = 0.
-1, 15
Let t(q) be the third derivative of -q**8/50400 - q**7/3150 - q**6/600 + 7*q**5/60 - 3*q**2. Let x(l) be the third derivative of t(l). Factor x(b).
-2*(b + 1)*(b + 3)/5
Let a(r) = r**2 - 9*r - 4. Let v be a(11). Let p be 4/(-18) - (-31)/v. Let -p*s**3 - s**2 - 1/4*s**5 + 0 - s**4 - 1/4*s = 0. What is s?
-1, 0
Let i(p) be the third derivative of 2/105*p**7 + 0*p + 0 + 2/3*p**3 + 2/3*p**4 + 2/15*p**6 - 9*p**2 + 2/5*p**5. Factor i(g).
4*(g + 1)**4
Let v(d) be the second derivative of -d**5/60 + d**4/9 - d**3/6 - 31*d. What is z in v(z) = 0?
0, 1, 3
Let z = -404/7 + 1637/28. What is c in z*c**5 + 0 - 3/4*c**2 + 3/4*c**4 + 0*c - 3/4*c**3 = 0?
-1, 0, 1
Let j(r) be the second derivative of 3*r**5/20 + 5*r**4/4 - r**3/2 - 15*r**2/2 + 48*r. Factor j(g).
3*(g - 1)*(g + 1)*(g + 5)
Let b(q) = 8*q**2 + 5. Let j(w) = 7*w**2 + 4. Let a(h) = -4*b(h) + 5*j(h). Solve a(l) = 0.
0
Let c(z) be the third derivative of z**7/3360 - z**6/480 + z**5/240 - z**3/6 + 3*z**2. Let o(s) be the first derivative of c(s). Factor o(b).
b*(b - 2)*(b - 1)/4
What is q in 2 + 8/3*q + 2/3*q**2 = 0?
-3, -1
Let v(o) be the first derivative of o**6/30 + 3*o**5/25 - 3*o**4/20 - 7*o**3/15 + 3*o**2/5 + 35. Factor v(k).
k*(k - 1)**2*(k + 2)*(k + 3)/5
Solve 6*n**3 - 6 + 0*n - 4*n**3 + n**3 - 9*n = 0.
-1, 2
Let r be 9/4 + (-12)/(-16). Suppose r = 3*w - 2*w. Factor 0 + 2/7*l**w + 2/7*l**2 + 0*l.
2*l**2*(l + 1)/7
Let t = -110 - -112. Let g(j) be the first derivative of 2 - 4/21*j**3 + 0*j + 1/7*j**t + 1/14*j**4. Factor g(r).
2*r*(r - 1)**2/7
Let o(r) be the second derivative of r**8/448 + r**7/105 + r**6/80 - r**4/96 - 3*r**2/2 + 2*r. Let g(k) be the first derivative of o(k). Factor g(i).
i*(i + 1)**3*(3*i - 1)/4
Factor 0*d - 5/2*d**4 + 0 - 5*d**2 + 15/2*d**3.
-5*d**2*(d - 2)*(d - 1)/2
Let p(l) be the second derivative of -1/42*l**4 + 0 + 4/21*l**3 - 2*l - 4/7*l**2. Find m, given that p(m) = 0.
2
Let f = 13 - 13. Let p = 73/237 + 2/79. Find b such that f - 1/3*b**4 + 1/3*b**3 - p*b + 1/3*b**2 = 0.
-1, 0, 1
Let x(w) = w**2 - 5*w - 4. Let r be 80/14 - (-6)/21. Let u be x(r). Let 2*l + 0*l**3 + 0*l**3 - 4*l**2 + u*l**3 = 0. What is l?
0, 1
Let o(q) = -21*q**2 - 30*q + 33. Let m(b) = -b**2 - b + 1. Let n(d) = -18*m(d) + o(d). Factor n(i).
-3*(i - 1)*(i + 5)
Let a(q) be the second derivative of 0*q**2 - 1/2*q**3 + 0 + 1/4*q**4 - 2*q. Determine r so that a(r) = 0.
0, 1
Let z(q) be the first derivative of -q**6/90 + q**5/20 - q**4/12 + q**3/18 - q - 1. Let v(d) be the first derivative of z(d). Factor v(o).
-o*(o - 1)**3/3
Suppose -20 = -2*x + 30. Suppose 0*i - 5*i = -x. Suppose -5/2*l**4 - 3/2*l**3 + 5/2*l**2 - 1/2*l + 0 + 2*l**i = 0. Calculate l.
-1, 0, 1/4, 1
Let z(j) = 9*j**2 - 43*j + 44. Let u(i) = -i**2 - i. Let b(l) = 5*u(l) + z(l). Let b(x) = 0. What is x?
1, 11
Let c(v) be the second derivative of -2*v + 0*v**2 + 0*v**3 - 1/10*v**5 + 0 + 1/12*v**4 + 1/30*v**6. Let c(l) = 0. Calculate l.
0, 1
Let m = 32 - 59/2. Let n = m + -2. Determine x, given that n*x**2 + 0 - 1/4*x**5 + 1/4*x + 0*x**3 - 1/2*x**4 = 0.
-1, 0, 1
Factor -6*s**4 - 2*s**2 - 4 + 18*s**4 + 12*s + 2*s**2 - 4*s**5 - 8*s**3 - 8*s**2.
-4*(s - 1)**4*(s + 1)
Let s(v) be the third derivative of v**7/1260 + v**6/360 - v**4/72 - v**3/36 - 18*v**2. What is r in s(r) = 0?
-1, 1
Let b = 5/3 + -19/12. Let l(m) be the first derivative of 1/10*m**5 + 0*m + b*m**6 - 1/8*m**4 - 2 + 0*m**2 - 1/6*m**3. Factor l(h).
h**2*(h - 1)*(h + 1)**2/2
Let t(z) be the second derivative of 2*z**7/189 + 8*z**6/135 + z**5/45 - 10*z**4/27 - 8*z**3/27 + 16*z**2/9 - z. Find c, given that t(c) = 0.
-2, 1
Let h(s) be the first derivative of s**4/54 - 2*s**3/27 + s**2/9 + 5*s + 5. Let c(k) be the first derivative of h(k). Factor c(n).
2*(n - 1)**2/9
Suppose 1 - 1/2*b**4 + 5/2*b - 1/2*b**3 + 3/2*b**2 = 0. Calculate b.
-1, 2
Let t(c) = c**3 + 6*c**2 + 8*c - 5. Let k be t(-4). Let s(o) = -2*o**2 - 12*o + 6. Let u(h) = h**2 + 8*h - 4. Let p(x) = k*s(x) - 8*u(x). Factor p(v).
2*(v - 1)**2
Let y(i) be the second derivative of i**6/30 - i**5/10 - 9*i. Let y(n) = 0. Calculate n.
0, 2
Let r(p) = -18*p**3 + 11*p - 3. Let y(u) = 12*u**3 - 7*u + 2. Let t(a) = 5*r(a) + 8*y(a). Let x be t(1). Factor -8/3*l**4 + 2/3 + 22/3*l**3 + 2/3*l - x*l**2.
-2*(l - 1)**3*(4*l + 1)/3
Suppose 5*b - 30 = -b. Suppose 10 - 2 = 4*n. Suppose 3*c**3 + b*c**4 + 10*c**4 + 12*c**2 + n*c**5 + 21*c**3 + c**5 = 0. What is c?
-2, -1, 0
Suppose 3*i = -c - 0 - 7, -5*i - 8 = -2*c. Let q be (15/(-40))/(1/i). Determine u, given that 3 + q*u**4 - 3/2*u**3 + 3*u - 9/4*u**2 = 0.
-1, 2
Let o = -8 + 8. Let s(b) be the second derivative of -1/12*b**3 + 2*b + o*b**4 + 0*b**2 + 1/40*b**5 + 0. Solve s(y) = 0.
-1, 0, 1
Let y(g) be the first derivative of 5*g**6/14 + 51*g**5/35 + 12*g**4/7 + 4*g**3/7 - 6. Let y(n) = 0. Calculate n.
-2, -1, -2/5, 0
Let f be 2*(1 + 9/6). Suppose -f*l + 137 - 7 = 0. Let 66*q**2 + 17*q**3 + 32*q**4 + 2 + 6*q - 97*q**3 - l*q = 0. What is q?
1/4, 1
Let w(p) be the third derivative of p**8/672 - p**7/140 + p**6/80 - p**5/120 + p**2. Solve w(f) = 0 for f.
0, 1
Let c be 33/7 - 12/(-42). Solve 3*p**5 - 4*p**3 - 2*p**c - 2*p**5 + 4*p**4 = 0 for p.
0, 2
Let g(t) = -5*t + 3. Let c be g(-5). Let f be (c/5)/(-2) - -3. Factor 1/5*n**2 - 1/5*n**3 - f + 1/5*n.
-(n - 1)**2*(n + 1)/5
Suppose 4*r - 4 = 4. Let l be 0/4 + -2 + r. Solve l - 2/5*m**2 - 2/5*m**3 + 0*m = 0.
-1, 0
Let k(n) be the third derivative of -3/7*n**3 - 1/14*n**4 - 10*n**2 + 0 + 0*n - 1/210*n**5. Factor k(z).
-2*(z + 3)**2/7
Suppose -2*z = -0*z - 6. Suppose 23 - 5 = 6*y. Factor 4*h**3 + 5*h**3 - 3*h - y*h**3 - z*h**3.
3*h*(h - 1)*(h + 1)
Suppose 0 = -p - z, -6*z = -3*p - 5*z + 8. Determine w so that 0*w**3 + 4*w - p*w**3 - 2*w + 0*w = 0.
-1, 0, 1
Let s(b) = b**3 - b**2 - 5*b + 5. Let m be s(1). Find a, given that m*a**2 + 1/3*a + 0 - 1/3*a**3 = 0.
-1, 0, 1
Suppose q + 2*r = -q + 6, 0 = 5*q + 3*r - 19. Let s(x) be the first derivative of -4 - 4*x - 5*x**2 + 8/5*x**q - 4/3*x**3 + 1/3*x**6 + 2*x**4. Factor s(y).
2*(y - 1)*(y + 1)**3*(y + 2)
Let c(g) be the second derivative of -g**9/15120 + g**8/4200 - g**6/900 + g**5/600 - g**3/2 - g. Let r(z) be the second derivative of c(z). Factor r(f).
-f*(f - 1)**3*(f + 1)/5
Let m(k) be the third derivative of -k**8/336 + k**6/40 - k**5/30 + 12*k**2. Determine y so that m(y) = 0.
-2, 0, 1
Let b(q) = -q**2 + 11*q - 7. Let x be 16/24 - (-56)/6. Let m be b(x). Factor 0 - 1/5*t - 1/5*t**4 - 3/5*t**m - 3/5*t**2.
-t*(t + 1)**3/5
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