 1)*(3*t + 2)/6
Let m(g) be the second derivative of -g**6/15 + g**5/2 - 7*g**4/6 + g**3 + 30*g. Find a such that m(a) = 0.
0, 1, 3
Let r(f) be the third derivative of f**7/210 + f**6/120 - 3*f**5/20 + 11*f**4/24 - 2*f**3/3 - 2*f**2. Let r(c) = 0. Calculate c.
-4, 1
Let r(d) = -d - 1. Suppose 0 = -b - 0*b - 1. Let w(t) = -4*t**2 - 6*t + 1. Let l(a) = b*w(a) - 3*r(a). Factor l(f).
(f + 2)*(4*f + 1)
Let a be (-16)/(-18)*(-2)/(-8). Solve 0 - a*w**4 + 2/9*w**2 + 0*w + 2/9*w**5 - 2/9*w**3 = 0 for w.
-1, 0, 1
Factor 8/9 - 2/9*i**2 + 2/9*i**3 - 8/9*i.
2*(i - 2)*(i - 1)*(i + 2)/9
Suppose -14 = -0*i - 7*i. Let c(z) be the first derivative of 25*z**4 + 4*z + 7/3*z**6 - 2 + 12*z**5 + 15*z**i + 80/3*z**3. Factor c(m).
2*(m + 1)**4*(7*m + 2)
Let f(u) be the first derivative of -1/6*u**6 + 0*u - 4/3*u**3 - 4 - 4/5*u**5 - 1/2*u**2 - 3/2*u**4. Find l, given that f(l) = 0.
-1, 0
Let b(k) be the second derivative of -k**7/210 + k**6/30 - 7*k**5/100 + k**4/20 - 28*k. Factor b(y).
-y**2*(y - 3)*(y - 1)**2/5
Let t(z) = 2*z**2 + 10*z + 6. Let n be t(-6). Factor 16*p**3 - n*p**3 + 2*p**4 + p**2 - p**2.
2*p**3*(p - 1)
What is t in -2/5*t**3 + 0 + 0*t + 0*t**2 + 0*t**4 + 2/5*t**5 = 0?
-1, 0, 1
Suppose 0 = -2*r - r + 5*y + 22, -2*r + 3*y + 14 = 0. Factor v**3 - r + 2*v + 4*v**2 + 0*v - 3*v**3.
-2*(v - 2)*(v - 1)*(v + 1)
Let j(l) = 7*l**2 - 3*l - 5. Let x(b) = 4*b**2 - b - 3. Let s(c) = 3*j(c) - 5*x(c). Factor s(z).
z*(z - 4)
Let u(d) be the second derivative of -d**4/3 + 16*d**3/3 - 32*d**2 - 7*d. Suppose u(g) = 0. Calculate g.
4
Let y(k) = k + 8. Let g be y(-6). Suppose -g*p = p. Factor 0*f**4 + 0*f**2 + p*f + 0 - 2/3*f**5 + 2/3*f**3.
-2*f**3*(f - 1)*(f + 1)/3
Let i(t) be the second derivative of t**4/8 - t**3/2 + 3*t**2/4 - 4*t - 5. Factor i(s).
3*(s - 1)**2/2
Let k(t) be the first derivative of 4*t**3/3 - 4*t**2 - 2. Determine b, given that k(b) = 0.
0, 2
Let l(d) be the third derivative of -2*d**7/315 - d**6/90 + d**5/45 + d**4/18 + 9*d**2. Factor l(q).
-4*q*(q - 1)*(q + 1)**2/3
Suppose -4*w + 8 = -4*x, 7*x + 5*w - 2 = 4*x. Let p be (-20)/(-48) + x/6. Solve -1/4*t**3 + p*t**5 + 0*t**4 + 0*t + 0 + 0*t**2 = 0 for t.
-1, 0, 1
Let n(v) = 4*v**3 - 2*v. Let a(z) = -17*z**3 - z**2 + 7*z. Let w(f) = -4*a(f) - 18*n(f). Factor w(y).
-4*y*(y - 2)*(y + 1)
Let g(t) be the first derivative of 0*t + 3/2*t**2 + 1/180*t**5 - 1 - 1/36*t**4 + 0*t**3. Let m(r) be the second derivative of g(r). Factor m(s).
s*(s - 2)/3
Let h = 2/409 - -2440/2863. Solve 6/7*j**3 + 0 - h*j**4 + 0*j + 2/7*j**5 - 2/7*j**2 = 0.
0, 1
Let c(k) be the first derivative of 2*k**6/3 - 4*k**5 + 9*k**4 - 28*k**3/3 + 4*k**2 + 1. Determine b so that c(b) = 0.
0, 1, 2
Solve 4*k**3 - 8/5*k - 14/5*k**2 - 6/5*k**4 + 8/5 = 0.
-2/3, 1, 2
Let n(b) be the first derivative of -2*b**3/21 - 8*b**2/7 - 32*b/7 + 8. Factor n(y).
-2*(y + 4)**2/7
Let l(u) = u**2 - u. Let p be l(2). Factor 2*w**3 - 5*w**2 + 3*w**2 + p*w + 6*w**2.
2*w*(w + 1)**2
Let o(s) be the first derivative of -s**6/75 + 4*s**4/15 - 16*s**2/5 + 3*s + 1. Let d(r) be the first derivative of o(r). Factor d(z).
-2*(z - 2)**2*(z + 2)**2/5
Let s(m) = m**3 + 4*m**2 - 6*m - 2. Let u be s(-5). Suppose -u = 4*p + 3*l - 14, -2*p = -4*l. Find w such that -2/7*w**p + 0*w + 2/7 = 0.
-1, 1
Factor 0*g**2 + 3/2*g**3 + 0 - 3/2*g.
3*g*(g - 1)*(g + 1)/2
Let t(o) = -o - 5. Let n be t(-5). Suppose -3*x + 9 = -n. Factor -q**x + q**4 + 2*q**3 - q**5 + 0*q**3 - q**2.
-q**2*(q - 1)**2*(q + 1)
Let h(d) = 5*d**2 - 5*d - 3. Let i(q) = 14*q**2 - 2 - 3 - 17*q - 3 + 3*q. Let j(w) = 8*h(w) - 3*i(w). Factor j(s).
-2*s*(s - 1)
Let d(a) = -5*a**2 - 12*a + 15. Let s = -9 + 3. Let k(g) = -14*g**2 - 35*g + 44. Let h(j) = s*k(j) + 17*d(j). Factor h(n).
-(n - 3)**2
Let b(l) be the second derivative of l**7/70 - 2*l**6/75 - l**5/25 + l**4/10 + l**3/30 - l**2/5 - 9*l. Let b(s) = 0. Calculate s.
-1, -2/3, 1
Let g(z) be the first derivative of 2*z**7/21 - 4*z**6/15 + 2*z**4/3 - 2*z**3/3 + 5*z + 1. Let l(k) be the first derivative of g(k). Factor l(y).
4*y*(y - 1)**3*(y + 1)
Let j(c) be the third derivative of 0*c**3 - 1/5*c**5 + c**2 - 1/2*c**6 + 0*c**4 - 1/28*c**8 + 0 - 17/70*c**7 + 0*c. Factor j(a).
-3*a**2*(a + 2)**2*(4*a + 1)
Let s(z) = z**3 - z**2 - z + 1. Let o(a) = a**4 + 4*a**3 - 3*a**2 - 3*a + 3. Let i(t) = o(t) - 3*s(t). Factor i(x).
x**3*(x + 1)
Let m(y) be the third derivative of 0 + 0*y - 1/480*y**6 - 1/24*y**3 - 1/32*y**4 - 1/80*y**5 - 4*y**2. Solve m(n) = 0.
-1
Let b be (-15)/(-18) + (-4)/6. Let a(r) be the third derivative of 0 + 0*r + 1/240*r**5 + 1/24*r**4 + 2*r**2 + b*r**3. Find t such that a(t) = 0.
-2
Let d be 7/10*(-20)/(-35). Let x = d + 1/10. Determine v so that 0 + 1/2*v**2 + x*v**3 - v = 0.
-2, 0, 1
Let a(k) be the second derivative of k**6/40 + k**5/10 + 7*k**4/48 + k**3/12 + 17*k. Determine i, given that a(i) = 0.
-1, -2/3, 0
Solve -7/3*t**2 + 2/3*t + 0 + 5/3*t**3 = 0.
0, 2/5, 1
Suppose 9*l + p - 55 = 4*l, 0 = -p - 5. Let c be (-3)/l + 9/4. Factor -1/3*a**c + a - 2/3.
-(a - 2)*(a - 1)/3
Let p(n) be the first derivative of -n**6/30 - 7*n**5/25 - 9*n**4/10 - 22*n**3/15 - 13*n**2/10 - 3*n/5 + 26. Solve p(s) = 0.
-3, -1
Let v(y) = -y**2 + 8*y + 5. Let x(a) = -a + 2. Let m be x(-6). Let w be v(m). Factor -7*r**3 - 5/3*r**w - 2/3*r - 17/3*r**4 - 11/3*r**2 + 0.
-r*(r + 1)**3*(5*r + 2)/3
Suppose -18*a = -5*a + 8*a. Factor -o**4 + 7/4*o**2 - 1/2*o + a + 5/4*o**3.
-o*(o - 2)*(o + 1)*(4*o - 1)/4
Let q(s) be the second derivative of -s**7/168 - s**6/120 + s**5/40 + s**4/24 - s**3/24 - s**2/8 - 13*s. Determine o, given that q(o) = 0.
-1, 1
Let p be (-1)/(4/5 + -1). Suppose p*r**3 + 0*r - 6*r + 10*r**2 - 8*r**3 - r**2 = 0. Calculate r.
0, 1, 2
Let n(k) be the second derivative of -k**7/42 - 7*k**6/30 - 19*k**5/20 - 25*k**4/12 - 8*k**3/3 - 2*k**2 + 3*k. Factor n(v).
-(v + 1)**3*(v + 2)**2
Suppose 0 = -4*f + 8 - 0. Factor -5*l**3 - f*l**3 + 6*l**2 + 10*l**3.
3*l**2*(l + 2)
Find g, given that -25/2 + 5/2*g - 1/8*g**2 = 0.
10
Let h(a) be the first derivative of 0*a**2 + 0*a**3 - 3/5*a**5 + 0*a + 2 + 3/4*a**4. Determine i, given that h(i) = 0.
0, 1
Let z(j) be the third derivative of -j**7/280 + j**6/60 - j**3/6 + 4*j**2. Let p(b) be the first derivative of z(b). Factor p(a).
-3*a**2*(a - 2)
Let n(y) be the second derivative of -y**6/30 + y**4/4 + y**3/3 - y. Factor n(a).
-a*(a - 2)*(a + 1)**2
Let b(y) be the first derivative of 2/27*y**3 + 3 + 1/9*y**2 + 0*y - 2/45*y**5 - 1/18*y**4. Solve b(j) = 0.
-1, 0, 1
Let x(b) be the third derivative of -b**6/40 - 3*b**5/20 - 3*b**4/8 - b**3/2 - 8*b**2. Find i, given that x(i) = 0.
-1
Let o(u) be the second derivative of u**6/240 - u**4/48 - u**2/2 - 3*u. Let q(p) be the first derivative of o(p). Find z, given that q(z) = 0.
-1, 0, 1
Let r(v) be the second derivative of -2*v**7/21 - 4*v**6/15 + 2*v**5/5 + 4*v**4/3 - 2*v**3/3 - 4*v**2 + 5*v. Solve r(a) = 0.
-2, -1, 1
Suppose 0 = 5*y - 4*y - 1. Let k be (0 - -1)*y/4. Factor k*h**3 + 1/4*h**2 + 0 + 0*h.
h**2*(h + 1)/4
Let d(g) be the third derivative of -g**5/180 + g**4/36 - g**3/18 + 12*g**2. Factor d(h).
-(h - 1)**2/3
Let c be 2/9 - 5188/(-14616). Let d = -1/174 + c. Factor 2/7*g**3 + 2/7*g - d*g**2 + 0.
2*g*(g - 1)**2/7
Let b be ((-36)/(-14) + -2)/(27/21). Factor -b + 10/9*g**2 - 2/3*g.
2*(g - 1)*(5*g + 2)/9
Let g = -6 + 15. Let y = 9 - g. Let 1/3*k + k**2 + y + k**3 + 1/3*k**4 = 0. What is k?
-1, 0
Find c such that -8*c - 8*c + 4*c + 12 + 123*c**2 - 120*c**2 = 0.
2
Let v(s) = -s**3 - 5*s**2 + s + 5. Let i be v(-5). Let o(j) be the second derivative of 3*j + 0 + i*j**2 - 1/15*j**3 - 1/20*j**4. Factor o(w).
-w*(3*w + 2)/5
Let d = 72 - 67. Let k(p) be the second derivative of 1/40*p**d + 2*p + 0*p**4 + 0*p**2 - 1/12*p**3 + 0. Factor k(m).
m*(m - 1)*(m + 1)/2
Let y(g) = -g**3 - 14*g**2 + 4. Let x = 21 + -35. Let d be y(x). Let -2*a**3 - d*a**2 + 9 - 9 = 0. Calculate a.
-2, 0
Find w such that 28/3*w - 4*w**5 - 16/3*w**3 + 8*w**2 + 8/3 - 32/3*w**4 = 0.
-1, -2/3, 1
Factor 3*x**4 + 3*x**4 - 6*x**2 + 5*x**3 + 5*x**3 - 2*x**5 - 8*x**4.
-2*x**2*(x - 1)**2*(x + 3)
Let o(a) be the third derivative of -a**7/525 - a**6/50 - 11*a**5/150 - a**4/10 - 22*a**2. Factor o(t).
-2*t*(t + 1)*(t + 2)*(t + 3)/5
Let v(k) be the first derivative of 2*k**3/21 - k**2/7 - 1. What is x in v(x) = 0?
0, 1
Let q(i) be the third derivative