et b(a) be the first derivative of -2*a**6/3 + 12*a**5/5 - 2*a**4 - 14. Factor b(x).
-4*x**3*(x - 2)*(x - 1)
Suppose 7*o - 2 - 12 = 0. Suppose -j = -2*j. Factor -1/3*i**o + 1/3 + j*i.
-(i - 1)*(i + 1)/3
Let l(w) be the third derivative of -w**8/36 - 4*w**7/315 + 7*w**6/90 + 2*w**5/45 - 36*w**2. Let l(p) = 0. What is p?
-1, -2/7, 0, 1
Let x = 68 - 66. Find m, given that 4/3 - 10/3*m**3 + 2/3*m**2 + 10/3*m - x*m**4 = 0.
-1, -2/3, 1
Suppose -4/5*z + 6/5 - 2/5*z**2 = 0. Calculate z.
-3, 1
Let z(p) be the first derivative of 4/7*p - 8/35*p**5 + 4 + 9/14*p**4 + 4/21*p**3 - 9/7*p**2. Find c, given that z(c) = 0.
-1, 1/4, 1, 2
Let s(j) be the third derivative of -j**8/4200 - j**7/2100 + j**3/3 + 3*j**2. Let g(q) be the first derivative of s(q). Find a such that g(a) = 0.
-1, 0
Let c be -15*((-2)/1)/2. Let g = c - 15. Factor g - 3/4*y**2 + 1/2*y - 7/2*y**3.
-y*(2*y + 1)*(7*y - 2)/4
Let d(g) be the first derivative of g**6/1620 - 3*g**3 + 9. Let n(c) be the third derivative of d(c). Let n(m) = 0. What is m?
0
Suppose -3*t = 4*d - 7, -5*t + 0 = 4*d - 1. Suppose 2*x - 2 - 6 = -3*i, -3*x - 5 = -d*i. Factor 2 + 3 - 4 - r**i - r + r**3.
(r - 1)**2*(r + 1)
Let c(f) be the second derivative of f**6/210 + f**5/20 + 5*f**4/84 - f**3/6 - 3*f**2/7 + 2*f - 17. Factor c(u).
(u - 1)*(u + 1)**2*(u + 6)/7
Let x(w) be the second derivative of w**6/240 - w**4/32 - w**3/24 + 33*w. What is u in x(u) = 0?
-1, 0, 2
Let q(w) = -w**3 - 6*w**2 - 11*w - 10. Let r be q(-4). Let z(j) be the first derivative of -6/5*j**4 - 6/5*j**3 - r - 2/5*j**2 + 0*j - 2/5*j**5. Factor z(d).
-2*d*(d + 1)**2*(5*d + 2)/5
Let i be (-2)/6*(-12)/2. Suppose 3*a - 11 + i = 0. Factor -1/3 + 1/3*q**2 + 1/3*q**a - 1/3*q.
(q - 1)*(q + 1)**2/3
Let u be 1/3*39/26. Solve 3/2*h + u*h**2 + 1 = 0.
-2, -1
Let i be (-48 - -47)/((-5)/4). Factor -i - 2/5*y**2 - 6/5*y.
-2*(y + 1)*(y + 2)/5
Let m(a) be the third derivative of 0*a + 1/120*a**5 + 3*a**2 + 1/48*a**4 + 0 + 0*a**3. What is q in m(q) = 0?
-1, 0
Let i(q) = -q**3 + 30*q**2 - 6*q. Let k(t) = -3*t**3 + 60*t**2 - 13*t. Let n(v) = 13*i(v) - 6*k(v). Factor n(h).
5*h**2*(h + 6)
Determine k, given that -2/3*k + 0 - 17/6*k**3 + 10/3*k**2 + 2/3*k**4 = 0.
0, 1/4, 2
Suppose 2*x = -x. Factor 3*l + 2*l**2 - l + x*l.
2*l*(l + 1)
Suppose 2/5 + 4/5*w + 2/5*w**2 = 0. What is w?
-1
Let n(t) = t**3. Let u(b) = -7*b**3 - 4*b**2 - 2*b. Let m(i) = 5*n(i) + u(i). Factor m(q).
-2*q*(q + 1)**2
Let v(b) be the third derivative of -b**8/84 - b**7/21 - b**6/15 - b**5/30 - 13*b**2. Determine d so that v(d) = 0.
-1, -1/2, 0
Suppose -23 = 3*n - 4*z, 4*n = 2*n - 2*z - 6. Let d = n - -5. Factor 2/9*y - 2/9*y**3 + d + 0*y**2.
-2*y*(y - 1)*(y + 1)/9
Suppose -2*p + 7*p - 5 = 0. Let -2*r**2 + 0*r**2 + 2*r**4 - 1 + p = 0. Calculate r.
-1, 0, 1
Let u(h) be the second derivative of 3*h**4/4 - 5*h**3/2 + 3*h**2 - 8*h. Let u(k) = 0. Calculate k.
2/3, 1
Let k(x) = 15*x**5 - 90*x**4 + 215*x**3 - 195*x**2 + 60*x. Let q(m) = -8*m**5 + 45*m**4 - 108*m**3 + 98*m**2 - 30*m. Let d(p) = 3*k(p) + 5*q(p). Factor d(s).
5*s*(s - 6)*(s - 1)**3
Factor -4*j - 29*j**3 + 10*j**3 - 8 + 11*j**3 + 12*j**3 + 8*j**2.
4*(j - 1)*(j + 1)*(j + 2)
Suppose -7 = -2*s + 4*t + 9, 3*s - 18 = 3*t. Let z = s - 1. What is j in 22*j**4 - 18*j**4 + 24*j**4 - 49*j**5 - j**3 - z*j**3 = 0?
0, 2/7
Let b be (3 - 38/12)*(-8 - 2). Factor -1/3*x - b*x**2 + 1/3 - x**3.
-(x + 1)**2*(3*x - 1)/3
Let l(y) be the second derivative of -y**5/230 + y**3/69 - 44*y. Factor l(i).
-2*i*(i - 1)*(i + 1)/23
Let p(r) = -5*r**3 + 9*r**2 + 10*r + 4. Let x(g) = 6*g**3 - 11*g**2 - 11*g - 5. Let a(v) = -5*p(v) - 4*x(v). Factor a(q).
q*(q - 3)*(q + 2)
Let d(g) = g + 2. Let t be d(6). Factor 4*n**2 + 0*n**3 - 9*n + 9*n + 4*n**4 - t*n**3.
4*n**2*(n - 1)**2
Let i = 42 + -251/6. Let k(d) be the third derivative of i*d**4 - 1/60*d**5 + 0*d - 2/3*d**3 - 3*d**2 + 0. Factor k(n).
-(n - 2)**2
Let q(s) be the first derivative of -1/3*s**2 + 2/9*s**3 - 1/18*s**4 - 3 - 3*s. Let d(y) be the first derivative of q(y). Solve d(x) = 0.
1
Let x be ((-2)/(-2))/((-6)/(-30)). Factor -3*y**x - 4*y**3 + 4*y**5 + y**5 + 0*y**5 + 2*y.
2*y*(y - 1)**2*(y + 1)**2
Let o(x) be the first derivative of 1/4*x**4 - 1/4*x**2 + 1/10*x**5 - 1 - 1/12*x**6 - 1/3*x**3 + 1/2*x. Let o(q) = 0. Calculate q.
-1, 1
Let d(l) be the first derivative of -l**3/3 - l**2/2 + 3. Let j(n) = -6*n**3 + 6*n. Let r(y) = -10*d(y) - j(y). Factor r(h).
2*h*(h + 1)*(3*h + 2)
Let g(p) be the third derivative of -p**5/660 - p**4/132 - 34*p**2. Find u, given that g(u) = 0.
-2, 0
Let u(i) be the first derivative of 4*i**5/5 + 4*i**4 - 5. Factor u(s).
4*s**3*(s + 4)
Factor 6/13*p - 4/13*p**2 + 0 - 10/13*p**3.
-2*p*(p + 1)*(5*p - 3)/13
Let x(z) be the third derivative of 0 + 1/140*z**5 - 3*z**2 + 9/14*z**3 - 3/28*z**4 + 0*z. Factor x(k).
3*(k - 3)**2/7
Suppose u + 3*p + 8 = 0, -2*u - 3*p + 1 - 5 = 0. Factor -2/3*w**5 + 0 + 0*w + 2/3*w**2 + 2/3*w**3 - 2/3*w**u.
-2*w**2*(w - 1)*(w + 1)**2/3
Let q(d) be the second derivative of d**7/6300 - d**6/1800 + d**4/6 + d. Let s(a) be the third derivative of q(a). Determine z, given that s(z) = 0.
0, 1
Let v(p) = -4*p**2 - 10*p - 8. Let w(n) = -5*n**2 - 11*n - 8. Suppose -10 + 0 = -5*x + 5*s, -2*x - 5*s + 11 = 0. Let i(l) = x*v(l) - 2*w(l). Factor i(g).
-2*(g + 2)**2
Let n(h) be the third derivative of h**5/60 - h**4/6 + h**3/2 + 30*h**2. What is t in n(t) = 0?
1, 3
Let q(s) = -s**3 + 8*s**2 - 7*s. Let y(f) = f**3 + f**2 + 7. Let k be y(0). Let p be q(k). Solve 1/4*d**2 - 3/4*d**3 + 0 + p*d = 0.
0, 1/3
Suppose 2*u - 18 = -u. Let z(k) be the second derivative of -1/80*k**5 + 0*k**3 + 0 + 0*k**4 + 0*k**2 - k + 1/120*k**u. Factor z(j).
j**3*(j - 1)/4
Determine z so that -2/5*z**2 + 1/5*z**5 + 0 - 1/5*z**3 + 0*z + 2/5*z**4 = 0.
-2, -1, 0, 1
Let u(n) be the second derivative of n**5/20 - n**4/12 - n**3/6 + n**2/2 - 8*n. Suppose u(t) = 0. What is t?
-1, 1
Let l = 28 - -8. Solve -24*r + r**3 + 12*r + 20*r**3 - l*r**2 = 0 for r.
-2/7, 0, 2
Suppose -2*r + r + 12 = 0. What is k in -3*k**4 + 21*k**3 - 3 - 9*k**3 - 15*k**2 + r*k - 3*k**2 = 0?
1
Let m(y) be the first derivative of y**6/600 + y**5/200 - y**4/20 - 4*y**3/3 - 1. Let d(t) be the third derivative of m(t). Let d(o) = 0. What is o?
-2, 1
Factor 5*q**2 - 113 + 113 - 25*q**3.
-5*q**2*(5*q - 1)
Suppose -2/3*a**4 + 0*a - 2/3*a**3 + 2/3*a**5 + 0 + 2/3*a**2 = 0. Calculate a.
-1, 0, 1
Let p be (-4)/((5 + -1)/(-2)). Let 1/2*a**p - a + 0 = 0. Calculate a.
0, 2
Let q = -38/15 - -16/5. Factor -q*x + 0 - 1/3*x**3 - x**2.
-x*(x + 1)*(x + 2)/3
Let f(k) be the first derivative of 0*k - 1/30*k**5 - 1/6*k**2 - 5/18*k**3 - 2 - 1/6*k**4. What is g in f(g) = 0?
-2, -1, 0
Let t(a) be the first derivative of 8*a**3/15 + 7*a**2/5 - 4*a/5 - 17. Suppose t(o) = 0. What is o?
-2, 1/4
Let h(a) be the third derivative of -2*a**7/735 + 16*a**6/105 - 128*a**5/35 + 1024*a**4/21 - 8192*a**3/21 - 18*a**2. Let h(v) = 0. Calculate v.
8
Let c(y) be the second derivative of 0*y**2 + 2/39*y**3 + 1/78*y**4 + 0 + 3*y. Factor c(a).
2*a*(a + 2)/13
Factor 3/5*o**4 + 18/5*o**2 - 12/5*o + 3*o**3 - 24/5.
3*(o - 1)*(o + 2)**3/5
Let n = 2095/126 - 116/7. Let g(i) be the second derivative of n*i**3 + 1/6*i**2 - 1/36*i**4 - 1/60*i**5 + 2*i + 0. Determine k, given that g(k) = 0.
-1, 1
Let w = 7 - 167/24. Let v(q) be the third derivative of 1/12*q**3 + 0 - q**2 + 0*q + 1/120*q**5 + w*q**4. Find b such that v(b) = 0.
-1
Let a(b) = -3*b**2 - 4*b - 6. Let i(n) = -7*n**2 - 8*n - 13. Suppose 0 = 2*g - 2 - 2. Let l(t) = g*i(t) - 5*a(t). Factor l(u).
(u + 2)**2
Let m(l) = l - 1. Suppose -4*q = -v + 1 - 52, 4*q - 3*v - 41 = 0. Let y(a) = a**4 - a**2 - 7*a + 7. Let b(w) = q*m(w) + 2*y(w). Solve b(r) = 0 for r.
-1, 0, 1
Let n = 1/70 + 13/70. Factor -4/5*x - n*x**4 - 6/5*x**2 - 1/5 - 4/5*x**3.
-(x + 1)**4/5
Let m = 27 - 25. Factor m*t + 8/5*t**2 + 4/5 + 2/5*t**3.
2*(t + 1)**2*(t + 2)/5
Suppose 0*t + t**3 + 0 - 7/5*t**4 + 2/5*t**2 = 0. Calculate t.
-2/7, 0, 1
Let a = -120 + 124. Factor 0*t**2 + 2/5*t + 0*t**a + 2/5*t**5 + 0 - 4/5*t**3.
2*t*(t - 1)**2*(t + 1)**2/5
Let y(a) = a**2 - a - 8. Let k be y(-3). Suppose -7*s - 5*t = -4*s + 25, k*s - 25 = 5*t. Factor -3/2*c + s - 3/2*c**2.
-3*c*(c + 1)/2
Determine c so that 2*c**2 + 8/5 - 24/5*c = 0.
2/5, 2
Let j be -1 - -9 - ((3 - -3) + -2). Factor -2/3*k**j + 8/3*k - 