j - 2)**2/2
Let g(q) be the second derivative of -q**5/90 - q**4/27 - 26*q. Factor g(t).
-2*t**2*(t + 2)/9
Let j(n) be the second derivative of n**6/180 + n**5/40 + n**4/36 - 8*n. Factor j(i).
i**2*(i + 1)*(i + 2)/6
Suppose 48 + 108 = -4*b. Let p = 59 + b. Find h such that 28*h**3 + 3*h**3 - p*h**2 + 4*h - 3*h**4 - 12*h**4 = 0.
0, 2/5, 2/3, 1
Let v(b) be the third derivative of -5*b**8/168 + 11*b**7/105 + b**6/50 - 14*b**5/75 - 2*b**4/15 + 33*b**2. Solve v(n) = 0 for n.
-2/5, 0, 1, 2
Let m(z) be the second derivative of -z**4/24 + z**2/4 + 14*z. Factor m(x).
-(x - 1)*(x + 1)/2
Let s be 7 - 3*5/30*14. Find z, given that -2/5*z + 6/5*z**2 + s + 2/5*z**3 - 6/5*z**4 = 0.
-1, 0, 1/3, 1
Factor 4*r - 4*r**3 - 4*r**4 + 4*r**2 - 1 + 12 - 11.
-4*r*(r - 1)*(r + 1)**2
Let j be (77968/(-6))/(21/(-9)). Let m = 5580 - j. Factor 26/7*l + 10/7*l**5 - 64/7*l**2 - 4/7 - 44/7*l**4 + m*l**3.
2*(l - 1)**4*(5*l - 2)/7
Suppose 0 = -4*n + 3*n. Factor 3/5*a**2 + n + 9/5*a.
3*a*(a + 3)/5
Factor 2/5*c**3 + 4/5 + 0*c**2 - 6/5*c.
2*(c - 1)**2*(c + 2)/5
Suppose -23*i - 6 = -26*i. Let v(p) be the second derivative of 0*p**4 + 0 - 1/60*p**5 + 3*p + 1/18*p**3 + 0*p**i. Solve v(c) = 0 for c.
-1, 0, 1
Let p(l) = 4*l**3 - 3*l**2 - 1. Let w(k) = -k**3 + 1. Let t(d) = -5*p(d) - 10*w(d). Suppose t(z) = 0. Calculate z.
-1/2, 1
Let v = -120886541/2478 + 292705/6. Let d = 2/59 + v. Factor 0 + 2/7*a**2 + d*a.
2*a*(a + 1)/7
Suppose 2*z - 4*z = 0. Let t be 8/(-7) + 2 - z. Solve -10/7*i**2 + 4/7 + t*i = 0 for i.
-2/5, 1
Let u(j) be the third derivative of -j**8/840 - 3*j**7/980 - j**6/630 + j**3/3 + 2*j**2. Let x(b) be the first derivative of u(b). Find q such that x(q) = 0.
-1, -2/7, 0
What is d in -2/7*d**4 - 50/7 - 120/7*d - 92/7*d**2 - 24/7*d**3 = 0?
-5, -1
Let f(m) = -m**3 - 3*m**2 + m + 1. Let n be f(-3). Let o be 2*n/(-54)*3. Find q such that 2/9*q + o - 2/9*q**2 - 2/9*q**3 = 0.
-1, 1
Let w(r) = -r**2 + r + 1. Let l(q) = 2*q**2 + 2*q**2 - 6 - q**2 - q + 0*q. Let v(i) = -l(i) - 4*w(i). Factor v(a).
(a - 2)*(a - 1)
Suppose 29 = 5*o + 9. Solve -h**2 - o*h + 2 - 6 + 0*h**2 = 0 for h.
-2
Let h(n) be the first derivative of 3*n**5/5 + 3*n**4/2 + n**3 + 23. Solve h(x) = 0 for x.
-1, 0
Let j(k) be the first derivative of -k**6/50 + k**4/10 - 3*k**2/10 + 2*k - 1. Let h(f) be the first derivative of j(f). Factor h(z).
-3*(z - 1)**2*(z + 1)**2/5
Let b(w) = 13*w**3 - 5*w**2 - 11*w - 2. Let p(q) = -2*q + 3. Let l be p(4). Let g(j) = -j**3 + j**2 + j. Let z(o) = l*g(o) - b(o). Factor z(v).
-2*(v - 1)*(2*v + 1)**2
Suppose -m + 2 = -7. Let a = m - 6. Factor 2/11*g + 2/11*g**2 - 2/11*g**4 + 0 - 2/11*g**a.
-2*g*(g - 1)*(g + 1)**2/11
Let j(q) be the third derivative of -q**5/210 + q**4/28 + 4*q**3/21 + 11*q**2. Determine o, given that j(o) = 0.
-1, 4
Let j(r) = -r**3 - 11*r**2 - 9*r + 14. Let o be j(-10). Suppose 5*p - 6*p = -o. Determine q so that 0 + 0*q**2 + 2/5*q**5 - 2/5*q**3 + 0*q**p + 0*q = 0.
-1, 0, 1
Let p = 40 - 37. Let u(m) be the first derivative of 2/3*m**p - 2*m + 0*m**2 - 1. Suppose u(v) = 0. What is v?
-1, 1
Let r(h) = -6*h**3 + 35*h**2 - 55*h - 13. Let a(v) = 3*v**3 - 18*v**2 + 27*v + 6. Let s(j) = -13*a(j) - 6*r(j). Factor s(f).
-3*f*(f - 7)*(f - 1)
Let q be (-10)/35 - (-30)/7. Factor 3*d**q - 3*d**4 - 3*d**4.
-3*d**4
Factor 31/2*o**2 + 1/2*o**3 + 255/2*o + 225/2.
(o + 1)*(o + 15)**2/2
Let d(q) be the third derivative of -1/48*q**3 + 1/96*q**4 + 0*q + 0 - 1/480*q**5 + 6*q**2. Find a, given that d(a) = 0.
1
Let i be (-10)/5*(-2)/7. Let s(q) be the second derivative of -1/14*q**4 + i*q**2 + 0 + 1/105*q**6 - 2*q - 1/35*q**5 + 4/21*q**3. Factor s(x).
2*(x - 2)**2*(x + 1)**2/7
Let n be (4/4)/(1/3). Let k(j) be the first derivative of -j**2 + 1/3*j**n + 3 - 3*j. Factor k(a).
(a - 3)*(a + 1)
Let t be (0*4/16)/(-1). Let w(v) be the third derivative of -1/32*v**4 + 1/24*v**3 + 0*v - v**2 + 1/80*v**5 + t - 1/480*v**6. What is o in w(o) = 0?
1
Let z be (-48)/32 + (-22)/(-4). Factor 4/3*u**2 + 1/3*u**5 + 0 + 2*u**3 + 1/3*u + 4/3*u**z.
u*(u + 1)**4/3
Let i(w) be the first derivative of 3*w**4/8 - 9*w**2/4 - 3*w + 6. Factor i(b).
3*(b - 2)*(b + 1)**2/2
Let z(a) be the first derivative of -a**6/14 + 9*a**5/35 - 9*a**4/28 + a**3/7 + 2. What is j in z(j) = 0?
0, 1
Suppose y + 2 = 0, -4*o = -o + 5*y - 5. Determine j, given that -4*j + 2*j + o*j**2 - 4*j**2 = 0.
0, 2
Let u(r) = -r + 2. Let d be u(0). Determine h, given that -7*h**2 + h + h**2 - 3*h + 2*h**d = 0.
-1/2, 0
Suppose -5*n - 2*k + 34 = 0, -3*n - 5*k = -14 - 14. Suppose -5*l + 17 = 2*f, 5*f + 14 = -n. Factor 0 + 0*b**3 + 0*b**2 + 2/3*b**l - 2/3*b**4 + 0*b.
2*b**4*(b - 1)/3
Let l = -5193 - -436225/84. Let j = l + 2/21. Factor 1/2*a**4 + 0*a**3 + 0 - j*a + 1/4*a**5 - 1/2*a**2.
a*(a - 1)*(a + 1)**3/4
Factor 2 + 6*r**2 - 13*r**3 + 10*r**3 - 3*r**4 - 2.
-3*r**2*(r - 1)*(r + 2)
Suppose 0 = 3*p - 12, q = -0*p - 3*p + 14. Solve -w**q + 2*w - w**2 - 2*w**5 - 2*w**2 + 8*w**4 - 4*w**4 = 0.
-1, 0, 1
Let x be ((-69)/12 - -5)/(3/(-2)). Let i(j) be the first derivative of -4/5*j**2 + 26/15*j**3 - x*j**4 - 8/5*j + 3. Find a, given that i(a) = 0.
-2/5, 1, 2
Let c(z) be the second derivative of -3*z**5/32 + 3*z**4/8 - z**3/4 + 22*z. Factor c(l).
-3*l*(l - 2)*(5*l - 2)/8
Let k be 4/(-2) - (-1 + -3). Factor 1/2*v**4 + 0 + 0*v**3 + 0*v + 0*v**k.
v**4/2
Let y be 3/15 - (-208)/10. Let x be (y + -21)/(1 + 1). Let -3/4*d**2 - 3/4*d**3 + 0*d + x = 0. What is d?
-1, 0
Suppose -2*a = a. Suppose -2*v = -a*v. Determine w, given that -2/5*w**4 + 0*w**2 + 0 + v*w + 0*w**3 - 2/5*w**5 = 0.
-1, 0
Let p = 2/231 + 25/77. Factor 0 + p*o**3 + 0*o - 1/3*o**2.
o**2*(o - 1)/3
Let n(z) = -5*z**2 - 9*z. Let t(d) = -2*d**2 - 4*d. Let a(q) = -6*n(q) + 14*t(q). Suppose a(x) = 0. Calculate x.
0, 1
Let x(i) be the third derivative of -i**9/211680 + i**7/17640 - i**5/12 + 2*i**2. Let f(h) be the third derivative of x(h). Suppose f(n) = 0. Calculate n.
-1, 0, 1
Let v(f) = -f**2. Let m be v(1). Let r be -2*((-18)/2 + m). Factor 8/3 + 50/3*j**4 + 8*j - r*j**3 - 22/3*j**2.
2*(j - 1)**2*(5*j + 2)**2/3
Let h(x) be the third derivative of x**5/20 + x**4/4 + x**3/2 - 17*x**2. Factor h(b).
3*(b + 1)**2
Let k(d) be the second derivative of 2*d**2 + 4/21*d**7 - 13/6*d**4 - 2*d + 11/15*d**6 + 0 - 5/3*d**3 + 1/10*d**5. Suppose k(c) = 0. What is c?
-2, -1, 1/4, 1
Let b(s) = -s**3 + 2*s**2 + s. Let v be b(2). Let a be 1 - 0 - (v - 4). Let -22/3*k - 4/3 - 14/3*k**a - 32/3*k**2 = 0. What is k?
-1, -2/7
Let r = -115/2 - -58. Let p = 171/4 - 42. Find g, given that -1/4*g**3 - r + p*g + 0*g**2 = 0.
-2, 1
Let x(h) = -3*h - 12. Let d be x(-8). Let j be d/(-66) + (-84)/(-99). Determine p, given that j*p - 4/3*p**2 + 0 = 0.
0, 1/2
Let x(n) be the third derivative of 0*n**3 - 2*n**2 + 1/15*n**5 + 0 + 0*n + 1/9*n**4 + 1/60*n**6 + 1/630*n**7. Solve x(t) = 0.
-2, 0
Let f = -17 - -17. Let v(z) be the first derivative of 1/5*z**5 + 1/2*z**4 + 1/3*z**3 - 2 + f*z**2 + 0*z. Solve v(t) = 0 for t.
-1, 0
Let y(c) = -2*c**2. Let n(v) = 2*v**2 + 0*v**2 - v**2 + 3*v**3 - 2*v**3 + v**4. Let l(w) = -2*n(w) - y(w). Factor l(g).
-2*g**3*(g + 1)
Let h(y) = -3*y**3 - 9*y**2 - y + 5. Let f(c) = 15*c**3 + 45*c**2 + 6*c - 24. Let g(s) = 4*f(s) + 21*h(s). Let g(u) = 0. Calculate u.
-3, -1, 1
Let z(s) be the second derivative of 1/30*s**5 + 1/18*s**3 + 5/72*s**4 - 2*s + 0 + 1/180*s**6 + 0*s**2. Find a, given that z(a) = 0.
-2, -1, 0
Let -8*d**2 - 5*d**3 + 16*d**2 - 12*d**2 - d**3 = 0. Calculate d.
-2/3, 0
Let m(a) be the third derivative of 1/100*a**5 + 0*a - 1/40*a**6 + 1/8*a**4 - 3/350*a**7 - 3*a**2 + 1/5*a**3 + 0. Suppose m(s) = 0. Calculate s.
-1, -2/3, 1
Let f = 9 - 9. Let a(o) be the first derivative of -1/4*o**4 + 1/5*o**5 - 1/3*o**3 + 1/6*o**6 + 0*o**2 - 2 + f*o. Solve a(c) = 0.
-1, 0, 1
Let f be 4/(-6) + 488/3. Let m = f - 482/3. Solve 0 - 2/3*b**3 + m*b**2 - 2/3*b = 0.
0, 1
Let t(r) be the third derivative of r**7/70 + r**6/40 - 3*r**5/10 + 31*r**2. Factor t(l).
3*l**2*(l - 2)*(l + 3)
Factor -2/5*r**2 + 0 + 4/5*r**3 - 4/5*r + 2/5*r**4.
2*r*(r - 1)*(r + 1)*(r + 2)/5
Let i(x) be the third derivative of x**5/210 - x**4/12 + 2*x**3/7 - 5*x**2. Determine l so that i(l) = 0.
1, 6
Let i(r) = r + 12. Let g be i(-8). Let o(d) be the first derivative of 3*d**2 - 15/8*d**g + 2 + 2*d - 1/6*d**3. Find y, given that o(y) = 0.
-2/3, -2/5, 1
