.
-1, 0, 1
Let a(k) be the first derivative of 1/9*k**3 - k - 5 + 1/3*k**2. Factor a(u).
(u - 1)*(u + 3)/3
Suppose 0 = 4*j + 4*x - 56, 0*x + 55 = 4*j + 5*x. Suppose 0 = 5*i - 0 - j. Factor -5*l**3 + 0*l + 3*l**i + 4*l + 2*l**2.
-2*l*(l - 2)*(l + 1)
Let g(p) be the second derivative of 0*p**2 - 1/45*p**6 + 0*p**4 + 4*p + 0 - 1/30*p**5 + 0*p**3. Find f such that g(f) = 0.
-1, 0
Let m be ((-44)/24)/(-11) + 5/15. Solve -m*j**3 + 1/2*j + 1/2 - 1/2*j**2 = 0.
-1, 1
Let k(n) be the second derivative of n**4/42 + 2*n**3/21 - 2*n. Let k(v) = 0. Calculate v.
-2, 0
Suppose -2*i - 15 = -5*i. Suppose i*v + 9 - 34 = 0. Factor 3*q**2 - 5 + 3*q**5 + v + 3*q**3 - 3*q**4 - 6*q**3.
3*q**2*(q - 1)**2*(q + 1)
Let c = 157/40 + -19/5. Let t(p) be the third derivative of 1/20*p**5 + 4*p**2 - 1/40*p**6 + 0 - 1/2*p**3 + c*p**4 + 0*p. Determine y so that t(y) = 0.
-1, 1
Factor 24*s + 18 + 4*s**2 - 8*s - 6.
4*(s + 1)*(s + 3)
Let c = 2 + -1. Let j be 5/(-10) - (c - 2). Determine k so that -j*k**2 + 0 - 1/2*k = 0.
-1, 0
Suppose -3*a - 2 + 13 = 2*w, 3*a = -5*w + 14. Factor -m**2 - m**2 - a*m**2 + 2*m**2.
-3*m**2
Factor 22*a + 16*a - 3*a**3 - 51*a + 25*a.
-3*a*(a - 2)*(a + 2)
Let g(r) = r**2 - r + 40. Let x be g(0). Suppose -2*o + x = 3*o. What is i in 2*i**2 + 15*i - o*i**3 - 15*i = 0?
0, 1/4
Let t(b) be the third derivative of 0*b - 4*b**2 + 0 + 1/40*b**6 + 0*b**3 - 1/8*b**4 + 0*b**5. Solve t(q) = 0.
-1, 0, 1
Suppose i + 0*a = -4*a + 21, 3*i + 5 = 5*a. Solve 6*l**4 - l**i - 2 + 3*l**5 - 4*l**2 + l**3 + 3*l**3 + 0*l**2 - 6*l = 0.
-1, 1
Let h(y) be the third derivative of y**6/30 - y**5/6 + y**4/3 - y**3/3 + 7*y**2. Factor h(p).
2*(p - 1)**2*(2*p - 1)
Factor 26 - 12 + 2*v + 2*v**3 - 4*v**2 - 14.
2*v*(v - 1)**2
Let k be 1 + (0 - -3)/3. Suppose 0*h**3 + 5*h**k - 5*h**2 + h**3 - h**4 = 0. Calculate h.
0, 1
Let o(p) be the second derivative of p**6/1260 + p**5/420 - p**4/42 + 2*p**3/3 + p. Let w(v) be the second derivative of o(v). Determine g, given that w(g) = 0.
-2, 1
Let a = -35 - -30. Let w = a - -5. Suppose w + 5/3*n**3 - 2/3*n - n**2 = 0. Calculate n.
-2/5, 0, 1
Let t(c) = 4*c**4 + 2*c**3. Let p(n) = n**4. Let k(h) = 2*p(h) - t(h). Determine g so that k(g) = 0.
-1, 0
Suppose -3*f = -2*f + 4*f. What is v in 2/3*v**2 + f*v**3 + 0 - 2/3*v**4 + 0*v = 0?
-1, 0, 1
Let z(u) be the second derivative of 2*u + 1/10*u**6 + 0*u**4 + 0 + 3/10*u**5 - 3/2*u**2 - u**3. Factor z(i).
3*(i - 1)*(i + 1)**3
Let z(b) be the first derivative of -b**5/20 + b**4/8 + b**3/3 - b**2/4 - 3*b/4 + 13. Factor z(m).
-(m - 3)*(m - 1)*(m + 1)**2/4
Let t(u) be the first derivative of -3*u**5/5 + 3*u**4/2 + 8*u**3 - 20. Factor t(g).
-3*g**2*(g - 4)*(g + 2)
Let o = -5 + 8. Find t such that -6*t + 4*t**2 + t**2 - 3*t**2 - 9 - o*t**2 = 0.
-3
Let p(v) be the second derivative of v**9/3780 + v**8/560 + v**7/210 + v**6/180 - 2*v**4/3 + 8*v. Let g(u) be the third derivative of p(u). Factor g(y).
4*y*(y + 1)**3
Let 2/3*r**4 - 8/3*r + 0 - 8/3*r**2 + 2/3*r**3 = 0. Calculate r.
-2, -1, 0, 2
Suppose -5*t = -2*t + 2*l + 2, 0 = 5*t + 3*l + 3. Let p = -7 + 22/3. Factor t - 1/3*o - p*o**2.
-o*(o + 1)/3
Let k be (-4)/(-18) - 75/(-27). Let b(a) be the third derivative of 0*a**k + 0 - a**2 + 0*a - 1/270*a**6 - 1/108*a**4 + 1/90*a**5. Factor b(i).
-2*i*(i - 1)*(2*i - 1)/9
Let n(y) = 2*y**2 - 6*y - 6. Let h(b) = -b**2 - b + 1. Let x(t) = -2*h(t) + n(t). Factor x(i).
4*(i - 2)*(i + 1)
Let q(o) be the third derivative of -o**7/420 + o**6/120 - o**5/120 - 7*o**2. Solve q(p) = 0.
0, 1
Let f(g) = -g**4 - g**3 - g**2 - g. Let i(l) = -2*l**5 - 6*l**4 + 2*l**3 - 2*l**2 - 8*l. Let d(s) = 4*f(s) - i(s). Factor d(y).
2*y*(y - 1)**2*(y + 1)*(y + 2)
Suppose -7*b = -2*b - 90. Suppose j = -4*j + 10. Factor b + 300*m**j + 250*m**3 + 7 + 120*m - 9.
2*(5*m + 2)**3
Let z = 1111/264780 + 2/1471. Let m(o) be the third derivative of o**2 + 1/360*o**6 + 0*o - 1/18*o**3 + 0 - 1/72*o**4 + z*o**5. Factor m(k).
(k - 1)*(k + 1)**2/3
Let f(t) be the third derivative of t**8/2352 - t**7/490 - t**6/420 + t**5/70 + t**4/168 - t**3/14 - 53*t**2. Let f(h) = 0. Calculate h.
-1, 1, 3
Let t(r) = 5*r + 119. Let x be t(-23). Factor 2/7*s**5 + 32/7*s**2 + 4/7 + x*s**3 + 18/7*s + 12/7*s**4.
2*(s + 1)**4*(s + 2)/7
Let d(t) be the second derivative of t**7/1155 + t**6/660 + 2*t**2 - 3*t. Let v(h) be the first derivative of d(h). Let v(p) = 0. Calculate p.
-1, 0
Let x be 13/117 - (-1)/(-9). Suppose x = t + t - 8. Factor -3/4*z**t - 1/4*z + 1/4*z**3 + 3/4*z**2 + 0.
-z*(z - 1)*(z + 1)*(3*z - 1)/4
Solve -1 - 1/4*n**2 + 5/4*n = 0 for n.
1, 4
Let u(n) be the first derivative of -n**6/2 + 6*n**5 - 18*n**4 - 10*n**3 + 75*n**2/2 - 32. What is l in u(l) = 0?
-1, 0, 1, 5
Suppose p - 15 = -13. Determine w, given that 1/3*w**p + 0*w + 0 = 0.
0
Factor 0 - 3/2*m**2 - 3/8*m - 9/8*m**3.
-3*m*(m + 1)*(3*m + 1)/8
Suppose 10 = 3*h + 10. Suppose -2/9*a**4 + 4/9*a**2 + 0*a + h*a**3 - 2/9 = 0. Calculate a.
-1, 1
Let p be (6/(-81))/((-8)/12). Let m(q) be the second derivative of -p*q**3 - 1/18*q**4 + 2*q + 0*q**2 + 0. Factor m(y).
-2*y*(y + 1)/3
Let n(t) be the second derivative of -3*t**5/80 + t**3/8 + 12*t. Factor n(l).
-3*l*(l - 1)*(l + 1)/4
Factor -2/3*r + 3*r**2 + 5/3*r**4 - 4*r**3 + 0.
r*(r - 1)**2*(5*r - 2)/3
Let l(z) be the first derivative of 3 - 1/4*z - 1/12*z**3 - 1/4*z**2. What is y in l(y) = 0?
-1
Let u be (3/(-6))/((-242)/88). Factor 2/11*q**2 - 4/11 - u*q.
2*(q - 2)*(q + 1)/11
Let o(d) be the third derivative of d**6/720 + d**5/180 + d**4/144 - 3*d**2. Suppose o(c) = 0. Calculate c.
-1, 0
Let u(q) be the third derivative of 0 + 3/20*q**5 - 1/40*q**6 + 0*q - 5*q**2 + 1/2*q**3 - 3/8*q**4. Factor u(d).
-3*(d - 1)**3
Let x(i) = -15*i**4 + 45*i**3 - 33*i**2 - 9*i. Let n(u) = -45*u**4 + 134*u**3 - 98*u**2 - 26*u + 1. Let h(f) = -6*n(f) + 17*x(f). Factor h(j).
3*(j - 1)**3*(5*j + 2)
Let n = 10 - 12. Let d(p) = -3*p**2 - p**2 - 8*p**2 + 5*p**3 + 21*p - 13. Let z(u) = -4*u**3 + 12*u**2 - 22*u + 14. Let b(j) = n*d(j) - 3*z(j). Factor b(s).
2*(s - 2)**3
Suppose 2 = 2*s - g - 4, -14 = -5*s + 2*g. Factor -j**3 + 1 + s*j**4 - 3*j**2 + j + 6*j**3 - 6*j**3.
(j - 1)**2*(j + 1)*(2*j + 1)
Let f(y) be the first derivative of -y**3 - 9*y**2/2 - 6*y + 4. Factor f(k).
-3*(k + 1)*(k + 2)
Let m(w) be the first derivative of -w**3/7 - 12*w**2/7 - 36*w/7 - 55. Determine i so that m(i) = 0.
-6, -2
Suppose 0 = -z - 2*z - 2*t + 7, -t = 1. What is b in -16/7 - 12/7*b**2 - 24/7*b - 2/7*b**z = 0?
-2
Find c such that -8*c - c**2 - 6*c - 1 + 12*c = 0.
-1
Let g = -6 - -9. Suppose g*f + 3*o = 0, 0*o + 14 = 2*f - 5*o. Factor i**3 + 13 + 11*i**f + 12*i - 5*i**2 - 5.
(i + 2)**3
Suppose 11*p - 9*p = 52. Let a be 13/p*6/5. Factor 0 + 3/5*d**4 - 6/5*d**2 + 0*d + a*d**3.
3*d**2*(d - 1)*(d + 2)/5
Let u(o) be the first derivative of -o**6/3 + 2*o**5/5 + o**4 - 4*o**3/3 - o**2 + 2*o - 9. Solve u(j) = 0 for j.
-1, 1
Let g(c) be the first derivative of 1/4*c**2 + 1/12*c**6 + 1/3*c**3 - 1/4*c**4 - 1/2*c + 3 - 1/10*c**5. Factor g(n).
(n - 1)**3*(n + 1)**2/2
Let b(r) be the third derivative of -r**8/1848 - 2*r**7/1155 + r**6/660 + r**5/165 + 16*r**2 + 2. Let b(g) = 0. Calculate g.
-2, -1, 0, 1
Let h(n) be the first derivative of -3/7*n**3 + 3/28*n**4 + 4 + 9/14*n**2 - 3/7*n. Factor h(j).
3*(j - 1)**3/7
Let v(c) be the first derivative of -3/25*c**5 + 8/5*c + 13/20*c**4 + 5 - 2/5*c**2 - 14/15*c**3. Determine y so that v(y) = 0.
-2/3, 1, 2
Let c(j) be the first derivative of -2 + 1/75*j**6 - j + 0*j**4 + 0*j**3 - 1/50*j**5 + 0*j**2. Let l(u) be the first derivative of c(u). Factor l(i).
2*i**3*(i - 1)/5
Let q = 2 - -1. Let o = 7 - 5. Let -q + o*d + 5 + d + d**2 = 0. Calculate d.
-2, -1
Let v(l) be the second derivative of 0*l**2 - 5/168*l**7 - 4*l - 1/60*l**6 + 0*l**4 + 0*l**5 + 0 + 0*l**3. Determine c so that v(c) = 0.
-2/5, 0
Let m(j) = 3*j**4 + 3*j**3 - 3*j - 3. Let p(v) = 3*v**4 + 3*v**3 - v**2 - 3*v - 2. Let h = 4 + -1. Let y(u) = h*p(u) - 2*m(u). Determine r, given that y(r) = 0.
-1, 0, 1
Let b(p) be the first derivative of -4*p**3/15 + 4*p**2/5 + 6. Factor b(o).
-4*o*(o - 2)/5
Let b be (2/6)/(2/18). Suppose s + m + b*m = 4, -m + 1 = 2*s. Suppose -2/5*g**2 + s - 2/5*g = 0. What is g?
-1, 0
Let b = -16 + 16. Let r(h) be the first derivative of -2/3*h**3 + 1/2*h**2 + 1 + b*h + 1/4*h**4. Solve r(z) = 0 for z.
0, 1
Let x be 30