= 0.
-2, -1
Let b be 2/((-2)/3) - -5. Let l(c) be the second derivative of 0 - 2*c - 2/9*c**b - 1/9*c**3 - 1/54*c**4. Factor l(i).
-2*(i + 1)*(i + 2)/9
Let q = 1 - 1. Suppose 5*j = -q*j + 4*r + 12, 0 = -3*j + 3*r + 9. Factor 2/5*p - 2/5*p**2 + j.
-2*p*(p - 1)/5
Let g = 884/3143 - -2/449. Find u such that -2/7*u**3 + 2/7*u**2 + 0 - g*u**4 + 2/7*u = 0.
-1, 0, 1
Let n = -77/2 - -389/10. Suppose n*q + 2/5*q**3 - 4/5*q**2 + 0 = 0. What is q?
0, 1
Let o = -60 + 181/3. Factor 1/3*a**4 - 1/3*a**3 + 0*a + 1/3*a**5 - o*a**2 + 0.
a**2*(a - 1)*(a + 1)**2/3
Factor 3/2 + 3/4*d - 45/4*d**2.
-3*(3*d + 1)*(5*d - 2)/4
Let a(w) be the second derivative of -w**8/10080 + w**7/945 - w**6/360 - w**4/3 + 3*w. Let i(h) be the third derivative of a(h). Let i(s) = 0. Calculate s.
0, 1, 3
Let w(n) = -8*n - 69. Let z be w(-9). Factor -4/5*q**z + 0 - 16/5*q - 16/5*q**2.
-4*q*(q + 2)**2/5
Suppose -5*t + 2 + 3 = 0. Find n such that t + 49/4*n**2 - 7*n = 0.
2/7
Let t(i) be the first derivative of 2*i**6/3 - 5*i**4 + 8*i**2 - 25. Let t(r) = 0. Calculate r.
-2, -1, 0, 1, 2
Let a(m) be the first derivative of -m**6/540 + m**5/180 - m**3 - 1. Let w(h) be the third derivative of a(h). Solve w(k) = 0 for k.
0, 1
Let c(d) be the second derivative of -d**5/240 + d**4/32 - d**3/12 - 2*d**2 - 5*d. Let t(y) be the first derivative of c(y). Find i, given that t(i) = 0.
1, 2
Let b(x) be the second derivative of x**5/20 - x**4/3 - x**3/6 + 2*x**2 + 4*x. Factor b(y).
(y - 4)*(y - 1)*(y + 1)
Let d(x) be the second derivative of -x**7/126 - 2*x**6/45 + x**5/12 + 16*x. Factor d(n).
-n**3*(n - 1)*(n + 5)/3
Suppose -3/5*j**2 + 0*j**3 + 1/5*j**4 + 0 + 2/5*j = 0. Calculate j.
-2, 0, 1
Let k be (-1)/(-2) - (546/(-12))/13. Let b = 20851/600 - 17/200. Determine n, given that 154/3*n**3 - b*n - 44*n**2 - 16/3 + 98/3*n**k = 0.
-2, -2/7, 1
Suppose 1/7*p**4 - 1/7*p**3 + 4/7*p - 4/7*p**2 + 0 = 0. What is p?
-2, 0, 1, 2
Let i = 0 - 6. Let h(a) = -a**3 - 7*a**2 - 8*a - 9. Let w be h(i). Find m, given that 0*m - 2/3*m**2 + 1/3*m**4 + 0*m**w + 1/3 = 0.
-1, 1
Let d(m) be the third derivative of -2/27*m**3 + 0*m - 11/270*m**5 + 0 + 13/108*m**4 - 4*m**2. Factor d(v).
-2*(v - 1)*(11*v - 2)/9
Let o(f) be the second derivative of 2*f + 0*f**3 + 0*f**4 + 0*f**2 + 1/20*f**5 + 0 - 1/30*f**6. Factor o(h).
-h**3*(h - 1)
Let n be (1*(-4 + 5))/1. Factor -1/2*g + 3/2*g**3 - n + 2*g**2.
(g + 1)**2*(3*g - 2)/2
Let v(u) be the first derivative of 2*u**6/3 + 4*u**5/5 - 2*u**4 - 8*u**3/3 + 2*u**2 + 4*u - 2. What is j in v(j) = 0?
-1, 1
Let a = 67/30 + -26/15. Solve a*d - 1/2*d**3 + 1/2*d**2 - 1/2 = 0 for d.
-1, 1
Let v be 0 - (-12 - 0)*2. Suppose -v = -4*c + 2*n, 4*c = c - 5*n - 8. Determine d, given that -1/2*d**5 + 0*d**2 - 1/2*d + d**3 + 0*d**c + 0 = 0.
-1, 0, 1
Let r(o) = -3*o + 7. Let n(g) = 2*g - 3. Let u(t) = 7*n(t) + 3*r(t). Let x be u(1). Factor 0*p**2 - x*p**5 + 0 - 4/5*p**3 - 4*p**4 + 0*p.
-p**3*(5*p + 2)**2/5
Let g(u) be the second derivative of -u**4/54 + 4*u**3/27 - u**2/3 + 6*u. Factor g(h).
-2*(h - 3)*(h - 1)/9
Let o(q) be the second derivative of 1/6*q**3 + 1/120*q**6 + 1/16*q**5 + 0*q**2 + 0 - 2*q + 1/6*q**4. Factor o(z).
z*(z + 1)*(z + 2)**2/4
Suppose -2*g - 3*g + 2*s = 0, -3 = g - s. Let 2*a + 2*a**g - 6 - 2*a**3 - 2 + 6 = 0. What is a?
-1, 1
Factor -w**5 - 3*w**3 + 3*w**3 + w**3.
-w**3*(w - 1)*(w + 1)
Suppose -5*i - 3*n + 0 - 15 = 0, 0 = 3*i - 2*n - 10. Let k = i - 0. Factor k - 1 + 4 + 0 - 3*j**2.
-3*(j - 1)*(j + 1)
Let x(z) = -z + 1. Let m(a) = -4*a**2 - 2*a - 18. Let w(p) = -m(p) - 10*x(p). Find n, given that w(n) = 0.
-2, -1
Let b(x) be the first derivative of x**6/2 + 3*x**5/5 - 3*x**4/2 - 2*x**3 + 3*x**2/2 + 3*x - 12. Find v, given that b(v) = 0.
-1, 1
Let x(o) be the third derivative of 0 - 1/60*o**6 + o**2 + 1/30*o**5 + 1/12*o**4 + 0*o - 1/3*o**3. Factor x(c).
-2*(c - 1)**2*(c + 1)
Let i(m) be the first derivative of -m**4/36 - 2*m**3/9 - 2*m**2/3 + 3*m + 3. Let v(s) be the first derivative of i(s). Suppose v(k) = 0. What is k?
-2
Suppose -2*o - 3 = -3*o. Let c = 2/5 - 0. Factor 0 + 2/5*h + 4/5*h**2 + c*h**o.
2*h*(h + 1)**2/5
Let f = -7 - -9. Let i = 5 - f. Solve 4/7*c**5 + 0 + 6/7*c**4 + 0*c + 0*c**i - 2/7*c**2 = 0 for c.
-1, 0, 1/2
Let j = 17280/7 + -2464. Solve 16/7*n**3 - 38/7*n**2 + 16/7*n - 2/7 + 40/7*n**4 - j*n**5 = 0 for n.
-1, 1/4, 1/2, 1
Let m(v) be the first derivative of 0*v + 4 - 2*v**2 - 10/3*v**3 + 2/5*v**5 - 3/2*v**4 + 1/3*v**6. Determine b, given that m(b) = 0.
-1, 0, 2
Let a(z) = z**2 - 1. Let q be a(1). Suppose q = -3*c - 2*r + 4, 0 = 3*c - 0*c + r - 8. Factor -2*t**5 - 2 + 6*t**c - 6*t**3 + 2 + 2*t**2.
-2*t**2*(t - 1)**3
Let u(b) be the third derivative of -3*b**7/350 - b**6/20 - 7*b**5/75 - b**4/15 + 8*b**2. Factor u(n).
-n*(n + 2)*(3*n + 2)**2/5
Suppose 3*n - y - 11 = 0, 3*n + y - 3*y = 10. Let o(k) be the second derivative of 2/3*k**3 + k**2 + 1/6*k**n + 2*k + 0. Let o(m) = 0. What is m?
-1
Let i(c) be the second derivative of -c**6/60 + c**4/24 + 44*c + 2. Factor i(b).
-b**2*(b - 1)*(b + 1)/2
Suppose -3*j + 10 = -2*o, 4*o + 3 + 3 = -j. Let q(y) be the first derivative of -1/9*y**j + 1/18*y**4 + 2/27*y**3 - 4 - 2/45*y**5 + 0*y. Factor q(d).
-2*d*(d - 1)**2*(d + 1)/9
Let h(u) = -4*u**2 + 2*u + 5. Let d(l) = -21 - 11*l + 4*l + 0*l**2 + 2 + 15*l**2. Let n(m) = 6*d(m) + 22*h(m). Let n(w) = 0. What is w?
-2, 1
Let z(w) be the third derivative of -w**8/10080 - w**7/630 - w**6/120 - w**5/30 - 8*w**2. Let v(c) be the third derivative of z(c). Factor v(p).
-2*(p + 1)*(p + 3)
Suppose -j = 3*j + 120. Let p be j/(-12)*(-12)/(-10). Factor -h**3 + 2*h**p + h**3 - 6*h**2 + 6*h - 2.
2*(h - 1)**3
Let y(h) be the first derivative of h**4/96 - h**3/24 + h**2/16 - 4*h - 5. Let l(o) be the first derivative of y(o). Factor l(t).
(t - 1)**2/8
Let n(d) be the second derivative of d**6/150 - d**4/60 - 10*d. Determine i, given that n(i) = 0.
-1, 0, 1
Let f(q) = -q**3 + 2*q**2 + 4. Let k be f(0). Suppose -8/7*y**3 + 0 + 2/7*y**k - 4/7*y + 10/7*y**2 = 0. Calculate y.
0, 1, 2
Let z(i) be the second derivative of 0 + 1/60*i**4 - 3*i + 1/5*i**2 - 1/10*i**3. Factor z(y).
(y - 2)*(y - 1)/5
Factor -3*d**2 - 17*d**3 - 9*d + 54*d**3 - 28*d**3 + 3*d**4.
3*d*(d - 1)*(d + 1)*(d + 3)
Let w(v) be the first derivative of -5*v**6/6 + 2*v**5 - 10*v**3/3 + 5*v**2/2 + 15. Factor w(f).
-5*f*(f - 1)**3*(f + 1)
Suppose 4*k + 4*f + 8 = 0, 3*f = -4*k + 6*f + 20. Solve -14/3*d**3 + 0 - 8/3*d**4 + 2/3*d - 4/3*d**k = 0.
-1, 0, 1/4
Suppose 3 = -b + 36. Let t be b/45 - (-3)/(-9). Factor 0*i**2 + 2/5*i**3 + 0 - t*i.
2*i*(i - 1)*(i + 1)/5
Let i(b) = -7*b - 3*b**2 + 6*b - 2 + 0*b**2. Let q(a) be the second derivative of a**4/3 + a**3/3 + 3*a**2/2 - 2*a. Let v(z) = -3*i(z) - 2*q(z). Factor v(k).
k*(k - 1)
Factor -2/15*x**2 - 2/5*x**3 + 0 + 2/5*x + 2/15*x**4.
2*x*(x - 3)*(x - 1)*(x + 1)/15
Suppose 3*u = -2*m, 2*u - 2 = -m - 1. Suppose 0*l = -l + u. Suppose -4/5*p**5 + 0 + 0*p**l - 2/5*p**4 + 2/5*p**3 + 0*p = 0. Calculate p.
-1, 0, 1/2
Let p = 16/9 - 10/9. Let i(h) be the first derivative of h**3 + 0*h - 3/5*h**5 + 5/4*h**4 - 1/2*h**2 - 2 - p*h**6. Solve i(k) = 0.
-1, 0, 1/4, 1
Suppose 3/5*y - 3/5*y**2 + 0 = 0. Calculate y.
0, 1
Let c be -1*((0 - 3) + 154/55). Factor 1/5*a**4 + 1/10*a**5 - c - 4/5*a**2 - 1/5*a**3 - 7/10*a.
(a - 2)*(a + 1)**4/10
Let r(q) = -q**5 - q**4 - q**2 + 1. Let z(k) = -6*k**5 - 7*k**4 + k**3 - k**2 + 3. Let f(g) = 6*r(g) - 2*z(g). Factor f(x).
2*x**2*(x + 1)**2*(3*x - 2)
Let u(n) be the second derivative of 0 - 1/12*n**4 + 0*n**2 - 1/20*n**5 + 0*n**3 + 3*n. Factor u(c).
-c**2*(c + 1)
Factor 0*j**3 + j**3 + j**2 - 9*j**4 + 8*j**4 - j.
-j*(j - 1)**2*(j + 1)
Let n(h) be the first derivative of 2/33*h**3 + 0*h - 2/11*h**2 + 7 + 1/22*h**4. Solve n(v) = 0 for v.
-2, 0, 1
Suppose -103*b = -104*b + 2. Solve -11/3*f**b + 19/3*f**3 + 2/3*f + 0 + f**5 - 13/3*f**4 = 0.
0, 1/3, 1, 2
Let f(r) be the second derivative of -r**5/120 + r**4/36 - r**3/36 - 10*r. Suppose f(l) = 0. What is l?
0, 1
Let 0*z**3 + 0*z + 2 - 5/2*z**2 + 1/2*z**4 = 0. What is z?
-2, -1, 1, 2
Let z(o) be the second derivative of o**7/1680 - o**6/180 + o**5/48 - o**4/24 - 7*o**3/6 + 8*o. Let f(b) be the second derivative of z(b). Factor f(c).
(c - 2)*(c - 1)**2/2
Let a(j) be the first derivative of j**6/45 - j**4/18 + 2*j + 3. Let o(k) be the first derivat