 = -t**3 + t**2 - t. Let x(k) = k**4 - k**3 - 2*k. Suppose 6*c = -3 + 21. Let b(a) = c*x(a) - 6*s(a). Suppose b(d) = 0. Calculate d.
-2, 0, 1
Suppose 2*l + 6*n - 3*n - 18 = 0, n = 0. Suppose 2*f = l - 3. Determine h, given that -1/4*h**f + 1/2*h**4 + 0*h + 0 + 0*h**2 - 1/4*h**5 = 0.
0, 1
Let h(w) be the first derivative of 3*w**4/22 + 14*w**3/33 + 5*w**2/11 + 2*w/11 - 1. Let h(u) = 0. Calculate u.
-1, -1/3
Let l(b) = -b**5 - 4*b**4 + 4*b**2 + 4*b - 4. Let n(a) = 2*a**5 + 8*a**4 + a**3 - 7*a**2 - 7*a + 7. Let h(t) = -7*l(t) - 4*n(t). Suppose h(z) = 0. What is z?
-2, 0
Let v(s) be the second derivative of s**7/56 + s**6/40 + 15*s. Solve v(p) = 0.
-1, 0
Let v(z) be the first derivative of 3*z**4/4 - z**3/3 + 5*z**2/2 - 3*z - 3. Let c(s) = -7*s**3 + 2*s**2 - 11*s + 7. Let r(g) = -4*c(g) - 9*v(g). Factor r(n).
(n - 1)*(n + 1)**2
Let w(p) be the third derivative of p**7/105 - 7*p**6/60 + p**5/2 - 3*p**4/4 + 25*p**2. Factor w(a).
2*a*(a - 3)**2*(a - 1)
Let n(z) be the third derivative of z**9/30240 + z**8/6720 - z**6/720 - z**5/15 + z**2. Let g(i) be the third derivative of n(i). Solve g(u) = 0 for u.
-1, 1/2
Let v be (-2)/(-12) - 153/(-54). Let t be (-10)/(-12) + (-1)/2. Factor 1/3*q + t*q**2 + 0 - 1/3*q**4 - 1/3*q**v.
-q*(q - 1)*(q + 1)**2/3
Let v(c) = -14*c**2 + 12*c. Let j(g) = -g**2 + g. Suppose -4 = 4*u - 20. Suppose m - 8 = -3*w, 2*w - 4*m = u*w - 22. Let n(i) = w*v(i) - 8*j(i). Factor n(r).
-2*r*(3*r - 2)
Let r(c) be the third derivative of 0*c**5 + 1/54*c**4 + 0*c + 2*c**2 + 1/27*c**3 - 1/270*c**6 - 1/945*c**7 + 0. Factor r(y).
-2*(y - 1)*(y + 1)**3/9
Let u(p) be the second derivative of p**7/126 - 4*p**6/45 + 2*p**5/5 - 8*p**4/9 + 8*p**3/9 - p. Suppose u(x) = 0. Calculate x.
0, 2
Let i(a) = a**3 + 4*a**2 - a - 4. Let k be i(-4). Let r = 161 - 159. Determine w, given that 1/3*w**5 + 1/3*w**3 + k*w + 0*w**r + 0 - 2/3*w**4 = 0.
0, 1
Let i(t) = 2*t**2 + 6*t + 12. Let u(b) = -2*b**2 - 5*b - 11. Let q(p) = 7*i(p) + 6*u(p). Factor q(k).
2*(k + 3)**2
Let g(m) = -15*m**5 - 44*m**4 - 41*m**3 - 10*m**2 + 2*m. Let q(o) = 240*o**5 + 705*o**4 + 657*o**3 + 159*o**2 - 33*o. Let n(a) = -33*g(a) - 2*q(a). Factor n(w).
3*w**2*(w + 1)**2*(5*w + 4)
Factor 3/4*n + 0 - 1/4*n**3 + 1/2*n**2.
-n*(n - 3)*(n + 1)/4
Let t = -18 + 28. Suppose 0 = 3*c + 4 - t. Determine m, given that -16/5*m**c + 4/5 + 6/5*m**3 + 6/5*m = 0.
-1/3, 1, 2
Factor 14*f - 27*f - 17*f + 5*f**2.
5*f*(f - 6)
Let u(a) be the second derivative of -a**4/27 + 16*a**3/27 - 8*a**2/3 - 42*a. Solve u(k) = 0.
2, 6
Let a(h) = -3*h**2 + 12*h. Let j(t) = 5*t**2 - 24*t. Let w(i) = 11*a(i) + 6*j(i). Let w(b) = 0. What is b?
-4, 0
Let g(q) be the first derivative of 2*q - 2 + 2/33*q**3 - 1/11*q**2 - 1/66*q**4. Let h(y) be the first derivative of g(y). Factor h(s).
-2*(s - 1)**2/11
Let q be (2 - 0)/(13 + -7). Factor p - 2/3 - q*p**2.
-(p - 2)*(p - 1)/3
Suppose 0 = 5*s + 5*u - 15 - 75, 0 = -4*s + 5*u + 90. Let k = s + -15. Determine c so that 11/3*c**3 + 10/3*c**k + 0*c - 2/3*c**2 - 19/3*c**4 + 0 = 0.
0, 2/5, 1/2, 1
Factor 6 + 6*o**2 - 2 - 10*o**2.
-4*(o - 1)*(o + 1)
Let v = 1220 - 3658/3. Suppose -v - t - 1/3*t**2 = 0. Calculate t.
-2, -1
Let j(w) = -2*w**4 + 4*w**2 + 5*w - 2. Let h(y) = y**4 - 2*y**2 - 3*y + 1. Let o be 12/(-6) - 10/(-2). Let g(a) = o*j(a) + 5*h(a). Determine c so that g(c) = 0.
-1, 1
Let t(r) be the first derivative of -r**4 - 4*r**3 - 4*r**2 - 23. Factor t(i).
-4*i*(i + 1)*(i + 2)
Let o(b) be the second derivative of b**7/378 - b**6/135 + b**5/180 + 2*b - 17. Find r such that o(r) = 0.
0, 1
Let o(w) be the second derivative of w**7/840 + w**6/160 + w**5/120 + 9*w**2/2 + 10*w. Let q(h) be the first derivative of o(h). Find u, given that q(u) = 0.
-2, -1, 0
What is d in 1/7*d**3 + 4/7*d**2 - 1/7*d - 4/7 = 0?
-4, -1, 1
Let r(j) = -j**3 + j - 1. Suppose -4*s + 2*s = 24. Let n(y) = -3*y**3 - 2*y**2 + 4*y - 4. Let o(t) = s*r(t) + 3*n(t). Solve o(k) = 0.
0, 2
Let p(w) = w - 5. Let l be p(8). Let h(c) be the first derivative of -2*c - 2/5*c**5 + 1 - 4*c**2 - 4*c**l - 2*c**4. Solve h(d) = 0 for d.
-1
Let w(u) = -u**3 - 10*u**2 - 10*u + 2. Let g be w(-9). Let d = g + -9. Factor 2*x + 4*x**2 - 8*x + 4*x**2 - 2*x**3 - 2*x**d + 2.
-2*(x - 1)**3
Let i(n) = -4*n - 4. Let b be i(-4). Suppose -5*z + b = -13. Factor 0 + 4/5*p**2 + 9*p**4 - z*p**5 + 0*p - 24/5*p**3.
-p**2*(p - 1)*(5*p - 2)**2/5
Let u(l) be the third derivative of -1/3*l**3 - 4*l**2 + 1/12*l**4 + 0 - 1/120*l**5 + 0*l. Factor u(w).
-(w - 2)**2/2
Let v(s) = 12*s**3 + 12*s**2 - 12*s - 12. Let z(u) = -8*u**3 - 8*u**2 + 8*u + 8. Let l(g) = -5*v(g) - 8*z(g). Factor l(x).
4*(x - 1)*(x + 1)**2
Let p = 9 - 7. Let v(r) be the third derivative of 1/60*r**5 - 1/9*r**3 + p*r**2 + 0*r + 0 - 5/72*r**4. Factor v(o).
(o - 2)*(3*o + 1)/3
Let z(k) be the third derivative of -5*k**8/32 + 163*k**7/420 - k**6/80 - 59*k**5/120 + k**3/3 - k**2. Suppose z(b) = 0. Calculate b.
-2/5, -1/3, 2/7, 1
Let l be 18 + (-2)/4*-4. Suppose 0 = u - 2*u - 3*f + 20, u + l = 5*f. Solve 3*s**2 + u*s**2 - s**2 + 2*s + 8*s**3 + 3*s**4 = 0.
-1, -2/3, 0
Let r be (-13)/5 - (-3)/1. Factor 0 - r*h - 2/5*h**2.
-2*h*(h + 1)/5
Let r be (-3 + 0)/3*-1. Suppose 1 + r = n. Factor 0 + 0*b + 2/3*b**n.
2*b**2/3
Suppose -a + 10 = 5. Let h(r) be the first derivative of 1/2*r**2 - 1/4*r**4 + 1/5*r**a + 0*r - 2 - 1/3*r**3. Factor h(f).
f*(f - 1)**2*(f + 1)
Let w(q) be the third derivative of q**7/49 - q**6/60 - q**5/105 - 8*q**2. Determine c so that w(c) = 0.
-1/5, 0, 2/3
Let n(l) be the first derivative of l**4/6 + 2*l**3/9 - l**2/3 - 2*l/3 - 6. Factor n(q).
2*(q - 1)*(q + 1)**2/3
Solve 4*f**2 - 3*f**2 - 37*f**4 + 4*f**3 + 36*f**4 - 4*f**5 = 0 for f.
-1, -1/4, 0, 1
Let h(y) be the first derivative of -4/21*y**3 + 0*y + 0*y**4 - 1/7*y**2 + 4/35*y**5 + 10 + 1/21*y**6. Solve h(n) = 0.
-1, 0, 1
Let y = 26 + -24. Suppose -1/4*r**y - 1/4*r + 1/4 + 1/4*r**3 = 0. Calculate r.
-1, 1
What is y in 0*y - 1/2*y**5 - 1/2*y**2 - 3/2*y**4 + 0 - 3/2*y**3 = 0?
-1, 0
Let h(x) = -2*x + 14. Let i be h(7). Let l be (0 - -2) + i/6. Factor -2/7*u**3 - 2/7*u - 4/7*u**l + 0.
-2*u*(u + 1)**2/7
Suppose -5*a + 2 = h - 0*h, -5*h - a = -10. Factor -4*i**3 + 7*i**3 - 4*i**2 + h*i + i**2 - i**4 - i.
-i*(i - 1)**3
Let i(l) = l**5 + l**4 + l**2. Let c be (3/(-1) - -2)*-4. Let q(s) = 3*s**5 + 13*s**4 - 24*s**3 + 20*s**2. Let h(a) = c*i(a) - q(a). Factor h(m).
m**2*(m - 4)**2*(m - 1)
Let t = -38 + 42. Let s(u) be the first derivative of 4/3*u + 2/15*u**5 + 1/3*u**2 + 2 - 2/3*u**3 - 1/6*u**t. Factor s(b).
2*(b - 2)*(b - 1)*(b + 1)**2/3
Let k(d) be the third derivative of d**8/294 - 4*d**7/245 + d**6/84 + d**5/21 - 3*d**4/28 + 2*d**3/21 - 8*d**2. Let k(q) = 0. What is q?
-1, 1/2, 1, 2
Factor -3*a**2 - 2*a**2 - 8*a - 1 + 6*a + 4*a**2.
-(a + 1)**2
Let t be (2*6/(-4))/(-1). Let c(a) be the third derivative of 0 + 1/18*a**t + 1/60*a**5 + a**2 - 1/18*a**4 + 0*a. Factor c(l).
(l - 1)*(3*l - 1)/3
Let x be (618/18)/((-1)/(-2)). Let d = -68 + x. Factor 0 + 1/3*f + 1/3*f**3 + d*f**2.
f*(f + 1)**2/3
Let d = -3429/5 - -686. Find l such that 4/5*l**5 - 1/5*l + 0 + 9/5*l**3 - 11/5*l**4 - d*l**2 = 0.
-1/4, 0, 1
Let j be -4*7/(-1 + -13). Factor j*n**4 + 54/7*n**2 + 4/7 + 46/7*n**3 + 26/7*n.
2*(n + 1)**3*(7*n + 2)/7
Let v(q) = -q**2 - 3 + 2*q + q + 0*q**2 - 2*q**3. Let r(x) = -x**3 - x**2 + x - 1. Let f(b) = -3*r(b) + v(b). Find i such that f(i) = 0.
-2, 0
Let p be 1/((-51)/27 - -2). Let i be 1 - (30/p + -3). Solve -i + 17/3*t**3 - 7*t**2 + 11/3*t - 5/3*t**4 = 0.
2/5, 1
Suppose -8*q + 31 = -1. Let n(k) be the second derivative of -2/21*k**3 + 1/14*k**q + 0 + 0*k**2 - 2*k + 1/15*k**6 + 6/35*k**5. Factor n(r).
2*r*(r + 1)**2*(7*r - 2)/7
Let a(f) be the first derivative of -f**5/15 + f**4/6 + f**2/2 + 7. Let p(c) be the second derivative of a(c). Find o, given that p(o) = 0.
0, 1
Let t(j) be the second derivative of j**6/6 - 11*j**5/4 + 15*j**4 - 40*j**3/3 - 160*j**2 + 33*j. What is n in t(n) = 0?
-1, 4
Let s = 71 - 209/3. Determine o, given that 2*o - s - 2/3*o**2 = 0.
1, 2
Let p = 1478/11 - 134. Determine y so that -p*y**2 + 2/11*y + 2/11*y**3 + 0 = 0.
0, 1
Let f(a) be the first derivative of 4 + 2/21*a**3 + 0*a**2 - 2/7*a. Determine p so that f(p) = 0.
-1, 1
Let s = 5 - 2. Suppose 4*l - c - 11 = 0, -30*l + 31*l - c = 5. Find m such that 2/7*m**s + 0 - 2/7*m*