
y**3*(y - 5)*(y - 1)/4
Let y(m) be the second derivative of m**6/10 + 3*m**5/10 - m**4/4 - m**3 - 20*m. Solve y(d) = 0 for d.
-2, -1, 0, 1
Let u = 145 - 721/5. What is x in u + 78/5*x**2 - 38/5*x = 0?
2/13, 1/3
Let x be 4/(-6) + 69/92. Let z(h) be the second derivative of h + 0 - 1/2*h**2 + 1/12*h**4 - 1/40*h**5 + x*h**3. Factor z(k).
-(k - 2)*(k - 1)*(k + 1)/2
Let n(c) = 12*c**4 - 18*c**3 - 15*c**2 - 6*c + 6. Let s(r) = -24*r**4 + 35*r**3 + 31*r**2 + 12*r - 11. Let i(b) = 11*n(b) + 6*s(b). Factor i(d).
-3*d*(d - 2)*(2*d + 1)**2
Suppose -z - 3*d + 0 = -1, 2*d = -2*z + 6. Suppose z*s - 8*s = -m + 23, -5*m = 5*s + 10. Factor -7*i**3 - 2*i**2 + 5*i**2 - i + 5*i**m.
-i*(i - 1)*(2*i - 1)
Let m(k) be the second derivative of -k**7/147 - k**6/35 - k**5/35 + k**4/21 + k**3/7 + k**2/7 - 7*k. Factor m(x).
-2*(x - 1)*(x + 1)**4/7
Suppose 3/10 + 6/5*b**2 - 13/10*b = 0. What is b?
1/3, 3/4
Suppose -7 = -r - 0*z + z, z - 23 = -5*r. Let j = -259/3 - -87. Suppose -10/3*y + 10/3*y**4 + 20/3*y**2 + j - 20/3*y**3 - 2/3*y**r = 0. What is y?
1
Suppose -4*m + 2*k + 28 = -0*k, 4*k = -2*m + 14. Find w such that 19 + w**2 - w**2 - m - 3*w**2 = 0.
-2, 2
Let i = -60 - -121/2. Let r(k) be the first derivative of -3/4*k**2 + i*k**3 + 3 - 3/2*k + 3/8*k**4. Suppose r(w) = 0. What is w?
-1, 1
Let v = 117 - 114. What is t in -1/2*t - 3/2*t**2 - 3/2*t**v - 1/2*t**4 + 0 = 0?
-1, 0
Let k(d) be the first derivative of 2/3*d - 4/3*d**2 - 10/9*d**3 + 4. Let k(o) = 0. Calculate o.
-1, 1/5
Let t be 2 + 4 + -2 + -2. Suppose 0 = 2*d + y - 11, -d + t*y - 2 = -0*y. Factor 0*a**2 + 0 + 0*a - 3/4*a**d + 1/4*a**3.
-a**3*(3*a - 1)/4
Let g(d) be the third derivative of 0 - 1/315*d**7 + 0*d**4 + 0*d**3 + 0*d - 2*d**2 - 1/90*d**6 - 1/90*d**5. Solve g(r) = 0 for r.
-1, 0
Let a(o) be the third derivative of 5*o**2 - 1/540*o**6 - 1/216*o**4 - 1/27*o**3 + 1/108*o**5 + 0*o + 0. Factor a(v).
-(v - 2)*(v - 1)*(2*v + 1)/9
Let v(a) be the second derivative of -a**6/60 + a**5/10 - a**4/12 - a**3/3 + 3*a**2/4 + 14*a. Factor v(m).
-(m - 3)*(m - 1)**2*(m + 1)/2
Let f(y) = 5*y**4 - 6*y**3 + 14*y - 1. Let k(q) = q**3 + q + 1. Let d(p) = -f(p) + 4*k(p). Let d(c) = 0. Calculate c.
-1, 1
Factor 15*w - 12*w**2 + 0*w**3 - 5 - 1 + 3*w**3 + 0.
3*(w - 2)*(w - 1)**2
Let c(t) be the third derivative of t**7/42 + t**6/8 + t**5/4 + 5*t**4/24 + 4*t**2. Factor c(z).
5*z*(z + 1)**3
Let c be (27/(-3) - -15) + -6. Solve c + 2/9*b**2 + 4/9*b = 0 for b.
-2, 0
Let b(q) = -5*q**4 + 5*q**3 + 2*q**2 - 2. Let n(j) = 51*j**4 - 51*j**3 - 21*j**2 + 21. Let a(v) = -21*b(v) - 2*n(v). Factor a(r).
3*r**3*(r - 1)
Let i(o) be the first derivative of 0*o**2 - 1/15*o**5 + o + 0*o**4 + 1/9*o**3 + 0*o**6 + 1/63*o**7 + 2. Let c(v) be the first derivative of i(v). Factor c(x).
2*x*(x - 1)**2*(x + 1)**2/3
Let c(v) be the first derivative of 0*v**3 + v**2 - 1/420*v**6 - 3 + 0*v + 1/42*v**4 - 1/210*v**5. Let u(y) be the second derivative of c(y). Factor u(a).
-2*a*(a - 1)*(a + 2)/7
Let u(p) = -4 - 3*p**2 - 6*p - 1 + 0 - 2*p**2. Let f(h) = -16*h**2 - 18*h - 16. Let t(y) = 2*f(y) - 7*u(y). Determine m so that t(m) = 0.
-1
Let u be (-22)/(-3) - (-10)/15. Suppose 4*q - 1 = -h + 7, 4*q + 5*h = -u. Factor -3*o**q + 4*o + 2*o - 3*o**2 + 0*o.
-3*o*(o - 1)*(o + 2)
Let c = 311/4020 + 2/335. Let y(l) be the second derivative of -2*l + 0 - c*l**4 + 1/30*l**6 + 1/6*l**3 + 0*l**2 - 1/20*l**5. Factor y(b).
b*(b - 1)**2*(b + 1)
Let z(x) be the second derivative of x**7/630 + x**6/120 + x**5/60 + x**4/72 + x**2/2 + 3*x. Let v(b) be the first derivative of z(b). Factor v(i).
i*(i + 1)**3/3
Let f(i) be the first derivative of -9*i**5/5 + 21*i**4/4 - 5*i**3 + 3*i**2/2 - 6. Find z such that f(z) = 0.
0, 1/3, 1
Determine c, given that -65/4*c**3 + 5/2 - 45/4*c**2 - 25/4*c**4 + 5/4*c = 0.
-1, 2/5
Let t be (-1)/5 + 318/(-10). Let s = t + 34. Factor 0 + 1/4*f + 1/4*f**3 + 1/2*f**s.
f*(f + 1)**2/4
Let o(w) = w**2 - 2*w - 1. Suppose 4*u + 13 = -5*x, 0 = 3*u - 0*u + 5*x + 16. Let r be o(u). Find h such that -h**r + h**4 + h**5 + 4*h**3 + h**3 - 6*h**3 = 0.
-1, 0, 1
Let n(b) = 2*b**4 - 17*b**3 - 15*b**2 - b. Let l(j) = -3*j**4 + 18*j**3 + 15*j**2. Let y(v) = 5*l(v) + 6*n(v). Factor y(c).
-3*c*(c + 1)**2*(c + 2)
Let n = -4 - -1. Let q = -3 - n. Factor 0*y + q - 2/3*y**2 + 2/3*y**3.
2*y**2*(y - 1)/3
Factor 2 - 7*l**2 - 7*l - 5*l + 9*l**3 + 19*l**2 + l.
(l + 2)*(3*l - 1)**2
Let b(f) = f**3 + f + 1. Let k be -2 - ((2 - 4) + 0). Let r be b(k). Find y, given that y**3 - y**2 + 1 - y + y**4 - r = 0.
-1, 0, 1
Let i be (-2)/(-3) - (-2 - -2). Let o = -526 + 528. What is r in 0 + 0*r + i*r**3 - 2/3*r**o = 0?
0, 1
Let n(t) be the first derivative of t**4/4 - 5*t**3/3 + 4*t + 1. Let m be n(5). Solve -2*s**3 + s**3 + 3*s**4 - 2*s**m = 0.
0, 1
Let c(u) = -15*u**2 - 210*u + 140. Let j(k) = -k**2 - 15*k + 10. Let f(g) = -6*c(g) + 85*j(g). What is n in f(n) = 0?
1, 2
Let k(g) be the first derivative of -g**3/6 - 3*g**2/4 - g - 5. Find r such that k(r) = 0.
-2, -1
Let f(h) = h**3 + 4*h**2 + 2*h - 1. Suppose g + 8 = -3*g. Let w be f(g). Factor 6*m + m**3 + 6*m**2 + 2 + 0*m**3 + m**w.
2*(m + 1)**3
Let i(k) be the second derivative of -2/15*k**6 + 0*k**3 + 0*k**5 + 7*k + 0*k**4 + 2/21*k**7 + 0*k**2 + 0. Let i(z) = 0. Calculate z.
0, 1
Let r(z) be the second derivative of -z**7/147 - z**6/35 - z**5/35 + z**4/21 + z**3/7 + z**2/7 + 2*z. Factor r(d).
-2*(d - 1)*(d + 1)**4/7
Suppose -3/5*w**4 + 6/5*w**3 + 0*w + 0 - 3/5*w**2 = 0. Calculate w.
0, 1
Suppose -10*p + 14 = -6. Factor 2 + 1/2*c**p + 2*c.
(c + 2)**2/2
Suppose -2*m = 2*m. Factor 3*d**3 - 6*d**3 + m*d + 2*d**3 + d.
-d*(d - 1)*(d + 1)
Let 0*j**4 + 0*j + 4/5*j**2 - 6/5*j**3 + 2/5*j**5 + 0 = 0. Calculate j.
-2, 0, 1
Let k(r) be the third derivative of 0*r + 7/120*r**5 + 0 - 1/24*r**4 - 3*r**2 - 1/48*r**6 + 0*r**3. What is b in k(b) = 0?
0, 2/5, 1
Factor -6*s**4 - 7*s**2 + 10*s**2 + 3*s**4.
-3*s**2*(s - 1)*(s + 1)
Let z(n) = -n**2 - 8*n + 6. Let x be 1 - 0 - (-10)/2. Let p(w) = -w**2 - 7*w + 5. Let m(u) = x*p(u) - 5*z(u). Factor m(i).
-i*(i + 2)
Let t(f) be the first derivative of f**6/900 - f**5/150 + 5*f**3/3 + 1. Let b(z) be the third derivative of t(z). Let b(w) = 0. Calculate w.
0, 2
Let g(l) = l**3 - l**2 + 4. Let p be g(0). Suppose -3*f = -8 - p. Factor 3/4*w**f - 1/2*w**3 + 0*w + 1/4 + 1/2*w**5 - w**2.
(w - 1)*(w + 1)**3*(2*w - 1)/4
Let k(w) be the first derivative of -2/3*w**3 - 2 + 2*w + 0*w**2. Determine y, given that k(y) = 0.
-1, 1
Let c(q) = 15*q**3 - 2*q**2 - 15*q + 15. Let v(g) = 7*g**3 - g**2 - 7*g + 7. Let o(h) = -6*c(h) + 13*v(h). Solve o(w) = 0.
-1, 1
Let j(t) be the third derivative of t**7/42 - t**6/8 + t**5/6 + 14*t**2. Factor j(k).
5*k**2*(k - 2)*(k - 1)
Let r(a) = 6*a**3 - 28*a**2 + 46*a - 8. Let t(u) = -2*u**3 + 9*u**2 - 15*u + 3. Let d(n) = -3*r(n) - 8*t(n). Suppose d(l) = 0. Calculate l.
0, 3
Let q(p) be the third derivative of p**6/240 + p**5/60 - p**4/48 - p**3/6 - 15*p**2. Factor q(h).
(h - 1)*(h + 1)*(h + 2)/2
Factor -7*o**2 - 9 + 0*o**3 + 2*o**2 - 3*o**3 - 21*o - 10*o**2.
-3*(o + 1)**2*(o + 3)
Let z(r) = -r**3 + 8*r**2 - 19*r + 9. Let m(i) = i**2. Let h(u) = -6*m(u) - 2*z(u). Factor h(l).
2*(l - 9)*(l - 1)**2
Let o be 4/(-22) - (685/165 - 5). Let p(d) be the first derivative of 1/6*d**4 + o*d + d**2 + 2/3*d**3 + 3. Factor p(m).
2*(m + 1)**3/3
Let l(p) be the first derivative of -1/60*p**5 + 0*p**2 - 2/3*p**3 + 0*p**4 + 1/180*p**6 + 0*p + 3. Let k(m) be the third derivative of l(m). Factor k(a).
2*a*(a - 1)
Let p be 30/42 - 28/98. Factor 0 - p*v**2 + 9/7*v.
-3*v*(v - 3)/7
Factor 0*j**2 - 2/9*j + 0 - 2/9*j**5 + 4/9*j**3 + 0*j**4.
-2*j*(j - 1)**2*(j + 1)**2/9
Let z be 345/12 + (-1)/4. Let c = -28 + z. Determine d so that 1/2 - d + c*d**2 = 0.
1
Let d be 2*-1*(-8)/20. What is v in -2/5 - 2/5*v**2 + d*v = 0?
1
Find d, given that 16/7 + 100/7*d**2 - 80/7*d = 0.
2/5
Let s(v) be the third derivative of 1/120*v**6 + 0*v + 1/336*v**8 + 0 + 1/105*v**7 + 0*v**4 + 0*v**5 + 0*v**3 - 3*v**2. Suppose s(i) = 0. What is i?
-1, 0
Let m(f) = f**2 - 7*f - 2. Let d(n) = n**2 + n + 2. Let o(j) = -2*d(j) - m(j). Solve o(b) = 0 for b.
2/3, 1
Let m(j) be the first derivative of j**2/2 + 11*j - 4. Let k be m(-8). What is p in 0*p**3 + 0*p**k - 5*p**4 - 2*p**3 = 0?
-2/5, 0
Suppose 0 = -0*r - 5*r. Factor t**3 + 0*t + r + 2/3*t**2.
t**2*(3*t