et s be (32/504)/(2/7). Let -2/9*p**4 + s*p**3 + 0 + 0*p + 0*p**2 = 0. Calculate p.
0, 1
Let u = -13893/1420 + 45/71. Let t = 47/5 + u. Factor -t + 1/4*p**2 + 0*p.
(p - 1)*(p + 1)/4
Let k(b) be the third derivative of -b**9/30240 + b**8/3360 - b**7/1260 - b**5/20 + 4*b**2. Let l(n) be the third derivative of k(n). Let l(s) = 0. What is s?
0, 1, 2
Suppose 2*v + 3*g - 1 = 14, -g + 18 = 5*v. Find s, given that s**v + s + 3/2*s**2 + 1/4 + 1/4*s**4 = 0.
-1
Let v(n) = 8*n**4 + 10*n**3 - 12*n**2 - 10*n + 4. Let p(o) = o**2 - 1. Let h(c) = 6*p(c) + v(c). Let h(x) = 0. What is x?
-1, -1/4, 1
Let c(v) be the second derivative of v**4/20 + 3*v**3/10 + 3*v**2/5 - 4*v. Find z such that c(z) = 0.
-2, -1
Let z(s) be the second derivative of -s**5/40 - s**4/8 + s**2 - 10*s. Determine x, given that z(x) = 0.
-2, 1
Let a(w) = w**2 + 13*w - 27. Let r be a(-15). Let s(k) be the first derivative of r + 0*k + 2/5*k**2 + 2/15*k**3. Determine f, given that s(f) = 0.
-2, 0
Let h(a) be the first derivative of -2/3*a - 6 - 1/9*a**3 + 1/2*a**2. Find f, given that h(f) = 0.
1, 2
Let k(v) be the third derivative of v**6/240 - v**5/20 + 11*v**4/48 - v**3/2 + 23*v**2. Determine u, given that k(u) = 0.
1, 2, 3
Let y be (-3 - -3)/(30/10) - -2. Factor 0 - 1/5*x**5 + 2/5*x**3 + 0*x**4 + 0*x**y - 1/5*x.
-x*(x - 1)**2*(x + 1)**2/5
Let a(i) be the first derivative of i**5/45 + i**4/6 + 4*i**3/9 + 4*i**2/9 + 2. Suppose a(c) = 0. Calculate c.
-2, 0
Let t(v) = v**3 - 2*v**2 + v. Let u be t(2). Suppose u*g + 3*o = 30, -2*o - 24 = -4*g + o. Determine y, given that 9*y - y**2 - g*y = 0.
0
Let c = 1 + 0. Let k = 1 + c. Solve 1/4*z**4 - 1/4*z**k - 1/4*z**3 + 0 + 1/4*z = 0.
-1, 0, 1
Let y = 0 - -1. Let z be (-5)/(-2) + 2/(-4). Let -3 - 1 + 3 - y + 4*l - z*l**2 = 0. What is l?
1
Let c(h) be the second derivative of 2*h**2 + 0 - 1/3*h**4 + 5*h + 1/10*h**5 - 1/3*h**3. Suppose c(y) = 0. What is y?
-1, 1, 2
Let u(h) = -2*h**2 + 5*h - 5. Let b(y) = -2*y**2 + 6*y - 6. Suppose 10 = -2*d, 4*o - 2*d + 7*d + 49 = 0. Let j(k) = o*u(k) + 5*b(k). Factor j(t).
2*t**2
Let z(l) = -15*l**4 - 15*l**3 + 111*l**2 + 240*l + 96. Let u(i) = i**4 + i**3 - 7*i**2 - 15*i - 6. Let r(n) = -33*u(n) - 2*z(n). Factor r(m).
-3*(m - 2)*(m + 1)**3
Solve 45/2*d**4 - 57/2*d**2 + 6 - 33*d**3 + 27*d**5 + 6*d = 0.
-1, -2/3, 1/2, 1
Let q(h) be the first derivative of h**4 + 14*h**3/3 - 12*h**2 + h + 11. Let c(f) be the first derivative of q(f). Find n, given that c(n) = 0.
-3, 2/3
Let n(b) be the third derivative of b**5/36 + 25*b**4/36 + 125*b**3/18 - 14*b**2. Factor n(o).
5*(o + 5)**2/3
Let h(p) = -6*p**5 - 9*p**4 - 3*p**3 + 3*p - 3. Let c(a) = -a**2 + 4*a + 2. Let u be c(5). Let k(v) = v - 1. Let l(i) = u*k(i) + h(i). Factor l(b).
-3*b**3*(b + 1)*(2*b + 1)
Let n(i) be the third derivative of 0*i**3 + 1/36*i**4 + 0*i + 0 + 1/180*i**5 - 1/630*i**7 - 2*i**2 - 1/180*i**6. Factor n(z).
-z*(z - 1)*(z + 1)*(z + 2)/3
Suppose 2*n - 4*d = 3*n + 114, -d - 486 = 4*n. Let z be n/(-56) + 3/(-7). Factor -5/4*k + z*k**2 - 1/2.
(k - 1)*(7*k + 2)/4
Let b(i) be the third derivative of i**7/42 + i**6/8 + i**5/4 + 5*i**4/24 - 4*i**2. Factor b(c).
5*c*(c + 1)**3
Let h be 0 + (-23)/9 - -3. Let k(o) be the first derivative of 1/9*o**2 - 1 + 2/27*o**3 - h*o. Factor k(t).
2*(t - 1)*(t + 2)/9
Factor -4*h**2 - 640*h + 640*h + 4.
-4*(h - 1)*(h + 1)
Let z be 440/560 + 2/(-4 + 0). Factor -1/7*x**4 - z*x + 0 - 5/7*x**2 - 4/7*x**3.
-x*(x + 1)**2*(x + 2)/7
Let k(x) be the first derivative of 2*x**3/27 + 2*x**2/3 + 2*x + 1. Factor k(v).
2*(v + 3)**2/9
Let k(x) be the second derivative of x**5/14 + 2*x**4/21 - x**3/21 - 3*x + 6. Factor k(f).
2*f*(f + 1)*(5*f - 1)/7
Let o(q) be the third derivative of -5*q**8/84 + 44*q**7/105 - 3*q**6/5 - 16*q**5/15 + 23*q**4/6 - 4*q**3 - 31*q**2. What is u in o(u) = 0?
-1, 2/5, 1, 3
Let x be -6*(-4 + 6/4). Factor 32 + 2*o**2 + 8*o + 2*o**4 + 40*o + 3*o**3 - x*o**3 + 0*o**3.
2*(o - 4)**2*(o + 1)**2
Let u(x) = -x**2 + 7*x + 10. Let b be u(8). Determine y, given that 2 + 0 + y - 4*y + y**b = 0.
1, 2
Let v be (-9)/4*(-16)/6. Let s = v - 4. Suppose -4*t**2 - s*t + t**3 + 0*t**2 - 3*t**3 = 0. Calculate t.
-1, 0
Suppose -u = -0*u - 11. Factor l**2 + 0*l**4 + 5*l - 9*l**3 + u*l**4 - 4*l**5 - 4*l.
-l*(l - 1)**3*(4*l + 1)
Let o(i) = -i - 1. Let u be o(-4). Let d(p) be the first derivative of -1/6*p**u + 1/2*p + 0*p**2 + 2. Suppose d(n) = 0. Calculate n.
-1, 1
Suppose 8 = 4*s + 24, -5*n + 3*s = -272. Let q be (-2)/13 - (-34)/n. Factor -3/4*g - 1/4 - q*g**2.
-(g + 1)*(2*g + 1)/4
Suppose 0 = 2*g - 0*q - 3*q - 11, 2*g - 17 = 5*q. Let n(i) be the first derivative of 0*i + i**2 - i**3 - 1/4*i**5 + g - 9/8*i**4. Factor n(j).
-j*(j + 2)**2*(5*j - 2)/4
Let t(g) = -5*g**2 + g + 5. Let i be t(3). Let d = i - -113/3. Factor 2/3*r + 0 + 4/3*r**2 + d*r**3.
2*r*(r + 1)**2/3
Suppose -4*v + 2*c - c + 11 = 0, 5 = 5*v - 3*c. Let p(q) = -q + 6. Let n be p(6). Factor n*w**3 - 2/3*w**2 - 1/3*w + 1/3*w**5 + 0 + 2/3*w**v.
w*(w - 1)*(w + 1)**3/3
Let r(u) be the third derivative of 0 - 1/360*u**6 + 0*u + 2/3*u**3 + 1/20*u**5 - 3/8*u**4 + 4*u**2. Let g(p) be the first derivative of r(p). Factor g(q).
-(q - 3)**2
Let c(v) = 8*v**4 + 39*v**3 + 77*v**2 + 47*v - 23. Let y(r) = -4*r**4 - 20*r**3 - 39*r**2 - 23*r + 11. Let m(d) = -6*c(d) - 14*y(d). Factor m(l).
2*(l + 2)**3*(4*l - 1)
Let p(y) be the first derivative of -y**6/35 - y**5/14 - y**4/42 + y**3/21 - 5*y - 6. Let q(a) be the first derivative of p(a). Suppose q(z) = 0. What is z?
-1, 0, 1/3
Let o = -1057 + 4231/4. Factor 21/4*z - 3/2 + 15/4*z**3 - 27/4*z**2 - o*z**4.
-3*(z - 2)*(z - 1)**3/4
Let -1/2*b + 0 + 1/6*b**2 = 0. What is b?
0, 3
Let n = -49 + 51. Factor 1/3*z - 1/3*z**n - 1/3*z**3 + 1/3.
-(z - 1)*(z + 1)**2/3
Factor 0*n**2 - 3*n**3 - 3*n**4 - 76*n**5 + 79*n**5 + 3*n**2.
3*n**2*(n - 1)**2*(n + 1)
Suppose 14/3*s**2 - 20/3*s**3 - 8/3 + 2*s**4 + 8/3*s = 0. Calculate s.
-2/3, 1, 2
Let t be (1/1 - -1)/1. Suppose -4 = -t*y - 0. Determine v so that 2*v**2 - v + 3*v - 4*v**y = 0.
0, 1
Suppose 2 = -4*r + 10. Solve -8*m**4 + 2*m**2 - 2*m**r - 4*m**2 + 2*m - 14*m**3 = 0.
-1, 0, 1/4
Suppose 0*i - 10*i**2 - i + 11*i**2 = 0. What is i?
0, 1
Let m = -65 - -146. Factor 6*x**3 + 9*x**3 + 3*x**4 + 9*x**3 + 54*x**2 + 0*x**3 - m.
3*(x - 1)*(x + 3)**3
Find m such that -1/5*m**3 + 0*m - 1/5*m**2 + 0 = 0.
-1, 0
Let k = 10 + -6. Let j(a) be the second derivative of 0*a**2 + 0 - 1/80*a**5 - 1/24*a**3 + a - 1/24*a**k. Factor j(o).
-o*(o + 1)**2/4
Let u(a) be the first derivative of a**4/7 - 8*a**3/21 - 10*a**2/7 + 24*a/7 + 21. Factor u(h).
4*(h - 3)*(h - 1)*(h + 2)/7
Factor 0*s - 2/7*s**3 + 0*s**4 + 0*s**2 + 2/7*s**5 + 0.
2*s**3*(s - 1)*(s + 1)/7
Let d = 658/5 - 131. Let f be (-2)/(-6)*0/6. Let d*j**4 + 0 - 3/5*j**3 + 0*j**2 + f*j = 0. What is j?
0, 1
Let r(o) be the first derivative of 3 + 1/2*o + 1/8*o**2 - 1/12*o**3. Determine i, given that r(i) = 0.
-1, 2
Let y(z) = 4*z - 101. Let h be y(26). Suppose -7/3*l**5 - 5/3*l**2 + 5/3*l**4 + h*l**3 - 2/3*l + 0 = 0. What is l?
-1, -2/7, 0, 1
Let 3/2 - 1/2*j**2 + 5/4*j - 1/4*j**3 = 0. What is j?
-3, -1, 2
Let m(f) be the first derivative of 0*f**4 + 0*f**3 + 0*f + 1/60*f**5 - 1/2*f**2 - 2. Let v(g) be the second derivative of m(g). Factor v(b).
b**2
Suppose -5*n = a - 7, 0 = a - 3*n - 0 - 15. Let z = a + -7. Find c such that 27*c**3 + 33*c**3 + 8 + 23*c**4 + 40*c + 74*c**2 - z*c**4 = 0.
-1, -2/3
Let v(y) be the first derivative of -5*y**6/6 + y**5 + 25*y**4/4 - 5*y**3/3 - 20*y**2 - 20*y + 23. Factor v(q).
-5*(q - 2)**2*(q + 1)**3
Suppose -3*s - 2*r - 12 = -5*s, 4*r = 3*s - 19. Determine a so that 0 - 1/5*a**2 + 4/5*a**s - 11/5*a**4 - 1/5*a + 9/5*a**3 = 0.
-1/4, 0, 1
Find z, given that -6*z**2 + 4*z**4 + z**4 - 14*z**2 + 15*z**3 + 0*z**4 = 0.
-4, 0, 1
Let q(v) = 10*v**5 - v**4 + 3*v**3 + 7*v. Let m(b) = -4*b**3 + 2*b - b**5 + 4*b**5 + 5*b**3 + 0*b**5. Let w(o) = -7*m(o) + 2*q(o). Factor w(u).
-u**3*(u + 1)**2
Let x(n) be the third derivative of -2*n**7/525 + 2*n**6/75 - n**5/15 + n**4/15 - 7*n**2. Find h, given that x(h) = 0.
0, 1, 2
Let h(j) be the second derivative of 5*j**5/24 + 5*j**4/12 + j**3/3 - 2*j**2 + 3*j. Let y(r) be the first derivative of h(r). What is f in y(f) = 0?
-2/5
Determine s so that 35/2*s**2 + 5/2*s**3 + 40*s + 30 = 0.
-3, -2
Factor -8/5 - 8/5*i - 2/5*i**2.
-2*(