culate r.
144
Let n(u) = -u**3 - u**2 + u + 23. Let j be n(0). Suppose -1 = 2*x - r, x - 5*x - 3*r + j = 0. Factor -9*t - 4 + 0 - 3*t**x - 2.
-3*(t + 1)*(t + 2)
Suppose -13 = -z + 3*a, -z + 5*z - a = 19. Factor -2*o**5 + 5*o - 7*o + 4*o**z - 4*o**2 + 4*o**5.
2*o*(o - 1)*(o + 1)**3
Factor 6*i**3 - 1/2*i**5 + 0 + 5/2*i + i**4 + 7*i**2.
-i*(i - 5)*(i + 1)**3/2
Find i, given that -12/7*i**3 - 3/7*i - 1/7*i**5 + 0 + 10/7*i**2 + 6/7*i**4 = 0.
0, 1, 3
Let b be 0/(-2*(-1)/2). Suppose -30 = -234*g + 224*g. Find r, given that 2/7*r**2 + 0*r + 6/7*r**4 - 2/7*r**5 + b - 6/7*r**g = 0.
0, 1
Let j(q) = q**2 + 2*q + 2. Suppose -4*w = w. Let i be j(w). Suppose -2*z + 2*z**i - 6*z**2 + 2*z**2 = 0. What is z?
-1, 0
Let a = -4026 - -4026. Factor 1/6 - 1/6*s**2 + a*s.
-(s - 1)*(s + 1)/6
Let g(z) = z**3 + z**2 + 2. Let r be g(0). Suppose 5*s + r*s = 9*s. Factor 1/2*n**2 + s + 1/4*n.
n*(2*n + 1)/4
Let u be -1 + ((-19)/(-6) - 2). Suppose 0 = -54*i + 50*i + 8. Find w such that 0*w + 0 + u*w**i = 0.
0
Let z be 1/(3*2/18). Find o such that 80 + 2*o**z + 30*o**2 - 24 + 150*o + 194 = 0.
-5
Solve 4 + 2/3*l**3 - 2/3*l**4 - 26/3*l + 14/3*l**2 = 0 for l.
-3, 1, 2
Suppose 20*x + 4 - 10 = -6. Suppose 3/4*o**5 - 3/2*o**2 - 9/4*o**3 + x + 0*o + 0*o**4 = 0. Calculate o.
-1, 0, 2
Let p(n) be the third derivative of -n**10/50400 - n**9/20160 + 7*n**5/60 + 18*n**2. Let q(b) be the third derivative of p(b). Factor q(i).
-3*i**3*(i + 1)
Let y(v) = -8*v**3 - 2*v**2 + 22*v - 6. Let l(h) = 7*h**3 + h**2 - 21*h + 5. Let s(o) = 6*l(o) + 5*y(o). Factor s(d).
2*d*(d - 4)*(d + 2)
Let 24/5*o**2 - 32/5*o + 0 - 2/5*o**5 + 16/5*o**3 - 6/5*o**4 = 0. Calculate o.
-4, -2, 0, 1, 2
Let l(s) be the third derivative of -s**6/80 + s**5/10 - 3*s**4/16 - 161*s**2. Determine x, given that l(x) = 0.
0, 1, 3
Let i(x) be the third derivative of x**8/13440 - x**7/2016 + x**6/720 - x**5/480 + 3*x**4/4 + 16*x**2. Let n(u) be the second derivative of i(u). Factor n(v).
(v - 1)**2*(2*v - 1)/4
Let c(v) be the third derivative of -v**8/1848 + 2*v**7/1155 + v**6/660 - v**5/165 + 83*v**2. Suppose c(l) = 0. Calculate l.
-1, 0, 1, 2
Suppose -16/11*r - 16/11*r**5 + 14/11*r**3 - 8/11 - 4*r**4 + 70/11*r**2 = 0. Calculate r.
-2, -1/4, 1/2, 1
Let m = -4 - -8. Suppose -2*v - 5*h - 11 + 0 = 0, 3*h + 1 = -m*v. Determine n, given that 3*n**v - 6*n**3 + 0*n**4 + 3*n**3 + 3*n**5 - 3*n**4 = 0.
-1, 0, 1
Let j = -71/24 + 427/120. Let 3*v - 18/5 - j*v**2 = 0. What is v?
2, 3
Let n = 244 - 240. Let l(t) be the second derivative of -1/90*t**5 + 1/54*t**n + 0 + 2/27*t**3 + 0*t**2 + 5*t. Find r, given that l(r) = 0.
-1, 0, 2
Let u(m) be the second derivative of -m**6/20 - 3*m**5/20 + 2*m**4 + m**3/2 - 45*m**2/4 - 113*m. Suppose u(z) = 0. What is z?
-5, -1, 1, 3
Let i(y) be the first derivative of -y**3/9 - 25*y**2 - 1875*y - 65. Factor i(z).
-(z + 75)**2/3
Let m(p) be the first derivative of -p**4/66 - 10*p**3/33 - 25*p**2/11 - 20*p - 3. Let b(k) be the first derivative of m(k). Suppose b(c) = 0. Calculate c.
-5
Let g(t) = 7*t**2 - t - 1. Let u be g(-1). Solve -3*i**3 + u*i - 6*i + 6 + 0*i + 3*i**4 - 9*i**2 + 2*i = 0.
-1, 1, 2
Let d(s) = -25*s**3 + 80*s**2 + 220*s - 80. Let c(y) = -13*y**3 + 39*y**2 + 110*y - 40. Let v(i) = 5*c(i) - 2*d(i). Factor v(x).
-5*(x - 4)*(x + 2)*(3*x - 1)
Let p(f) be the third derivative of f**10/529200 - f**8/70560 + 17*f**5/30 + 21*f**2. Let h(m) be the third derivative of p(m). Factor h(u).
2*u**2*(u - 1)*(u + 1)/7
Let s be (26/65)/(12/45). Factor 0 - s*u + 9/4*u**2 - 3/4*u**3.
-3*u*(u - 2)*(u - 1)/4
Let u(v) be the first derivative of -2*v**3/27 + 2*v**2/3 + 148. Find b, given that u(b) = 0.
0, 6
Find a, given that 1/4*a**2 + 2209/4 + 47/2*a = 0.
-47
Let n(k) = 3*k**4 - 15*k**3 + 27*k**2 - 15*k. Let z(o) = -9*o**4 + 45*o**3 - 80*o**2 + 44*o. Let v(p) = 17*n(p) + 6*z(p). Factor v(x).
-3*x*(x - 3)*(x - 1)**2
Suppose -4*x + 13 = g, -3*x + 0*x = 2*g - 16. Suppose -5*h + x + 1 = -3*t, 3*h - 13 = -t. Factor 6/5*u**2 + 3/5*u - 3/5*u**h - 6/5.
-3*(u - 2)*(u - 1)*(u + 1)/5
Let t(l) be the third derivative of -l**8/2016 - l**7/315 - l**6/180 + l**5/180 + 5*l**4/144 + l**3/18 - 31*l**2. Suppose t(o) = 0. Calculate o.
-2, -1, 1
Let n be 6/(-24) + (-61)/(-4). Suppose 3*h - n = -3. Factor -12 + 12 - f**h.
-f**4
Let r(v) be the second derivative of 0*v**2 - 6*v + 0 + 1/12*v**3 - 1/24*v**4. Factor r(j).
-j*(j - 1)/2
Let u(s) be the second derivative of -s**6/210 - 13*s**5/210 + 2*s**4/21 + s**3/3 + 9*s**2 - 23*s. Let c(n) be the first derivative of u(n). Solve c(j) = 0.
-7, -1/2, 1
Suppose x = -x - 2*u + 4, -4*u = 0. Let c(l) be the first derivative of -1/9*l**3 - l + x - 2/3*l**2. Factor c(v).
-(v + 1)*(v + 3)/3
Let k(w) be the first derivative of 3 + 1/12*w**6 + 1/5*w**5 + 0*w + 0*w**2 + 1/8*w**4 + 0*w**3. Factor k(z).
z**3*(z + 1)**2/2
Let a be 7 + -6 + -8 - -7. Let g(f) be the second derivative of 0*f**4 + 4*f - 1/56*f**7 + 1/40*f**6 + 0*f**5 + 0 + 0*f**3 + a*f**2. Find o such that g(o) = 0.
0, 1
Let q(n) be the first derivative of -21*n**5/5 - 6*n**4 + 13*n**3 + 3*n**2 - 22. What is j in q(j) = 0?
-2, -1/7, 0, 1
Let x = 49349 - 443657/9. Solve -268/9*f**2 - x - 4/3*f**3 - 1540/9*f = 0.
-11, -1/3
Let r = 6631 - 6631. Factor -9/8*s**2 + 3/2 + r*s + 3/8*s**3.
3*(s - 2)**2*(s + 1)/8
Suppose 4*d = j - 22, 19 = 3*j - j - 3*d. Suppose -3*c + j = -2*c. Find m, given that -6*m**4 + c*m + 3*m**3 - 5*m - 9*m**5 + 2*m**3 + 6*m**2 + 7*m**3 = 0.
-1, 0, 1/3, 1
Suppose -2*r + 3*d = 1 - 19, -3*r + 2*d = -17. Suppose 4*t + 4*v = -0 + 4, -4*t - 5*v + r = 0. Factor 8 + 0 + t + 2*l**2 - 5*l - 7*l**2.
-5*(l - 1)*(l + 2)
Let h be (-7)/2*1216/(-2128). Solve -32/9*w - 8/9*w**3 + 2/3 + 34/9*w**h = 0 for w.
1/4, 1, 3
Let x(j) be the third derivative of 0*j + 1/100*j**5 - 1/150*j**6 + 0*j**4 + 0 + 0*j**3 - 5*j**2 + 1/1050*j**7. Solve x(p) = 0 for p.
0, 1, 3
Let r = 484 - 482. Let j(w) be the third derivative of 0*w + 0 + 1/30*w**5 + 1/6*w**3 - 5/48*w**4 - 1/240*w**6 - 5*w**r. Suppose j(v) = 0. What is v?
1, 2
Let p(v) = 3*v**2 - 39*v + 150. Let t(y) = y**2 - 10*y + 37. Let m(c) = -4*p(c) + 15*t(c). Solve m(h) = 0 for h.
-5, 3
Let s(v) be the second derivative of v**5/20 - 7*v**4/3 + 221*v**3/6 - 169*v**2 + 2*v - 124. Determine t, given that s(t) = 0.
2, 13
Let y(w) be the first derivative of -3 + 7*w**4 + 4*w**2 - 17/5*w**5 + 2/3*w**6 - w - 22/3*w**3. Determine i, given that y(i) = 0.
1/4, 1
Let a(u) be the first derivative of 3/4*u**4 - 3/4*u - 3/2*u**3 - 3/20*u**5 + 3/2*u**2 - 17. Find g such that a(g) = 0.
1
Let y(c) be the first derivative of -6/5*c + c**2 - 2/15*c**3 - 1/10*c**4 + 3. Find g, given that y(g) = 0.
-3, 1
Factor -4*r + 1/3*r**2 + 35/3.
(r - 7)*(r - 5)/3
Let a(u) be the second derivative of -u**5/20 - 5*u**4/6 - 23*u**3/6 - 7*u**2 + 15*u + 1. Suppose a(d) = 0. What is d?
-7, -2, -1
Let p(c) be the third derivative of 4*c**7/1785 - 5*c**6/204 + 3*c**5/85 + 37*c**4/204 - 10*c**3/51 - 78*c**2 + 1. Solve p(w) = 0.
-1, 1/4, 2, 5
Let s(h) be the first derivative of -36*h**5/5 - 21*h**4 + 428*h**3/3 - 126*h**2 + 40*h + 183. Find m such that s(m) = 0.
-5, 1/3, 2
Let w(v) = 8*v**2 + 10*v + 2. Suppose 0 = -4*i + 7*i - 108. Let a(z) = -25 - 25*z**2 - 30*z - 16 + i. Let u(l) = 6*a(l) + 17*w(l). Factor u(x).
-2*(x + 1)*(7*x - 2)
Let n(j) be the third derivative of j**8/84 - 6*j**7/35 + 16*j**6/15 - 56*j**5/15 + 8*j**4 - 32*j**3/3 - j**2 - 149. Factor n(d).
4*(d - 2)**4*(d - 1)
Let s = -248 - -488. Let f be -8*6/s*-4. Factor -f + 6/5*k**2 + 2/5*k.
2*(k + 1)*(3*k - 2)/5
Let h = 3/10652 - -21271/117172. Let h*m**2 - 18/11 + 16/11*m = 0. What is m?
-9, 1
Solve 9/2*q + 1/2*q**2 - 5 = 0 for q.
-10, 1
Suppose -z + 12 = z. Let i(m) = -4*m - 4. Let o(g) = 2 - 2*g**2 - 1 + g**2. Let r(h) = z*o(h) + i(h). Factor r(n).
-2*(n + 1)*(3*n - 1)
Let t(a) be the third derivative of -a**5/120 - 7*a**4/48 - 5*a**3/6 - 228*a**2. Factor t(b).
-(b + 2)*(b + 5)/2
Suppose -a + 1 + 6 = 0. Suppose -a*q + 3*q = 0. Factor q*y**2 - y - 4*y**2 + 3*y**2 + 0*y**2.
-y*(y + 1)
Let l(c) be the second derivative of c**5/10 + 31*c**4/42 + 4*c**3/7 + 57*c. What is m in l(m) = 0?
-4, -3/7, 0
Factor 4*d + 27 + 0 + 0 + d**4 - 6*d**2 - 10 - d**3 - 9.
(d - 2)**2*(d + 1)*(d + 2)
Let z be ((-4)/10)/(3/(-15)). Factor 0 + b + 8/3*b**z - 2/3*b**4 + b**3.
-b*(b - 3)*(b + 1)*(2*b + 1)/3
Sup