 of m(d). Solve k(y) = 0.
2
Let 1/4*a**2 + 1/4 - 1/2*a = 0. What is a?
1
Suppose 4*p + 4 = -5*l, -9*l - 4 = -8*l + 4*p. Solve y + l - 1/2*y**2 = 0.
0, 2
Let x be 1/4 - 5/(-12). Let d be 2/(-8) + (-245)/(-84). Factor -8/3 + d*l - x*l**2.
-2*(l - 2)**2/3
Let l(p) be the first derivative of 4*p**5 + 115*p**4/4 + 50*p**3 + 35*p**2/2 - 20*p - 27. Factor l(v).
5*(v + 1)**2*(v + 4)*(4*v - 1)
Let h(t) = -8*t**3 - 6*t**2 + 2*t - 5. Let x(l) = 4 + 3*l**2 + 3*l**2 + 4*l**3 + 3*l**3 - l. Let d(g) = 4*h(g) + 5*x(g). Factor d(m).
3*m*(m + 1)**2
Let h(k) be the second derivative of -5*k**4/6 - 5*k**3/2 - 5*k**2/2 - 2*k. What is m in h(m) = 0?
-1, -1/2
Let 0*t**2 + 6*t**2 - 8*t + 11*t + 0*t**2 - 3 = 0. What is t?
-1, 1/2
Determine m so that 2/3*m**2 + 2*m - 8/3 = 0.
-4, 1
Let -56/23*d**2 - 44/23*d**3 + 0 - 16/23*d - 10/23*d**4 = 0. Calculate d.
-2, -2/5, 0
Let n(i) be the third derivative of 5*i**8/1008 + 5*i**7/63 + i**6/2 + 3*i**5/2 + 15*i**4/8 - 4*i**2. Suppose n(s) = 0. Calculate s.
-3, -1, 0
Let 18*n**3 - 12*n**3 + n**4 - 3*n**2 + 2*n + 10*n**4 - 6*n**2 - 6*n**5 = 0. What is n?
-1, 0, 1/3, 1/2, 2
Let n(w) be the first derivative of -w**4/36 - 4*w**3/27 - 2*w**2/9 - 44. Find k, given that n(k) = 0.
-2, 0
Let f(t) be the first derivative of 6*t**5/5 - t**4 - 32*t**3/3 - 14*t**2 - 6*t + 11. Solve f(b) = 0.
-1, -1/3, 3
Let z be 0 - 0 - 24/(-6). Factor 2*q**z - 8*q**3 - 12*q + 17*q**3 + q**4.
3*q*(q - 1)*(q + 2)**2
Let v(y) be the first derivative of y**6/30 + y**5/30 - y**4/12 - 5*y**2 + 6. Let h(d) be the second derivative of v(d). Find f, given that h(f) = 0.
-1, 0, 1/2
Let t be 856/(-90)*(-6)/300. Let r = t - -4/125. Factor -4/9 - 2/3*s - r*s**2.
-2*(s + 1)*(s + 2)/9
Let f(o) be the third derivative of -o**8/6720 + o**7/840 - o**6/240 + o**5/10 - 3*o**2. Let a(h) be the third derivative of f(h). Let a(w) = 0. Calculate w.
1
Let b(c) = -c**3 - c + 1. Let r(d) = -5*d**4 - 9*d**3 + 15*d**2 + 21*d + 14. Let m(l) = 4*b(l) - r(l). Let m(h) = 0. Calculate h.
-1, 2
Let z be 2/14*(-3 - -5). Factor 2/7*u**2 + 0 - 2/7*u**3 + 0*u + 2/7*u**5 - z*u**4.
2*u**2*(u - 1)**2*(u + 1)/7
Let n(y) be the second derivative of y**6/120 - y**5/30 + y**4/24 - y**2/2 + 2*y. Let v(h) be the first derivative of n(h). Factor v(t).
t*(t - 1)**2
Let s be (3 - (-26)/(-10))*5. Solve 2*q - 16*q**2 + 6*q**2 + 12*q**s - 4*q**3 = 0 for q.
-1/2, 0, 1
Let -6/11*l - 2/11*l**3 + 6/11*l**2 + 2/11 = 0. Calculate l.
1
Suppose 0 = 5*a + 6 - 31. Suppose a*i - 11 = -1. Factor i + 2*c - 2 - 2*c**3.
-2*c*(c - 1)*(c + 1)
Let k(f) = 21*f**3 + 3*f**2 - 43*f + 19. Let r(z) = 5*z**3 + z**2 - 11*z + 5. Let u(d) = -6*k(d) + 22*r(d). Solve u(l) = 0.
-1, 1/4, 1
Let m(g) be the first derivative of 49*g**6/3 + 7*g**5/5 - 59*g**4/2 - 11*g**3/3 + 10*g**2 + 4*g - 13. What is w in m(w) = 0?
-1, -2/7, 1/2, 1
Let v(g) = -2*g. Let n be v(-1). Let u be -1 + (1 - n - -4). Factor b**3 + b**2 - b + b**4 - 5*b**u + 3*b**2.
b*(b - 1)*(b + 1)**2
Let d(u) be the second derivative of -5*u**7/42 + 4*u**6/3 - 15*u**5/4 - 10*u**4/3 + 40*u**3/3 + 3*u. Find b such that d(b) = 0.
-1, 0, 1, 4
Let t(a) be the second derivative of -1/28*a**4 - 1/105*a**5 + 2/21*a**3 + 1/140*a**6 + 1/2*a**2 + 0 + a. Let k(r) be the first derivative of t(r). Factor k(w).
2*(w - 1)*(w + 1)*(3*w - 2)/7
Let p = -45252997/195 - -232063. Let f = -2/39 - p. Find x, given that -8/5 - f*x**2 + 24/5*x = 0.
2/3
Suppose -30 = 2*q - 10. Let r be ((-9)/q)/(9/12). Factor -4/5 - 2/5*z**2 + r*z.
-2*(z - 2)*(z - 1)/5
Let s(x) be the second derivative of -x**7/9 + 16*x**6/45 - 11*x**5/30 + x**4/9 - 12*x. Find c, given that s(c) = 0.
0, 2/7, 1
Let m = 227/2 + -113. Factor m*p**5 + 0*p**2 + 0 - 1/2*p**3 + 0*p + 0*p**4.
p**3*(p - 1)*(p + 1)/2
Let u = 233/177 - -1/59. Factor 2/3 + 0*s**2 + u*s - 2/3*s**4 - 4/3*s**3.
-2*(s - 1)*(s + 1)**3/3
Let a(g) = -g**2 - g**4 + 0*g**2 + 0 - 2 + 1 - g**5. Let w(q) = 5*q**5 + 8*q**4 - q**3 + 6*q**2 + 6. Let x(n) = -6*a(n) - w(n). Determine z so that x(z) = 0.
0, 1
Solve -3*c**4 + 4*c + 6*c - 10*c**3 - 5*c**2 + 8*c**4 + 0*c = 0 for c.
-1, 0, 1, 2
Let q(t) = 18*t**3 - 15*t**2 - 12*t - 6. Let n(w) = -w**3 - w**2 + w + 1. Let b(o) = -6*n(o) - q(o). What is i in b(i) = 0?
-1/4, 0, 2
Suppose -9*u + 8*u = 0. Factor -8/7*b**2 - 2/7*b**4 + u*b - 8/7*b**3 + 0.
-2*b**2*(b + 2)**2/7
Let m(v) = -v - 2. Let t be m(-3). Let h be ((0 + 1)/2)/t. Factor -1/2*u**2 - h*u**3 + 1/4*u + 1/4*u**4 + 1/4 + 1/4*u**5.
(u - 1)**2*(u + 1)**3/4
Let v(k) be the first derivative of -2*k**3/33 - 2*k**2/11 - 2*k/11 + 2. Factor v(b).
-2*(b + 1)**2/11
Let v = -42 + 23. Let g = v - -19. Factor 0*a**2 + 1/3*a**5 + 0 - 1/3*a**4 + 0*a**3 + g*a.
a**4*(a - 1)/3
Let y(q) be the second derivative of -q**5/4 + 5*q**4/3 + 10*q. Suppose y(b) = 0. Calculate b.
0, 4
Let z be -1*(0 - -1) - -1. Suppose z = 3*k + k. Factor k + 1/3*o**2 + 0*o - 1/3*o**3.
-o**2*(o - 1)/3
Let q(d) = d**2 - d + 1. Let z be q(2). Factor -2*h**5 + 4*h**2 + 2*h**3 - z*h**2 - h**3 + h**5 - h**4.
-h**2*(h - 1)*(h + 1)**2
Let a(v) = 3*v**3 - 27*v**2 + 76*v - 86. Let w(i) = -3*i**3 + 27*i**2 - 77*i + 85. Let o be 1 - (-4 + -2 + 3). Let m(d) = o*a(d) + 5*w(d). Factor m(u).
-3*(u - 3)**3
Let d(w) = 2*w - 18. Let n be d(9). Let r(h) be the third derivative of -1/300*h**6 - 1/50*h**5 + 0*h + h**2 - 1/30*h**4 + 0*h**3 + n. Factor r(y).
-2*y*(y + 1)*(y + 2)/5
Let d(s) = 2*s**2 + 8*s + 13. Let c(g) = 1 - 4*g - g**2 - 8 + 0*g**2. Suppose -o + h + 24 = 3*o, 2*o = -h + 6. Let k(u) = o*c(u) + 3*d(u). Factor k(r).
(r + 2)**2
Solve -226 - 4*s**3 + 8*s + 4*s**2 + 226 = 0 for s.
-1, 0, 2
Let k(o) = -o**3 + 4*o**2 + o - 4. Let h(a) = 3*a**3 - 11*a**2 - 3*a + 11. Let j(v) = 6*h(v) + 21*k(v). Find y such that j(y) = 0.
-1, 1, 6
Suppose -22 = -10*g - g. Let -2/5 + 2/5*l**g + 2/5*l - 2/5*l**3 = 0. What is l?
-1, 1
Suppose -42 = -3*o - 0*o. Let a = 14 - o. Factor -l**2 + 4/3*l**3 + a - 1/3*l.
l*(l - 1)*(4*l + 1)/3
Suppose -3/4*v**5 + v**4 - v**2 + 0 - v + 7/4*v**3 = 0. Calculate v.
-1, -2/3, 0, 1, 2
Solve -9/8*z**2 - 5/8*z - 1/4*z**4 - 7/8*z**3 - 1/8 = 0.
-1, -1/2
Let r(h) be the second derivative of -2/9*h**3 + 0 - 1/3*h**2 - 1/18*h**4 - h. Factor r(u).
-2*(u + 1)**2/3
Solve 0*c**2 - 2/7*c**4 - 4/7*c**3 + 2/7 + 4/7*c = 0.
-1, 1
Let y = -22 - -22. Factor 5/3*l**3 - 1/3*l**2 + 0*l + y + l**5 - 7/3*l**4.
l**2*(l - 1)**2*(3*l - 1)/3
Let q(a) be the third derivative of a**8/2688 - a**7/420 + a**6/240 + a**5/240 - 5*a**4/192 + a**3/24 - a**2. Let q(w) = 0. Calculate w.
-1, 1, 2
Let n be (7/(-175))/((-14)/15). Let t(z) be the second derivative of n*z**5 - 2/7*z**2 + 2*z - 4/21*z**4 + 1/3*z**3 + 0. Factor t(l).
2*(l - 1)**2*(3*l - 2)/7
Let b(n) be the third derivative of 0*n**6 + n**2 + 0*n + 0 + 0*n**4 + 0*n**5 + 1/504*n**8 + 1/315*n**7 + 0*n**3. Factor b(j).
2*j**4*(j + 1)/3
Solve 4*y**2 + 0 + 5*y**3 + 4/5*y = 0.
-2/5, 0
Determine k so that -4/7*k**2 + 3/7 + 1/7*k**4 + 2/7*k - 2/7*k**3 = 0.
-1, 1, 3
Suppose -8/7 - 4/7*r**2 - 12/7*r = 0. What is r?
-2, -1
Let c be (-51)/(-15) - 6/15. Factor 2/5*m**4 + 2/5*m**2 + 0*m - 4/5*m**c + 0.
2*m**2*(m - 1)**2/5
Let z(o) be the first derivative of -1/12*o**4 + 2 + 0*o**3 - 1/20*o**5 + 0*o**2 + o. Let n(t) be the first derivative of z(t). Factor n(y).
-y**2*(y + 1)
Let w(j) = -j**3 - 3*j**2 + 4*j + 2. Let k be w(-4). Let -16 - 24*v**3 - 4*v**4 - 20*v**2 + 10*v**k - 46*v**2 - 48*v + 4*v**2 = 0. Calculate v.
-2, -1
Let s be 6/(-4)*12/(-3). Let p(h) = 7*h + 5 + 3*h**2 - s*h**2 - 4*h**2. Let t(c) = 3*c**2 - 3*c - 2. Let i(r) = -2*p(r) - 5*t(r). Factor i(j).
-j*(j - 1)
Let x(v) = 5*v**5 - v**4 - 7*v**3 + 16*v**2 - 17*v + 4. Let s(i) = -11*i**5 + i**4 + 15*i**3 - 32*i**2 + 35*i - 8. Let p(j) = 3*s(j) + 7*x(j). Factor p(n).
2*(n - 1)**4*(n + 2)
Let o(t) be the third derivative of -t**6/180 - 3*t**5/10 - 65*t**4/12 - 169*t**3/9 - 14*t**2. Factor o(m).
-2*(m + 1)*(m + 13)**2/3
Let g = -203279/120 + 1694. Let p(t) be the third derivative of -g*t**5 - 1/3*t**3 - 2*t**2 + 0 + 0*t - 1/12*t**4. Factor p(a).
-(a + 2)**2/2
Let m(j) = j**2 - j. Let p(b) = 9*b**2 - 9*b. Let o = -14 - -8. Let g(u) = o*p(u) + 51*m(u). Factor g(h).
-3*h*(h - 1)
Let a be -3*1 + 70/22. Suppose 0 = -15*s + 9*s + 12. Let -a*l**s - 4/11 - 6/11*l = 0. What is l?
-2, -1
Factor 4/9*g - 22/9*g**2 + 10/3*g**3 + 0.
2*g*(3*g - 1)*(5*g - 2)/9
Let i(h) be the