-14*h + 13*h - 21, 0 = -4*h - 4. Let f(q) be the first derivative of 1/3*q**2 + 0*q - a - 2/9*q**3. What is k in f(k) = 0?
0, 1
Suppose 3*c = -6 - 72. Let i be (-522)/(-351) - (-4)/c. Find h, given that 3*h**4 + 19/3*h**3 - 13/3*h**2 + i - 7/3*h**5 - 4*h = 0.
-1, 2/7, 1, 2
Let q(u) be the second derivative of -3*u**5/80 + u**4/8 + 3*u**3/8 - 95*u. Find w such that q(w) = 0.
-1, 0, 3
Suppose 0 = 63*g - 87*g + 24. Factor 3/4*q - g + 1/4*q**2.
(q - 1)*(q + 4)/4
Let j(u) = 4*u**3 + 10*u**2 - 32*u - 120. Let f(z) = 5*z**3 + 8*z**2 - 36*z - 120. Let m(r) = 6*f(r) - 7*j(r). Factor m(h).
2*(h - 10)*(h - 3)*(h + 2)
Solve -7*a - 138*a**3 + 150*a**4 - 36*a**2 + 31*a - 21*a**5 - 249*a**4 = 0 for a.
-2, -1, 0, 2/7
Let v(b) = 6*b**2 - 34*b + 22. Let i(o) = -17*o**2 + 101*o - 63. Let h(w) = 2*i(w) + 7*v(w). Factor h(x).
4*(x - 1)*(2*x - 7)
Let r(n) be the first derivative of n**5/5 + 49*n**4/4 + 95*n**3/3 + 47*n**2/2 + 445. Factor r(w).
w*(w + 1)**2*(w + 47)
Let l(z) be the first derivative of -z**5/5 + 7*z**3/3 - 3*z**2 - 91. Suppose l(d) = 0. What is d?
-3, 0, 1, 2
Factor -14*x - 8/5*x**2 + 18/5.
-2*(x + 9)*(4*x - 1)/5
Let n(q) be the second derivative of 0 + 1/20*q**5 + 1/6*q**3 + 0*q**2 + 1/6*q**4 - 4*q. Factor n(l).
l*(l + 1)**2
Let v(f) be the second derivative of f**5/630 - f**4/252 - 2*f**3/63 + 7*f**2/2 + 25*f. Let w(j) be the first derivative of v(j). Find i such that w(i) = 0.
-1, 2
Let i(v) be the second derivative of -v**6/120 + v**5/20 - 2*v**3/3 - 11*v**2 + 9*v. Let q(u) be the first derivative of i(u). Solve q(c) = 0 for c.
-1, 2
Let o(l) be the first derivative of -2*l**5/35 - 2*l**4/7 - 4*l**3/7 - 4*l**2/7 - 2*l/7 - 81. Suppose o(a) = 0. Calculate a.
-1
Suppose -248 = -28*x + 4. Let o(z) be the first derivative of 2/25*z**5 + x - 4/15*z**3 + 0*z + 0*z**2 - 1/10*z**4. Factor o(p).
2*p**2*(p - 2)*(p + 1)/5
Suppose 2*o - 4*o + 36*o = 0. Factor 0*n**3 + 0*n**2 - 1/2*n**5 - n**4 + 0*n + o.
-n**4*(n + 2)/2
What is f in 21*f - 3/5*f**2 - 102/5 = 0?
1, 34
Let 0 + 21*n**4 - 660/7*n**2 - 156*n**3 - 96/7*n = 0. What is n?
-2/7, 0, 8
Let y(i) be the third derivative of -i**5/40 + 25*i**4/16 - 21*i**3 - i**2 - 58. Factor y(b).
-3*(b - 21)*(b - 4)/2
Find n such that -20*n**2 + 4*n**4 - 4*n**2 + 11*n - 12 + 21*n = 0.
-3, 1
Suppose -12/5*n**2 - 2/5*n**3 + 6*n - 16/5 = 0. Calculate n.
-8, 1
Let b(q) be the second derivative of -3*q + 18/7*q**3 + 3/7*q**4 + 1/35*q**5 + 54/7*q**2 + 0. Factor b(x).
4*(x + 3)**3/7
Let b(r) be the third derivative of 0 + 32*r**2 + 0*r - 1/24*r**6 + 1/6*r**5 - 1/42*r**7 + 0*r**4 + 0*r**3. Let b(c) = 0. What is c?
-2, 0, 1
Let b(v) be the third derivative of -v**7/350 + 9*v**6/100 - 4*v**5/5 - 9*v**4/20 + 81*v**3/10 - 158*v**2. Let b(s) = 0. What is s?
-1, 1, 9
Let y(l) be the third derivative of -l**5/20 + 7*l**4/2 - 98*l**3 + 17*l**2. Factor y(u).
-3*(u - 14)**2
Let g(n) = 14*n - 6. Let u be g(-3). Let i be ((-6)/10)/((u/30)/2). Solve i + 15/8*v - 9/8*v**2 = 0 for v.
-1/3, 2
Let c(f) be the third derivative of -f**8/336 + 11*f**7/70 - 53*f**6/20 + 383*f**5/30 - 235*f**4/8 + 75*f**3/2 + 3*f**2 - 9*f. Determine s so that c(s) = 0.
1, 15
Suppose -2*s - 2*s = 36. Let w = s + 24. Factor 6*p**2 + 7*p**2 + 2 - w*p**2 + 2 + 2*p.
-2*(p - 2)*(p + 1)
Let l(r) be the second derivative of -5*r + 1/35*r**5 + 0 + 2/21*r**4 + 0*r**2 + 2/21*r**3. Factor l(t).
4*t*(t + 1)**2/7
Let t(d) be the second derivative of -d**7/1680 - d**6/720 + 5*d**3/6 - 2*d. Let m(q) be the second derivative of t(q). What is p in m(p) = 0?
-1, 0
Let s(g) = -g**4 - g**3 + g**2 + 2*g - 1. Let u(w) = 180*w**3 + 8*w**2 - 688*w + 176. Let x(c) = -16*s(c) - u(c). Determine r so that x(r) = 0.
-2, 1/4, 2, 10
Let r(a) be the first derivative of -2*a**2 + 7/2*a**4 - 10/3*a**3 + 0*a - 7. Factor r(b).
2*b*(b - 1)*(7*b + 2)
Let m(t) = -24*t + 818. Let y be m(34). Factor 10/3*q - 1/3*q**y - 25/3.
-(q - 5)**2/3
Let b(u) = -2 - u**2 + 0 + 5*u**3 - 9*u + 10*u**2 + 3. Let s = 222 + -205. Let g(h) = -14*h**3 - 26*h**2 + 26*h - 3. Let t(v) = s*b(v) + 6*g(v). Factor t(a).
(a - 1)**3
Let n = 144 + -109. Let t = 38 - n. Suppose 48/5*b - 21/5*b**t + 3*b**2 + 12/5 = 0. What is b?
-1, -2/7, 2
Suppose 1737*t = 1734*t + 9. Let k(m) be the second derivative of 0 - 1/36*m**4 - 1/2*m**2 + 2/9*m**t - 7*m. Solve k(x) = 0.
1, 3
Let m(w) be the first derivative of w**6/120 + w**5/15 + w**4/6 + 10*w**2 + 6. Let o(y) be the second derivative of m(y). Suppose o(i) = 0. What is i?
-2, 0
Factor -636/5*v + 3*v**3 + 216/5 + 234/5*v**2.
3*(v - 2)*(v + 18)*(5*v - 2)/5
Suppose 0 = -2*p - 0 + 2. Let q(k) be the first derivative of p + 1/12*k**4 - 1/9*k**3 + 0*k - 1/6*k**2 + 1/15*k**5. Factor q(r).
r*(r - 1)*(r + 1)**2/3
Let t(h) be the first derivative of 2*h**5 + 5/6*h**6 + 0*h**4 + 0*h - 10/3*h**3 - 5/2*h**2 - 9. Factor t(p).
5*p*(p - 1)*(p + 1)**3
Let o(z) be the third derivative of z**6/60 - 7*z**5/30 + 7*z**4/6 - 8*z**3/3 - 293*z**2. Factor o(n).
2*(n - 4)*(n - 2)*(n - 1)
Let d(x) = -x**2 + 12*x + 26. Let y be d(12). Factor 12 + y*q - 11*q - 6*q - 3*q**2.
-3*(q - 4)*(q + 1)
Let b(a) = a**3 - a**2 + a - 1. Let z = 2 - 0. Let j be b(z). Suppose -k**2 + 3*k**4 - j + 5 + 4*k**2 - 6*k**3 = 0. Calculate k.
0, 1
Let l(g) be the first derivative of 0*g**3 - 1/20*g**5 + 0*g**2 + 0*g + 9 - 1/16*g**4. Factor l(b).
-b**3*(b + 1)/4
Factor -8940*c + 1198/5*c**2 - 8/5*c**3 - 2250.
-2*(c - 75)**2*(4*c + 1)/5
Let w(j) be the first derivative of 9*j**6/2 - 27*j**5 - 9*j**4/2 + 82*j**3/3 + 39*j**2/2 + 5*j + 368. Let w(o) = 0. What is o?
-1/3, 1, 5
Let a(s) = 11*s**3 + 15*s**2 + 4*s - 2. Let j = -109 + 107. Let q(w) = 78*w**3 + 105*w**2 + 27*w - 15. Let x(u) = j*q(u) + 15*a(u). Suppose x(f) = 0. What is f?
-1, -2/3, 0
Find l such that -l + 7/2*l**4 + 11/2*l**2 + 0 - 8*l**3 = 0.
0, 2/7, 1
Suppose 3*g = -g + 12, 9 = 3*i - 2*g. Let q(x) = x - 2. Let t be q(i). Factor 2*r**3 - 5*r**2 + 8*r**t - 9*r**3 - 4 + 8*r.
(r - 2)**2*(r - 1)
Factor -1/2*m**3 - 1/2*m**2 + 6 + 4*m.
-(m - 3)*(m + 2)**2/2
Determine n so that 26*n**4 + 10*n**2 + 20*n + 5*n**2 - 46*n**4 - 15*n**3 - 5*n**2 + 10*n**2 - 5*n**5 = 0.
-2, -1, 0, 1
Let w = 31061/5240 + -413/131. Let f = w - 19/8. Solve 0 + 0*v**3 - f*v**5 + 2/5*v - 4/5*v**2 + 4/5*v**4 = 0 for v.
-1, 0, 1
Let v(i) = -9*i**3 + 478*i**2 - 52*i - 50. Let b be v(53). Solve 1/3*g**b - 2/3 + 0*g**2 - g = 0 for g.
-1, 2
Let m(f) = 11*f**2 + 14*f - 4. Let y(t) = -6*t**2 - 8*t + 2. Let u(w) = -4*m(w) - 7*y(w). What is z in u(z) = 0?
-1, 1
Let d(m) be the first derivative of 2/9*m**3 - 19 - 5/12*m**2 - 1/24*m**4 + 1/3*m. Factor d(u).
-(u - 2)*(u - 1)**2/6
Let p(b) = b**2 - b + 84. Let a be p(0). Let y = 88 - a. Solve 0*w**3 - 3/4*w**2 + 0 + 1/4*w**y + 1/2*w = 0.
-2, 0, 1
Let z(s) = 1053*s + 8426. Let n be z(-8). Factor 9/2*t**3 + 39*t**n + 0 - 27/2*t.
3*t*(t + 9)*(3*t - 1)/2
Suppose 7*z = 19*z - 60. Suppose 0 = 2*i - 5*y - 8, -4*i - z*y = -y - 16. Determine x, given that -i*x**2 - 2*x**5 + 4/5 + 8/5*x**3 + 16/5*x**4 + 2/5*x = 0.
-1, -2/5, 1
Let t(x) be the first derivative of 5*x**4/4 - 5*x**3/3 - 10*x**2 + 20*x - 248. Factor t(a).
5*(a - 2)*(a - 1)*(a + 2)
Let f(s) be the first derivative of -3/5*s**3 - 9/10*s**2 - 13 - 3/5*s - 3/20*s**4. Let f(k) = 0. What is k?
-1
Factor -1/3*u - 2/3 + 1/3*u**2.
(u - 2)*(u + 1)/3
Let h(j) = 4*j**3 - 303*j**2 + 5778*j - 5473. Let f(t) = 4*t**3 - 302*t**2 + 5776*t - 5474. Let p(o) = 3*f(o) - 2*h(o). Find m, given that p(m) = 0.
1, 37
Let j(a) be the first derivative of -4*a**3/9 + 26*a**2/3 - 16*a + 28. Factor j(l).
-4*(l - 12)*(l - 1)/3
Let p = -60 + 67. Let v(i) = -3*i**2 - 5*i - 10. Let x(a) = -5*a**2 - 9*a - 19. Let t(q) = p*v(q) - 4*x(q). Solve t(o) = 0.
-2, 3
Let a(u) = -u**2 - 8*u + 9. Let c(n) = 8*n - 8. Let s be -1 - (-3 + (4 - -2)). Let z = 19 + -24. Let y(i) = s*a(i) + z*c(i). Factor y(m).
4*(m - 1)**2
Let x = 1194 - 1194. Factor x*q + 0 + 4/7*q**3 + 4*q**2.
4*q**2*(q + 7)/7
Suppose -3*x + t = -4*x + 4, 4*x + 5*t - 20 = 0. Let l = 35 + -33. Let -1/2*p - p**l + x = 0. Calculate p.
-1/2, 0
Let i(g) be the first derivative of g**2 + 0*g + 1/4*g**4 - 4 + g**3. Find b such that i(b) = 0.
-2, -1, 0
Factor 1/3*d**2 + 4096/3 - 128/3*d.
(d - 64)**2/3
Let r(n) be the second derivative of -n**9/30240 + n**8/4480 + n**7/5040 - n**6/480 + 11*n**4/6 + n. Let i(c) be the third der