e t so that -4/3 + 0*t + 1/3*t**2 = 0.
-2, 2
Let b(g) be the second derivative of -g**7/189 + g**6/27 + 7*g**5/30 + 23*g**4/54 + 8*g**3/27 + 26*g. Find p such that b(p) = 0.
-1, 0, 8
Let m = -10 + 13. Solve m*t**3 + 6*t**2 + 0*t**2 - 2*t**3 + 2*t**3 = 0.
-2, 0
Let t(p) = -7*p**3 - p**2 + 1. Let k be t(1). Let g = k + 9. Factor -7/4*h**g - 1/2 - 9/4*h.
-(h + 1)*(7*h + 2)/4
Let f(r) be the third derivative of -r**7/210 - r**6/40 + r**5/30 + r**4/2 + 4*r**3/3 - 7*r**2. Suppose f(c) = 0. Calculate c.
-2, -1, 2
Let q(t) be the second derivative of -t**4/3 - 2*t**3 - 40*t. Factor q(s).
-4*s*(s + 3)
Let n = -59/2 + 119/4. Factor 1/2 + 3/4*o + n*o**5 - o**3 - 1/2*o**2 + 0*o**4.
(o - 2)*(o - 1)*(o + 1)**3/4
Factor 28/5*s - 38/5*s**2 - 8/5 + 5*s**3 - 8/5*s**4 + 1/5*s**5.
(s - 2)**3*(s - 1)**2/5
Let y(t) = -25*t - 100. Let v be y(-4). Factor 1/4*l**3 - 1/2*l**2 + 0 + v*l.
l**2*(l - 2)/4
Let v be (-2)/(-20) + (-4)/(-10). Determine m, given that -v*m**2 - 1/2*m**3 + 1/2*m + 1/2 = 0.
-1, 1
Let s(a) be the second derivative of -27*a**6/10 + 18*a**4 - 32*a**3 + 24*a**2 - 4*a. Let s(u) = 0. Calculate u.
-2, 2/3
Let i be 2 + -5 - 76/(-24). Let b(h) be the first derivative of -1 + 0*h + 0*h**2 + i*h**4 + 0*h**3. Solve b(t) = 0.
0
Let y(x) be the second derivative of -x**4/6 + x**2 + 8*x. Factor y(d).
-2*(d - 1)*(d + 1)
Let b(w) be the third derivative of -5*w**5/12 - 5*w**4/12 + 15*w**2. Let b(v) = 0. Calculate v.
-2/5, 0
Let u(f) = -f + 14. Let v be u(10). Suppose h + 4*t + 0*t = 6, t = -4*h + 9. What is q in 0 - 2/7*q - 2/7*q**h + 2/7*q**v + 2/7*q**3 = 0?
-1, 0, 1
Let x(q) be the first derivative of 3*q**4/16 + q**3/2 - 3*q**2/8 - 3*q/2 - 4. Factor x(v).
3*(v - 1)*(v + 1)*(v + 2)/4
Let z(v) be the first derivative of v**4/12 - 5*v**3/9 + 2*v**2/3 + 7. Factor z(a).
a*(a - 4)*(a - 1)/3
Let v(p) be the second derivative of 1/2*p**2 + 1/60*p**5 + 0*p**3 + 0 + 2*p + 0*p**4. Let l(u) be the first derivative of v(u). Factor l(c).
c**2
Let p be (-12)/12*(-1)/40. Let s(h) be the third derivative of -1/2*h**4 + 0 - p*h**6 - 1/5*h**5 + 0*h - 4*h**2 + 0*h**3. Factor s(w).
-3*w*(w + 2)**2
Let m(h) be the first derivative of -5 - 1/3*h**3 - 2*h - 3/2*h**2. Factor m(a).
-(a + 1)*(a + 2)
Let g(v) be the second derivative of 1/42*v**7 - 2*v - 3/20*v**5 - 1/30*v**6 - 1/3*v**3 + 0 + 5/12*v**4 + 0*v**2. Let g(a) = 0. What is a?
-2, 0, 1
Let t(s) = s - 4. Let d be t(8). Let i(g) be the second derivative of 0 + 1/5*g**5 + 2*g + g**2 + 1/15*g**6 - 1/21*g**7 - 1/3*g**d - 1/3*g**3. Factor i(l).
-2*(l - 1)**3*(l + 1)**2
Let n(i) be the second derivative of -5*i + 0*i**3 - 1/36*i**4 - 1/60*i**5 + 0*i**2 + 0. Find x, given that n(x) = 0.
-1, 0
Let h be (-1 - -1)*3/6. Suppose 0 = 3*u - h - 6. Suppose 4 - 6*y - 2*y**3 + 6*y**2 - 4 + u = 0. What is y?
1
Suppose 0*n - 4*n + 16 = 0. Let z be 16/30*6/8. Find l such that 0*l - 2/5*l**n - 2/5*l**5 + z*l**2 + 2/5*l**3 + 0 = 0.
-1, 0, 1
Let k(l) = -l**4 - l**3 + 1. Let u = 5 + -2. Let n(f) = 6*f**4 + 11*f**3 - 6*f**2 + 4*f - 8. Let r(v) = u*n(v) + 21*k(v). Determine i, given that r(i) = 0.
1
Let m(y) = y - 15. Let l be m(15). Let g(p) be the second derivative of 0*p**2 - 1/9*p**3 - 1/6*p**4 + l - 2*p. Factor g(u).
-2*u*(3*u + 1)/3
Suppose -4*l - 6 - 6 = -4*t, -4*t - 4*l = -28. Let u(c) be the first derivative of 0*c**3 + 0*c**4 + 1/10*c**t + 2 - 1/12*c**6 + 0*c + 0*c**2. Factor u(n).
-n**4*(n - 1)/2
Factor 0*r**2 + 3*r**2 + r**2 - 8*r**2 + 4.
-4*(r - 1)*(r + 1)
Suppose -4*k + 7*k - 12 = 3*z, -4*k - 5*z = -16. Find f such that -4 + f**k + 10*f**3 - 4*f - 10*f**4 - 6*f - 5*f**4 + 18*f**2 = 0.
-1, -2/7, 1
Let f(z) be the first derivative of z**5/10 + 5*z**4/8 + 4*z**3/3 + z**2 - 1. Let f(u) = 0. Calculate u.
-2, -1, 0
Find y such that -15*y**4 - 11*y**3 - 23*y**3 + 12*y - 5*y**3 - 12*y**2 = 0.
-2, -1, 0, 2/5
Let i be (-4)/10*(-325)/195. Find v, given that i*v**2 + 0 - 2/3*v = 0.
0, 1
Let v be ((-6)/(-9))/(-4 + (-114)/(-27)). Factor -1/2*b**v + 1/2 - 1/2*b**2 + 1/2*b.
-(b - 1)*(b + 1)**2/2
Let w = -75 - -77. Let a(g) be the third derivative of 0*g - 1/315*g**7 + 1/45*g**5 - 1/9*g**3 + 0 + 0*g**6 + 0*g**4 - 4*g**w. Factor a(b).
-2*(b - 1)**2*(b + 1)**2/3
Let r(m) = -2*m**2 - 1. Let p(q) = -11*q**2 - q - 5. Let s(w) = -6*p(w) + 34*r(w). Factor s(v).
-2*(v - 2)*(v - 1)
Solve 32/17*i**5 + 8/17*i**4 + 2/17*i + 2/17*i**2 - 24/17*i**3 + 0 = 0 for i.
-1, -1/4, 0, 1/2
Let -4/5 + 4/5*b**2 + 0*b = 0. What is b?
-1, 1
Let a(g) be the second derivative of 3*g**5/20 + g**4 + 5*g**3/2 + 3*g**2 + 2*g + 3. Factor a(u).
3*(u + 1)**2*(u + 2)
Let d(l) = l**3 - 4*l**2 - 2*l - 6. Let p be d(5). Let o = p + -9. Let -2/3 + o*q + 2/3*q**2 = 0. What is q?
-1, 1
Let x(b) be the first derivative of -b**5/30 - b**4/12 - b**3/18 + 22. Find d, given that x(d) = 0.
-1, 0
Let n(z) = z + 7. Let r be n(-5). Find j, given that -3*j**3 + 3*j**5 - 3*j**r + 4 - 4 + 3*j**4 = 0.
-1, 0, 1
Let c(b) be the first derivative of b**9/4536 + b**8/1260 + b**7/1260 - 2*b**3/3 - 3. Let n(l) be the third derivative of c(l). Suppose n(t) = 0. What is t?
-1, 0
Let m(w) = -9*w**4 - 2*w**3 + 2*w**2 - 6*w - 6. Let a(h) = h**4 - h**3 - h**2 + h + 1. Let u(y) = 30*a(y) + 5*m(y). Factor u(x).
-5*x**2*(x + 2)*(3*x + 2)
Let m(c) = -c**3 + 4*c**2 - c - 6. Let r be m(3). Factor r - 3/5*f + 6/5*f**2 - 3/5*f**3.
-3*f*(f - 1)**2/5
Suppose -8*g = 2*g - 3*g. Find i such that 1/4*i + g + 1/4*i**3 + 1/2*i**2 = 0.
-1, 0
Let s(q) = q**5 - q**3 - q**2 - q. Let j(l) = 13*l**5 - 10*l**4 + 7*l**3 - 25*l**2 - 7*l. Let i(t) = -2*j(t) + 22*s(t). Determine h, given that i(h) = 0.
0, 1, 2
Let k(b) be the second derivative of b**7/10080 - b**5/480 + b**4/6 + 2*b. Let a(t) be the third derivative of k(t). Let a(p) = 0. What is p?
-1, 1
Let s(n) be the third derivative of -n**6/300 - n**5/75 - n**4/60 - 7*n**2. Determine h so that s(h) = 0.
-1, 0
Let g(a) be the second derivative of a**7/63 - 2*a**5/15 + a**4/9 + a**3/3 - 2*a**2/3 - 65*a. Find j, given that g(j) = 0.
-2, -1, 1
Let r be (-1)/(5/((-60)/9)*8). Let b(s) be the first derivative of -1/12*s**4 - 2/9*s**3 + 0*s + 2 - r*s**2. What is f in b(f) = 0?
-1, 0
Let o = 6 + -3. What is u in 1 - 3*u**o + 1 - u**2 + 5*u**2 - 5*u**2 - u**4 + 3*u = 0?
-2, -1, 1
Let g(h) = h**3 - 3*h + 2*h**2 + h**3 + 1 + h. Let t be g(1). Let -2*a**3 + 0*a**t + 5*a**4 - 3*a**4 = 0. What is a?
0, 1
Let q be -8 + (-4)/(2/(-1)). Let w be q/(-10) - 110/(-25). Suppose w*d**3 + 17*d + 5*d**3 + 16 - 36*d**2 + 7*d = 0. What is d?
-2/5, 2
Let u(b) be the second derivative of -b**7/840 + b**6/240 + b**5/20 - b**4/4 - 9*b. Let f(d) be the third derivative of u(d). Factor f(k).
-3*(k - 2)*(k + 1)
Let w = -303 + 305. Factor -12/5*b**w + 8/5*b**3 - 2/5*b**4 - 2/5 + 8/5*b.
-2*(b - 1)**4/5
Let d(a) be the second derivative of a**5/130 + a**4/78 - a**3/39 - a**2/13 + 12*a. Determine i so that d(i) = 0.
-1, 1
Suppose 0*x + 5*x - 4*q - 14 = 0, -4*q = 4. Factor -1/4*m**3 - 1/4*m**x - 3/4*m**5 + 5/4*m**4 + 0 + 0*m.
-m**2*(m - 1)**2*(3*m + 1)/4
Let c(p) be the third derivative of -p**5/450 + p**4/60 + 5*p**2. Factor c(j).
-2*j*(j - 3)/15
Let n(g) = 1. Let k(x) = -3 + 3 + 6*x - 3*x**2 + 1. Let b(s) = k(s) - 4*n(s). Factor b(f).
-3*(f - 1)**2
Let u = -50/9 + -13/36. Let w = -31/6 - u. Factor -1/4*q**3 - 1/4 - 3/4*q**2 - w*q.
-(q + 1)**3/4
Suppose 0 = r + r - 6. Let o**2 - 8*o**4 + 3*o**3 + r*o**4 + o**2 = 0. Calculate o.
-2/5, 0, 1
Let m(x) be the first derivative of 2*x**3/3 - x**2 - 4*x + 12. Factor m(v).
2*(v - 2)*(v + 1)
Solve 12/5*z**2 + 2/5 + 2/5*z**4 - 8/5*z - 8/5*z**3 = 0.
1
Let b be 4/(-4) - 6*-1. Let i(n) be the third derivative of 0*n**4 + 0*n**3 + 0*n - 1/60*n**b + 0 - n**2. Factor i(m).
-m**2
Let d(g) be the second derivative of g**6/165 + 3*g**5/110 + g**4/22 + g**3/33 + 6*g. Factor d(n).
2*n*(n + 1)**3/11
Let p be (-1 + 1/1)/(-2). Let x = -5 + 8. Factor -l - 2 - x*l**2 + 6*l**2 + p*l.
(l - 1)*(3*l + 2)
Let i(c) = 4*c - c**4 + 2*c**2 - c**4 - 4*c**3 - 3*c**2. Let u(z) = -18*z**4 - 36*z**3 - 8*z**2 + 36*z. Let o(b) = -52*i(b) + 6*u(b). Factor o(t).
-4*t*(t - 1)*(t + 1)*(t + 2)
Let l = 52556 - 208361/4. Let v = 468 - l. Factor 0*f - 3/4*f**3 - 3 + v*f**2.
-3*(f - 2)**2*(f + 1)/4
Let d(q) = -8*q**3 + 12*q**2 - 8*q + 8. Let b(w) = -9*w**3 + 12*w**2 - 7*w + 9. Let t(m) = 4*b(m) - 5*d(m). Factor t(k).
4*(k - 1)**3
S