3
Suppose 23*q = 20*q + 3. Let v be (-8)/(-2) + q/(-1). Solve -1/7*i**v - 3/7*i + 3/7*i**2 + 1/7 = 0 for i.
1
Suppose 3/4*t**3 + 0 + 3/2*t + 9/4*t**2 = 0. Calculate t.
-2, -1, 0
Let r(c) be the first derivative of c**5/120 - c**3/12 + 3*c**2 + 10. Let f(q) be the second derivative of r(q). Let f(k) = 0. What is k?
-1, 1
Let z(b) be the second derivative of b**7/70 + 3*b**6/40 + 3*b**5/20 + b**4/8 + b**2 - 4*b. Let l(h) be the first derivative of z(h). Find g such that l(g) = 0.
-1, 0
Let d(k) be the first derivative of -39/2*k**2 + 21/5*k**5 + 2 + 27*k**3 - 69/4*k**4 + 6*k. Factor d(q).
3*(q - 1)**3*(7*q - 2)
Factor 3*p**2 + p + 9/4*p**3 + 1/2*p**4 + 0.
p*(p + 2)**2*(2*p + 1)/4
Let p(h) = h**3 - 11*h**2 + 2*h + 8. Let g be p(11). Let f = g - 119/4. Let -1/2*n + f + 1/2*n**3 - 1/4*n**2 = 0. What is n?
-1, 1/2, 1
Let x(r) be the first derivative of -r**3 + 3/4*r**4 - 3/2*r**2 - 1 + 3/5*r**5 + 0*r. Factor x(n).
3*n*(n - 1)*(n + 1)**2
Determine f, given that f**2 - f - 240 + 240 = 0.
0, 1
Let o(c) = c**2 - 4*c - 6. Let w be o(6). Suppose 0*n = -3*n + w. Factor -6*v + 6*v - n*v**2.
-2*v**2
Factor -4*n**4 - 3*n**4 + 3*n**4 + 3*n**4 - n**3.
-n**3*(n + 1)
Let v be -1*(7 - 4) + 5. Let -2/5*g**3 + 2/5*g**v + 2/5*g - 2/5 = 0. What is g?
-1, 1
Let j(g) be the first derivative of g**5/180 + g**4/36 + g**3/18 - 9*g**2/2 + 7. Let m(k) be the second derivative of j(k). Factor m(n).
(n + 1)**2/3
Suppose -2*s = 13 - 3, 4*s + 40 = 5*k. Suppose k*m = -m + 15. Let 2*q**2 - 2*q**5 + q**4 + 0*q**5 + 5*q**4 - 6*q**m = 0. What is q?
0, 1
Let -4*u**2 + 22 + 6*u - 14 - 2*u = 0. What is u?
-1, 2
Let v(q) = -2*q**2 - 44*q + 2. Let l be v(-22). Determine f so that -2/5*f**4 - 4/5*f**3 + 0*f - 2/5*f**l + 0 = 0.
-1, 0
Let u = -2 + 4. Suppose -u*a + 5*a - 9 = 0. Let -15*n**3 - 17*n**4 - 6*n**5 - 4*n + 39*n**4 - 15*n**a + 18*n**2 = 0. Calculate n.
0, 2/3, 1
Factor -2/5*y**2 - 4/15*y + 0 - 2/15*y**3.
-2*y*(y + 1)*(y + 2)/15
Factor 3/2 - 1/4*v**2 - 1/4*v.
-(v - 2)*(v + 3)/4
Let p(d) = d - 8. Let b be p(12). Factor -4*a**b + 2*a**2 + a**3 - 3*a**3 - 2*a**5 - 2*a**2.
-2*a**3*(a + 1)**2
Let b(y) be the first derivative of 2 + 0*y**2 + 0*y + 3/4*y**4 - 1/2*y**6 + y**3 - 3/5*y**5. Factor b(x).
-3*x**2*(x - 1)*(x + 1)**2
Let s = -350 - -604. Let i = s - 1264/5. Factor 0 + 0*g + i*g**2 + 3/5*g**3.
3*g**2*(g + 2)/5
Suppose 2*y - 7 = 4*m + m, 5*m + 1 = -4*y. Let f(d) = -3*d**3 - 6*d**2 - 3*d - 6. Let b(l) = -l**2 - l - 1. Let z(w) = m*f(w) + 6*b(w). Factor z(a).
3*a*(a - 1)*(a + 1)
Let x(y) = -y**2 + 1. Let h(t) = t**3 + 6*t**2 + t - 8. Suppose -5 = z + d - 0*d, -4*d - 8 = 0. Let n(i) = z*h(i) - 24*x(i). Factor n(a).
-3*a*(a - 1)**2
Let q(p) = 10 + 7 - 5 - p + 3*p. Let s be q(-6). Determine i so that s*i**2 + 0 + 2/5*i**3 - 2/5*i = 0.
-1, 0, 1
Let p be 10*11*(-7)/(-28). Let j = p - 161/6. Factor -j*m + 2/3*m**2 + 0.
2*m*(m - 1)/3
Let f(r) = 2*r + 6. Let o be f(-3). Let j(x) be the second derivative of -1/6*x**2 + o*x**5 - 1/90*x**6 + 0 + 0*x**3 + 1/18*x**4 - 4*x. Factor j(u).
-(u - 1)**2*(u + 1)**2/3
Suppose 2*n + 5 = 13. Suppose d - 8 = -n. Let -2/9*s**3 - 2/9*s**d + 0 + 2/9*s**2 + 2/9*s = 0. Calculate s.
-1, 0, 1
Let w(q) be the second derivative of -5*q - 1/15*q**6 + 0*q**3 + 0*q**2 + 0 - 1/15*q**5 - 1/63*q**7 + 0*q**4. Factor w(m).
-2*m**3*(m + 1)*(m + 2)/3
Factor -3 + 5/2*o - 1/2*o**2.
-(o - 3)*(o - 2)/2
Let i(r) = 4*r**2 - 1. Let a(b) = b - 3*b + b**2 - 1 + b + 0*b**2. Let u(l) = 3*a(l) - i(l). Factor u(m).
-(m + 1)*(m + 2)
Let g be (2/2 - 2) + (-3 - -7). Let m(n) be the first derivative of g - 1/5*n**2 + 1/10*n**4 + 2/15*n**3 - 2/5*n. Solve m(v) = 0.
-1, 1
Factor -4/3*m**4 + 0 - 4/3*m**2 + 2*m**3 + 1/3*m**5 + 1/3*m.
m*(m - 1)**4/3
Determine o so that 3/4*o**3 - o + 4*o**2 + 0 - 13/4*o**4 + o**5 = 0.
-1, 0, 1/4, 2
Suppose -f + 4*i + 9 = 0, f - 3*f = 3*i + 4. Let s be 0/f*(1 + -2). Solve -2/7*d**2 + s + 2/7*d = 0.
0, 1
Let h be -4 + -1 - 2/(-1). Let t = 5 + h. Determine z so that z**4 - 2*z**3 + 5*z - 3*z - 3*z**4 + 2*z**t = 0.
-1, 0, 1
Let n be (-98)/(-70) + (-6)/(-10). Let o = -1/17 + 21/68. Factor -1/4 - o*p**n - 1/2*p.
-(p + 1)**2/4
Suppose 4*w + 14 + 2/7*w**2 = 0. Calculate w.
-7
Let i(m) = m**5 - m**4 + m**2 - m. Let p(d) = -7*d**5 - 3*d**4 - 30*d**3 - 52*d**2 - 27*d - 9. Let y(g) = -6*i(g) - p(g). Find b, given that y(b) = 0.
-3, -1
Let d(i) = -10*i**4 - 30*i**3 - 90*i**2 - 105*i - 45. Let v(h) = 11*h**4 + 29*h**3 + 90*h**2 + 106*h + 46. Let l(a) = -6*d(a) - 5*v(a). Factor l(x).
5*(x + 1)*(x + 2)**3
Suppose -t + 3 + 1 = 0. Let w(j) be the second derivative of 7/10*j**5 + 2*j**2 + 0 + 8/3*j**t - 2*j + 11/3*j**3. Determine d so that w(d) = 0.
-1, -2/7
Let f(r) be the second derivative of r**5/10 + r**4/2 + r**3 + r**2 - 4*r. Factor f(u).
2*(u + 1)**3
Let n = -12510/17 + 736. Factor 0 + 0*v**2 + 8/17*v - 6/17*v**3 - n*v**4.
-2*v*(v - 1)*(v + 2)**2/17
What is n in -6/13*n**2 + 0*n + 4/13*n**3 + 0 = 0?
0, 3/2
Let k = -3436/7 + 492. Find b such that -k*b**2 + 6/7*b + 0 + 2/7*b**3 = 0.
0, 1, 3
Determine x so that -2/11*x**4 + 0*x + 0 - 8/11*x**3 - 6/11*x**2 = 0.
-3, -1, 0
Let h = 18 + -16. Factor h*g + 3*g**2 + 3 + 10*g - 6*g.
3*(g + 1)**2
Let w(y) = y**3 - 3*y**2 + 2*y - 2. Let t be w(2). Let d be (t/(-10))/((-1)/(-2)). Determine m so that -d*m**3 + 4/5 + 6/5*m + 0*m**2 = 0.
-1, 2
Let i(k) = -10*k**3 - k**2 + 4*k + 7. Let o = -7 + 11. Let y(j) = 3*j**3 - j - 2. Let u(a) = o*i(a) + 14*y(a). Find h such that u(h) = 0.
0, 1
Suppose 2/9*v**3 + 2 - 10/9*v**2 + 2/3*v = 0. Calculate v.
-1, 3
Let p(q) be the first derivative of -q**5/210 - q**4/84 + 2*q**3/21 + q**2 + 4. Let y(v) be the second derivative of p(v). Factor y(l).
-2*(l - 1)*(l + 2)/7
Factor -k - 8*k**2 + k**3 + 8*k**2.
k*(k - 1)*(k + 1)
Suppose 0 = 4*i + 5*h - 71, 37 + 8 = 3*i + h. Let a = i + -12. Solve 0 - 2/9*t**3 + 2/3*t**a - 4/9*t = 0 for t.
0, 1, 2
Factor 0*b - 2/13*b**4 - 2/13*b**5 + 2/13*b**3 + 0 + 2/13*b**2.
-2*b**2*(b - 1)*(b + 1)**2/13
Let w be (30/18)/(2/6). Suppose -3 = -w*d + 3*g, 4*g + 0 = -5*d + 31. Suppose -1 - 3*k**4 + 11/2*k + 19/2*k**d - 11*k**2 = 0. Calculate k.
1/2, 2/3, 1
Factor 3*b**3 - b**2 + 6*b**2 - 6*b + 0*b + 4*b.
b*(b + 2)*(3*b - 1)
Let q(k) be the first derivative of -k**6/1080 - k**5/360 + 5*k**3/3 + 1. Let p(g) be the third derivative of q(g). Factor p(o).
-o*(o + 1)/3
Let j(c) = -7*c**3 + 3*c**2 - 8*c - 6. Let r(w) = -7*w**2 - w - 1 - w**3 + 7*w**2. Let h(i) = j(i) - 6*r(i). Factor h(y).
-y*(y - 2)*(y - 1)
Let q be 7/6*(-3)/(-63). Let k(j) be the second derivative of -1/18*j**3 - q*j**4 - 1/60*j**5 + 0*j**2 + 0 + 3*j. Factor k(x).
-x*(x + 1)**2/3
Let n(y) be the third derivative of y**6/60 - y**5/30 - 5*y**4/6 - 8*y**3/3 + 2*y**2 - 25*y. Factor n(p).
2*(p - 4)*(p + 1)*(p + 2)
Let s(f) be the first derivative of -5*f**4/4 + 10*f**3/3 + 5*f**2/2 - 10*f + 28. Solve s(h) = 0 for h.
-1, 1, 2
Let y(g) be the first derivative of -g**4/12 - 2*g**3/9 + g**2/6 + 2*g/3 + 2. Solve y(p) = 0 for p.
-2, -1, 1
Let x(p) be the first derivative of -7*p**4/4 + 23*p**3/2 - 9*p**2 - 3*p + 1. Let b(t) be the first derivative of x(t). Factor b(h).
-3*(h - 3)*(7*h - 2)
Let b be (1 - 105/108) + 0. Let u(c) be the second derivative of 0 - b*c**4 - 2*c + 1/9*c**3 + 0*c**2. Factor u(l).
-l*(l - 2)/3
Let u(b) be the third derivative of b**5/90 + b**4/12 + 7*b**2. Factor u(m).
2*m*(m + 3)/3
Let r = 49 + -31. Suppose j + r*j**3 - 36*j**3 + 17*j**3 = 0. Calculate j.
-1, 0, 1
Let b(u) be the third derivative of 2*u**5/45 + 5*u**4/36 + u**3/9 + 6*u**2. Factor b(h).
2*(h + 1)*(4*h + 1)/3
Let t(c) be the second derivative of c**7/168 - c**6/120 - 3*c**5/40 - c**4/24 + 5*c**3/24 + 3*c**2/8 - 14*c. Suppose t(r) = 0. Calculate r.
-1, 1, 3
Let b be ((-14)/4)/((-9)/6). Let d(j) = -j + 2. Let p be d(0). Factor -5/3*n - 1/3 - n**3 - b*n**p.
-(n + 1)**2*(3*n + 1)/3
Let a be ((-4)/12)/((-1)/2). Let u(z) be the first derivative of 0*z - a*z**3 + 0*z**2 + 0*z**4 + 2/5*z**5 + 1. Determine o, given that u(o) = 0.
-1, 0, 1
Let i(f) be the third derivative of -f**8/80640 + f**7/20160 + f**5/30 - 6*f**2. Let c(a) be the third derivative of i(a). Solve c(m) = 0.
0, 1
Let h = 469 - 469. Solve -5/3*g**3 + 2/3*g**2 - 3*g**5 + h + 0*g - 16/3*g**4 = 0 for g.
-1, 0, 2/9
Suppose -p + 3*u + 17 = p, 5*p = -3*u + 11. Let 2*a**2 - 2*a + 0*a + 2*a**4 +