1
Let x(y) = -y**4 + y**3 + y**2 + y + 1. Let o(u) = -5*u**4 + 2*u**3 + 3*u**2 + 4*u + 4. Let i(r) = o(r) - 4*x(r). Find g, given that i(g) = 0.
-1, 0
Let n(s) be the first derivative of -s**6/2 + 18*s**5/5 - 39*s**4/4 + 12*s**3 - 6*s**2 - 9. Factor n(a).
-3*a*(a - 2)**2*(a - 1)**2
Let h be 4/(-22) + (-24)/(-11). Factor 0 - j**h + 1 + 1 - 1.
-(j - 1)*(j + 1)
Let u(s) = -s**4 + 2*s**3 + 6*s - 3. Let z be (-3)/(-2)*(-4)/6. Let w(n) = -n**3 - n + 1. Let m(a) = z*u(a) - 4*w(a). What is y in m(y) = 0?
-1, 1
Let g(p) be the first derivative of -21*p**5/5 - 129*p**4/8 - 24*p**3 - 69*p**2/4 - 6*p - 33. What is i in g(i) = 0?
-1, -4/7, -1/2
Let x(w) = w**4 + 5*w**3 + 18*w**2 - 8*w - 13. Let v(z) = -10*z**3 - 35*z**2 + 15*z + 25. Let h(n) = 3*v(n) + 5*x(n). What is g in h(g) = 0?
-1, 1, 2
Suppose -44 = 10*d - 64. Factor -2/3*q + 1/3*q**d + 0.
q*(q - 2)/3
Suppose 5*l = 2*l + 39. Let a = l - 9. Suppose 0 - 1/2*x**5 - x**a + 0*x**2 - 1/2*x**3 + 0*x = 0. What is x?
-1, 0
Let k(j) be the second derivative of j**5/40 + j**4/8 - 3*j**2/2 - 3*j. Let q(h) be the first derivative of k(h). Factor q(t).
3*t*(t + 2)/2
Let i(a) = a**2 + 4*a + 1. Let m be i(-5). Let 60*k**3 - 7*k + k - 12 + 33*k**4 - m*k + 6*k**5 + 33*k**2 = 0. Calculate k.
-2, -1, 1/2
Let d(l) = -l + 6. Let h be d(3). Let z(m) be the second derivative of 1/10*m**5 - 2/9*m**4 - 1/63*m**7 + 0*m**2 + 2/45*m**6 - 4/9*m**h + 4*m + 0. Factor z(q).
-2*q*(q - 2)**2*(q + 1)**2/3
Let t(s) = s**4 - s**3 - s + 1. Let q(f) = -4*f**4 + 6*f**3 - f**2 + 4*f - 5. Let i(r) = q(r) + 5*t(r). Factor i(g).
g*(g - 1)*(g + 1)**2
Let c(f) = 3*f**2 + 10*f**2 - 14*f**2. Let q(i) = -i**2 + 3 + 5 - 3*i**2 - 8*i. Let a(s) = 6*c(s) - q(s). Suppose a(z) = 0. What is z?
2
Let y = 192 - 290. Let x = y - -298/3. Determine a, given that 2/9*a**5 + 0 + x*a**3 + 2/9*a - 8/9*a**4 - 8/9*a**2 = 0.
0, 1
Let j = 514 + -514. Factor 0*r + 1/2*r**3 + 1/2*r**2 + j.
r**2*(r + 1)/2
Let k(v) be the first derivative of v**8/56 + v**7/105 - v**6/20 - v**5/30 + v**2/2 - 2. Let g(u) be the second derivative of k(u). Find r, given that g(r) = 0.
-1, -1/3, 0, 1
Let j be (-10 + 9)*(-1)/3*0. Let o(h) be the first derivative of 2/7*h**2 + 2/21*h**3 + 4 + j*h. Factor o(b).
2*b*(b + 2)/7
Let g(y) be the second derivative of y**7/21 + 2*y**6/5 + 41*y. Factor g(s).
2*s**4*(s + 6)
Let z be ((-3)/27)/(8/(-6) - -1). Let -1/3 - z*c**2 + 2/3*c = 0. Calculate c.
1
Let r(q) be the first derivative of 9*q**4/4 + 5*q**3 - 3*q**2 - 5. Factor r(h).
3*h*(h + 2)*(3*h - 1)
Suppose 12*o - 3 + 10*o**5 - 40*o**2 + 25*o**4 + 18 - 30*o**3 + 15*o - 7*o = 0. What is o?
-3, -1, -1/2, 1
Let v(k) be the second derivative of -k**5/5 - k**4 + 8*k**2 - 5*k. Let v(a) = 0. Calculate a.
-2, 1
Let a be (-11)/66 - 26/(-12). Let t(c) be the first derivative of -2/3*c - 1 - 2/3*c**a - 2/9*c**3. Factor t(g).
-2*(g + 1)**2/3
Suppose 4*j - z = -2, 1 = z - 1. Let u(l) be the first derivative of 0*l + 1/4*l**4 + 1/3*l**3 - 1 + j*l**2. Factor u(i).
i**2*(i + 1)
Let b(g) = g**3 + 2*g**2 - 3*g - 3. Let m be b(-2). Suppose m*d + 8 = 7*d. Let -3*c**2 + d*c**5 - c**2 + 2*c - 4*c + 4*c**4 = 0. Calculate c.
-1, 0, 1
Suppose -5*p = 5*b - 20, -2*p - 4*b = 2 - 6. Let a(c) = c - 4. Let r be a(p). Suppose -l**5 + l**5 + 2*l**3 - 2*l**5 + 2*l**4 - r*l**2 = 0. Calculate l.
-1, 0, 1
Let r be (-2)/(1/(-3)*3). Factor -1/4 - 1/4*v**r + 1/2*v.
-(v - 1)**2/4
Let j(z) be the first derivative of -z**3/2 - 9*z**2/4 + 6*z - 17. Factor j(r).
-3*(r - 1)*(r + 4)/2
Let i be (2/5)/((-2)/(-10)). Suppose 2*s**i - s + s - 2*s = 0. What is s?
0, 1
Let k(u) be the second derivative of -u**7/168 - u**6/60 + u**5/40 + u**4/12 - u**3/24 - u**2/4 - 5*u. Determine o, given that k(o) = 0.
-2, -1, 1
Let c(u) = -7*u**3 - 2*u**2 - 6. Let w(i) = 8*i**3 + 2*i**2 + 7. Let b = -8 - -15. Let x(o) = b*c(o) + 6*w(o). Factor x(p).
-p**2*(p + 2)
Let x(d) be the second derivative of 0*d**3 + 0 + 1/189*d**7 - 6*d + 0*d**4 + 0*d**5 + 0*d**2 - 2/135*d**6. Factor x(l).
2*l**4*(l - 2)/9
Let o(y) be the third derivative of y**5/100 + 3*y**4/40 + y**3/5 - 26*y**2. Factor o(i).
3*(i + 1)*(i + 2)/5
Let k = 16 + -31/2. Factor -1/2*x**2 + 0 - k*x.
-x*(x + 1)/2
Let r = 317 + -633/2. Factor 0 + 2/3*y**2 - r*y**4 + 0*y - 1/6*y**5 + 0*y**3.
-y**2*(y - 1)*(y + 2)**2/6
Let r(w) = -2*w**2 - 14*w + 11. Let j(b) = -b**2 - 5*b + 4. Let t(c) = -11*j(c) + 4*r(c). Let t(a) = 0. What is a?
0, 1/3
Let v(b) = -b**3 + 4*b**2 - b - 4. Let q be v(4). Let d(s) = -2. Let w(z) = z**2 - z. Let y(n) = q*w(n) + d(n). Suppose y(l) = 0. Calculate l.
1/2
Suppose -36 + 36 + 28*l**2 + 4*l**4 + 24*l**3 + 8*l**2 = 0. Calculate l.
-3, 0
Let -6 + 18*h - 11*h - 9*h**3 + 14*h - 3*h**4 - 27*h**2 + 24*h**3 = 0. Calculate h.
1, 2
Let j = -15245/6 + 2561. Solve -13/3*o**2 - 3/2*o + 1/3 + j*o**3 - 56/3*o**5 + 4*o**4 = 0 for o.
-1, -2/7, 1/4, 1
Let w(c) = 2*c - 6. Suppose 5*n + 8 - 28 = 0. Let r be w(n). Solve -4*h - 5*h**2 - 2 - 2*h**3 - h**r - 2*h = 0 for h.
-1
Suppose 17*r - 14 = 10*r. Suppose 4/7*n + 2/7*n**r + 0 = 0. What is n?
-2, 0
Let b(k) be the second derivative of -2/15*k**3 + 3/100*k**5 - 2/75*k**6 + 0*k**2 + 1/210*k**7 + 0 + 6*k + 1/15*k**4. Factor b(t).
t*(t - 2)**2*(t - 1)*(t + 1)/5
Let v(z) be the third derivative of -2/315*z**7 + 1/36*z**4 + 0 + 0*z**3 + 0*z**6 - 2*z**2 + 1/45*z**5 + 0*z - 1/504*z**8. Factor v(a).
-2*a*(a - 1)*(a + 1)**3/3
Suppose -3*y = -5*v - 21, -5*y = -0*y + 3*v - 1. Find t, given that y*t - 4*t**2 - 11*t**3 + 7*t**3 + 6*t**3 = 0.
0, 1
Let a(x) = x**2 + x. Let t be a(1). Factor -4*z**2 + 2*z**2 + 0*z**t - 5*z**3 + 2*z**4 + 5*z**5.
z**2*(z - 1)*(z + 1)*(5*z + 2)
Suppose 0 = -7*m + 2*m + 10. Suppose -2*g + 36 = 7*g. Factor c**2 - 2*c**3 + 2*c**g + 0*c**m - 3*c**2 + 2*c.
2*c*(c - 1)**2*(c + 1)
Let j(w) be the third derivative of -w**9/90720 - w**8/7560 - w**7/2520 - 2*w**5/15 + 8*w**2. Let z(p) be the third derivative of j(p). Solve z(r) = 0 for r.
-3, -1, 0
Let m(f) be the second derivative of 0 - 7/60*f**6 - f**2 - 1/20*f**5 - 2/3*f**3 + 2*f + 7/8*f**4. Suppose m(p) = 0. Calculate p.
-2, -2/7, 1
Factor 9*n**4 + 13*n**3 - 10*n - 10*n**3 + 0*n**5 + 4*n + 3*n**5 - 9*n**2.
3*n*(n - 1)*(n + 1)**2*(n + 2)
Let a(h) be the first derivative of h**3/3 + h**2/2 - h + 1. Let f(d) = 8*d**2 + 6*d - 7. Let u(c) = -14*a(c) + 2*f(c). Let u(s) = 0. What is s?
0, 1
Let f(c) be the third derivative of -c**5/5 - 4*c**4/3 + 2*c**3 + 5*c**2. Solve f(y) = 0.
-3, 1/3
Let b = -17263/1632 - -180/17. Let n(q) be the third derivative of -3*q**2 + 0 + 0*q**3 + 0*q + 1/240*q**5 + b*q**4. Factor n(g).
g*(g + 1)/4
Suppose 2*t + 6 = 5*l + 21, -4*l - 4 = 0. Suppose y = -t*y. Factor 0 + 3/4*k**4 + y*k**3 - k**2 + 1/4*k**5 + 0*k.
k**2*(k - 1)*(k + 2)**2/4
Suppose -5 = 4*z + 3, 4*y + 5*z + 2 = 0. Factor 0*f + 2*f**4 + 3*f**y - f**5 - 5*f**2 + f.
-f*(f - 1)**3*(f + 1)
Let g(w) = 6*w**4 - 6*w**3 - 5*w - 5. Let q(b) = -3*b**4 + 3*b**3 + 3*b + 3. Let i(v) = 3*g(v) + 5*q(v). Solve i(n) = 0 for n.
0, 1
Let h(s) be the first derivative of 2*s**6 + 27*s**5/5 - 3*s**4/2 - 9*s**3 - 3*s**2 + 1. Solve h(p) = 0 for p.
-2, -1, -1/4, 0, 1
Suppose -i + 272 = 270. Suppose -1/4*h**i + 1/2 - 1/4*h = 0. Calculate h.
-2, 1
Let v = 578/1261 - -60/97. Determine q so that 0 + v*q**2 + 4/13*q = 0.
-2/7, 0
Let v be 54/(-7) + 2/(-7). Let p(j) = j**3 + 8*j**2 - 3*j - 11. Let q be p(v). Factor q*s**3 - 27*s**2 - 7*s**4 + 9*s + 10*s**3 - 2 + 4*s.
-(s - 1)**3*(7*s - 2)
Let b(l) be the second derivative of l**7/56 - 3*l**6/40 - 3*l**5/20 + 2*l + 2. Factor b(t).
3*t**3*(t - 4)*(t + 1)/4
Determine a so that -16 + 38 + 18 - 10*a - 5*a**2 = 0.
-4, 2
Let s(n) be the second derivative of -n**8/280 - 2*n**7/105 - n**6/75 + 4*n**5/75 - 3*n**2 - 3*n. Let j(q) be the first derivative of s(q). Factor j(y).
-2*y**2*(y + 2)**2*(3*y - 2)/5
What is a in 0*a**2 + 0 - 1/2*a**4 - 3/2*a**3 + 2*a = 0?
-2, 0, 1
Let g(x) be the third derivative of 1/40*x**5 + 1/80*x**6 + 0*x**4 - 1/140*x**7 + 5*x**2 - 1/224*x**8 + 0*x + 0*x**3 + 0. Factor g(t).
-3*t**2*(t - 1)*(t + 1)**2/2
Let y(z) be the second derivative of z**6/120 + z**5/60 - z**4/24 - z**3/6 + z**2/2 - z. Let x(k) be the first derivative of y(k). Factor x(g).
(g - 1)*(g + 1)**2
Let j(v) = 3*v**3 - 27*v**2 + 24*v - 18. Let r(l) = 2*l**2 + 1. Let h(b) = j(b) + 6*r(b). Factor h(z).
3*(z - 2)**2*(z - 1)