i(b) be the first derivative of 1/12*b**3 - 1 - 1/16*b**4 + 0*b**2 + 0*b. Let i(q) = 0. Calculate q.
0, 1
Let c(z) = -z + 13. Let i be c(11). Let x(w) be the first derivative of -2*w - i + 2/5*w**5 - w**4 + 0*w**3 + 2*w**2. Factor x(t).
2*(t - 1)**3*(t + 1)
Factor 2*h + 11 - 27 + 13 + h**2.
(h - 1)*(h + 3)
Let c = 4/125 + 96/125. Solve 0*x + 2/5*x**4 + 0*x**3 + 2/5 - c*x**2 = 0.
-1, 1
Let w(n) be the second derivative of -n**4/42 - 3*n. Factor w(f).
-2*f**2/7
Let d(r) = -r**2 - 13*r - 12. Let q be d(-12). Let x(v) be the second derivative of 0 - 2*v - 1/36*v**4 + q*v**3 + 0*v**2. Solve x(t) = 0.
0
Determine h so that -2/3*h**2 - 50/3 + 20/3*h = 0.
5
Let d(m) = 7*m**2 - 22*m + 27. Let h(r) = -6*r**2 + 21*r - 27. Let l(p) = 3*d(p) + 4*h(p). Let l(w) = 0. What is w?
3
Let n(j) = 13*j - 414. Let t be n(32). What is q in -4/5*q**4 + 16/5 + 16/5*q**3 - 12/5*q**t - 16/5*q = 0?
-1, 1, 2
Suppose 5*u - 12 = 2*m, u - 5*m = 5*u - 3. Factor 11*l**2 - 7*l + 3*l**u + 13*l**2 + 25*l + 3 + 12*l**3.
3*(l + 1)**2*(4*l + 1)
Suppose 6/5*j**4 - 2*j**3 + 4/5*j**2 + 0*j + 0 = 0. What is j?
0, 2/3, 1
Let c(a) = -2*a**3 - 8*a**2 - 6*a + 10. Suppose 30 = m + 2*m. Let r(t) = t**2 + t - 1. Let y(f) = m*r(f) + c(f). Determine g, given that y(g) = 0.
-1, 0, 2
Let l(p) = 5*p**3 - 7*p**2 - 3*p - 3. Let m(f) = 44*f**3 - 62*f**2 - 28*f - 26. Let t(b) = 52*l(b) - 6*m(b). Find c such that t(c) = 0.
-1, 0, 3
Factor -36 + 15*t + 17*t**2 + 9*t - 21*t**2.
-4*(t - 3)**2
Let f(j) = -j - 1. Let k be f(-3). Let x be -2 - (k + (-16)/4). Suppose 0*z + x + 2/7*z**2 = 0. Calculate z.
0
Let w(g) = 11*g**4 - 19*g**3 + 26*g**2 - 6*g - 6. Let c(k) = -k**4 - k**3 - k**2 + k + 1. Let x(h) = 6*c(h) + w(h). Suppose x(d) = 0. Calculate d.
0, 1, 4
Factor -2*p**3 + 0*p - 5/3*p**2 + 0 - 1/3*p**4.
-p**2*(p + 1)*(p + 5)/3
Let s = 2 + 0. Factor -2 - k**4 + 3 - 2*k + s*k**3 + 0*k**4 + 0.
-(k - 1)**3*(k + 1)
Find x such that 0 - 5/2*x**3 + 15*x**2 - 45/2*x = 0.
0, 3
Let 31*m**2 + 18*m**5 - 20*m**3 + 18*m**5 - 23*m**2 + 10*m**4 - 34*m**4 = 0. What is m?
-2/3, 0, 1/3, 1
Let q(x) be the first derivative of 4*x**3/3 - 8*x**2 + 16*x - 8. Factor q(i).
4*(i - 2)**2
Let d(n) be the third derivative of 2*n**5/45 + 17*n**4/36 + 4*n**3/9 + 53*n**2. Determine b, given that d(b) = 0.
-4, -1/4
Let n be 1/(-3) - 4/(-12). Determine v so that n*v**3 - 2*v**2 + 2*v**3 + 4*v**3 + 3*v**5 - 6*v**4 - v**5 = 0.
0, 1
Suppose 5*t + 0*t - 25 = 0. Let f(p) = -p + 7. Let l be f(t). Factor -4*b - 16*b**3 - 4 + 6*b**4 + 4 + 14*b**l.
2*b*(b - 1)**2*(3*b - 2)
Solve 0 + g + 3/2*g**2 + 1/2*g**3 = 0 for g.
-2, -1, 0
Let t(s) be the second derivative of -s**5/180 + s**4/18 - 2*s**3/9 + 3*s**2/2 + 4*s. Let d(w) be the first derivative of t(w). Factor d(c).
-(c - 2)**2/3
Let z(d) be the first derivative of 1 + 1/2*d**3 + 0*d + 3/4*d**2. Factor z(a).
3*a*(a + 1)/2
Let o(t) be the first derivative of t**4/20 + 2*t**3/15 + t**2/10 - 6. Factor o(u).
u*(u + 1)**2/5
Let p be -1 + (22/18)/1. Let l(w) be the first derivative of -1 - 1/3*w**2 + 0*w + p*w**3. Determine o so that l(o) = 0.
0, 1
Let r(c) be the first derivative of -c**7/63 + c**6/15 - c**5/10 + c**4/18 - 2*c + 6. Let n(t) be the first derivative of r(t). Determine p so that n(p) = 0.
0, 1
Let 2/19*a**4 + 4/19*a**3 + 0 - 2/19*a**2 - 4/19*a = 0. What is a?
-2, -1, 0, 1
Let k be 10*(-2)/(2*-1). Suppose -5*v = -15 - k. Factor -4 + 6*l + 2*l**5 + 0*l**5 - 8*l**3 + 0*l**v + 4*l**2.
2*(l - 1)**3*(l + 1)*(l + 2)
Factor -4/7*l**2 + 0 + 2/7*l**3 + 2/7*l.
2*l*(l - 1)**2/7
Let n = -27/5 + 121/15. Determine a so that 2/3*a**5 + 2/3*a + n*a**4 + 4*a**3 + 8/3*a**2 + 0 = 0.
-1, 0
Let w(f) be the first derivative of 3 + 12*f**2 - 7/2*f**4 + 8*f - 6*f**3. Factor w(x).
-2*(x - 1)*(x + 2)*(7*x + 2)
Let t(g) = g**3 - g**2 - 1. Let m(h) = -h**4 + 4*h**3 - 3*h**2 - 6. Let z(b) = 5*m(b) - 30*t(b). Solve z(r) = 0 for r.
-3, 0, 1
Let x(n) be the first derivative of n**6/75 - n**5/25 + n**4/30 - 3*n + 3. Let g(f) be the first derivative of x(f). Find p such that g(p) = 0.
0, 1
Let u be 3/(-5)*(-7 + 2). Let -4*l**2 + 5*l**3 + 2*l**4 - 2*l**u - 16 + 3*l**3 - 24*l = 0. What is l?
-2, -1, 2
Let z be 22/6 + (-13 - -11) + 1. Find q, given that z*q**2 + 16/3*q**3 + 0*q + 0 + 2*q**4 = 0.
-2, -2/3, 0
Suppose -v - 2*s + 8 = 0, 0*s + 4 = 5*v - 2*s. Let -6*u**4 - 2*u**2 - 2*u**5 - v*u**2 + 10*u**4 + 2*u = 0. What is u?
-1, 0, 1
Let r(t) = 5*t**4 - t**3 - 4*t**2 - 2. Let x(l) = -31*l**4 + 7*l**3 + 25*l**2 + 13. Let g(n) = 39*r(n) + 6*x(n). Factor g(h).
3*h**2*(h + 1)*(3*h - 2)
Let m be (-19 + (-3)/1)/1. Let v be (-15)/m - (-10)/(-20). Factor v - 2/11*f**2 + 0*f.
-2*(f - 1)*(f + 1)/11
Let l(w) = w**2 + w - 1. Let n(v) = -3*v**2 + 20*v - 29. Let u(f) = -7*f**2 + 40*f - 58. Let y(m) = 5*n(m) - 2*u(m). Let o(x) = 2*l(x) - y(x). Factor o(k).
3*(k - 3)**2
Suppose -8*z = -3*z - 10. Find s such that -4 + s**2 + 4*s + 9*s**2 - 2*s - 8*s**z = 0.
-2, 1
Find w such that 6*w**4 - 6*w**3 - 8/3*w**2 + 0 + 8/3*w = 0.
-2/3, 0, 2/3, 1
Find q such that -37*q + 7 + 4*q**3 + 69*q - 71 + 28*q**2 = 0.
-4, 1
Let c(g) be the first derivative of -2*g**3/3 - 5*g**2 - 12*g + 42. Find z, given that c(z) = 0.
-3, -2
Let a(g) = -g**2 + 8*g + 5. Let d(p) = p**2 - 7*p - 4. Let s(i) = -2*a(i) - 3*d(i). Let v be s(5). Factor -3*k**2 + 2*k**3 - k**3 + k + v*k**3 + k**4 - 2*k**4.
-k*(k - 1)**3
Let m be (-98)/(-28) + (-1)/2. Suppose 4*t = -m*p - 6, 4*p - 5*t - 4 = 19. Factor 4/7*q - 10/7*q**p + 6/7*q**3 + 0.
2*q*(q - 1)*(3*q - 2)/7
Let w = -2 + 5. Let k(v) be the first derivative of 1/4*v + 1/12*v**w - 1/4*v**2 + 2. Solve k(f) = 0.
1
Let t(y) be the second derivative of 2*y**6/5 + 4*y**5/5 - 2*y**4/3 - 8*y**3/3 - 2*y**2 - 25*y. Suppose t(v) = 0. What is v?
-1, -1/3, 1
Let i(a) = 5*a**4 + 10*a**3 + 10*a - 7. Let r(t) = -4*t**4 - 9*t**3 + t**2 - 9*t + 6. Let d(m) = -5*i(m) - 6*r(m). Factor d(x).
-(x - 1)**4
Let v(h) be the second derivative of 1/80*h**5 - 1/24*h**3 + 0 - 4*h - 1/48*h**4 + 1/8*h**2. Factor v(l).
(l - 1)**2*(l + 1)/4
Let o be (-9)/(-2) - 5/10. Let j(p) = -46*p**4 - 64*p**3 + 22*p**2 + 24*p - 12. Let x(t) = -t**4 + t**3 + 1. Let y(r) = o*x(r) + j(r). Factor y(m).
-2*(m + 1)**2*(5*m - 2)**2
Suppose 5*q = 4*q + 10. Let u be (-8)/q + (-364)/(-105). Factor 4/3 + x**2 - u*x.
(x - 2)*(3*x - 2)/3
Suppose 1/10*w**5 + 24/5*w + 9/10*w**4 + 8/5 + 16/5*w**3 + 28/5*w**2 = 0. Calculate w.
-2, -1
Let d(i) = 8*i**2 + i + 4. Let a(q) = 15*q**2 + 7 + 0 + 2*q + 0*q + 0. Let t(j) = 4*a(j) - 7*d(j). Determine p so that t(p) = 0.
-1/4, 0
Let z be (-66)/20*(-1)/9. Let t = z - -2/15. Solve -t*v**3 + 0*v + 0*v**2 - 1/2*v**4 + 0 = 0 for v.
-1, 0
Let p(s) be the first derivative of s**6/8 + 3*s**5/4 + 3*s**4/2 + s**3 + 33. Factor p(w).
3*w**2*(w + 1)*(w + 2)**2/4
Let h(z) be the second derivative of z**6/6 - z**5/2 - 5*z**4/3 + 5*z**3/3 + 15*z**2/2 - 26*z. Factor h(d).
5*(d - 3)*(d - 1)*(d + 1)**2
Let p = -19 - -20. Let g be 6 - 3 - p/4. Factor 9/4*s**3 - g*s**4 - 1/4*s**2 - 1/4*s + 0 + s**5.
s*(s - 1)**3*(4*s + 1)/4
Let u(o) be the second derivative of -o**5/90 + 5*o**4/54 - 2*o**3/9 - 2*o + 10. Suppose u(t) = 0. What is t?
0, 2, 3
Let v = -4 - -4. Let o be 0/(1*(-5 - -4)). Factor o*x - 1/2*x**2 + v.
-x**2/2
Let w(j) be the third derivative of 1/60*j**5 + 0*j + 0 + 1/18*j**3 - 1/360*j**6 - 1/24*j**4 - 4*j**2. Solve w(r) = 0.
1
Factor 2/5*x**2 + 1/5*x**5 + 2/5*x**3 + 1/5 - 3/5*x - 3/5*x**4.
(x - 1)**4*(x + 1)/5
Let q = 100/301 + -2/43. Let y be 30/28 - 2/4. Let y*v + q + 2/7*v**2 = 0. What is v?
-1
Let y(j) be the first derivative of j**4/4 + 2*j**3/3 - 2*j**2 - 8*j + 1. Suppose y(q) = 0. Calculate q.
-2, 2
Let q(g) be the second derivative of 0*g**2 - 1/21*g**3 + 0 + 1/42*g**4 + g. Factor q(u).
2*u*(u - 1)/7
Let l be (-1)/4*(-2 + 2). Let d(g) be the first derivative of -4 - g**2 - 7/3*g**3 + l*g - 9/4*g**4 - g**5 - 1/6*g**6. Factor d(u).
-u*(u + 1)**3*(u + 2)
Let u be (-2)/(2/9 - (-44)/(-36)). Determine q so that 6/7*q**u + 4/7 + 10/7*q = 0.
-1, -2/3
Factor 33*z**2 - 9*z**3 + 3*z**5 - 5*z**3 - 13*z**3 + 3*z**4 - 12*z.
3*z*(z - 1)**3*(z + 4)
Factor 3*h**5 - 2*h + 4*h**3 - 3*h**5 + 3*h**5 - 5*h**5.
-2*h*(h - 1)**2*(h + 1)**2
Let k(q) be the third derivative of 0*q - 2*q**2 - 1/1176*q**8 + 0*q**3 + 0*q**4 - 1/210*q**5 + 0 + 1/420*q**6 + 1/735*q**7. Factor k(j).
-2*j**2*(j - 1)**