40 - z**3/3 - 2. Let r(o) be the third derivative of q(o). Factor r(y).
3*y*(y - 1)**2*(y + 1)**2
Suppose 0 = 4*p - 7*p + 6. Factor 3*d**2 + 16 + 6*d**p - 15*d - 5*d**2 - d.
4*(d - 2)**2
Let i(o) be the first derivative of -4*o**2 - 8/3*o**3 - 1/2*o**4 + 0*o - 3. Factor i(d).
-2*d*(d + 2)**2
Suppose -j**2 + j + j**3 - j**2 - j**2 + j = 0. What is j?
0, 1, 2
Let w(p) be the third derivative of 1/150*p**6 - 1/525*p**7 + 0*p**5 - 1/30*p**4 + 2*p**2 + 0*p + 0 + 1/15*p**3. Solve w(d) = 0 for d.
-1, 1
Suppose 0 = -2*z - 1 - 1. Let i(n) = n**2 + 5*n + n + n**2. Let q(j) = j**2 + j - 1. Let a(s) = z*i(s) + 4*q(s). Suppose a(c) = 0. Calculate c.
-1, 2
Let i be 16/(-28)*14/(-12). What is h in 2/9*h**3 - 4/9 + 0*h**2 - i*h = 0?
-1, 2
Let i**5 - 35*i**2 - 6*i**5 + 15*i**4 + 3*i**3 + 2*i**3 - 7 + 27 = 0. Calculate i.
-1, 1, 2
Suppose -2*r - 30 = -2*i - 4, 2*i - 4*r - 28 = 0. Let z(s) = -3*s**2 + 102*s - 135. Let w(f) = f**2 - 41*f + 54. Let d(u) = i*w(u) + 5*z(u). Factor d(o).
-3*(o - 3)**2
Let y(g) be the third derivative of 0*g**6 + 0 - 1/336*g**8 + 0*g**3 + 1/24*g**4 - 1/30*g**5 - 5*g**2 + 1/105*g**7 + 0*g. Let y(r) = 0. What is r?
-1, 0, 1
Let i be (1/(-5))/(78/(-65)). Let c(a) be the first derivative of 0*a + 1/12*a**4 + i*a**2 - 1 - 2/9*a**3. Determine q so that c(q) = 0.
0, 1
Let h(m) be the second derivative of m**4/30 - m**3/15 - 2*m**2/5 + 19*m. Factor h(z).
2*(z - 2)*(z + 1)/5
Let g(n) = 17*n**2 - 19*n. Let l(q) = -6*q**2 + 6*q. Let y(i) = 3*g(i) + 8*l(i). Factor y(w).
3*w*(w - 3)
Let a = -1/333 - -556/333. Let x(k) be the first derivative of -14/9*k**3 + 4/3*k + a*k**2 + 3. Factor x(u).
-2*(u - 1)*(7*u + 2)/3
Let v(z) be the second derivative of -z**4 + 1/15*z**6 + 0 + 0*z**5 + 7*z - 3*z**2 - 8/3*z**3. Factor v(j).
2*(j - 3)*(j + 1)**3
Let i(a) be the third derivative of 0*a**5 + 2/1365*a**7 + 0*a + 1/780*a**6 + 1/2184*a**8 - a**2 + 0 + 0*a**4 + 0*a**3. Factor i(w).
2*w**3*(w + 1)**2/13
Let j(b) be the second derivative of b**4/6 - b**3/3 - 14*b. Suppose j(p) = 0. Calculate p.
0, 1
Let w(r) be the second derivative of 4*r**6/5 + 7*r**5/5 + r**4/3 + 63*r. Solve w(i) = 0 for i.
-1, -1/6, 0
Factor 4*d**4 - d**5 + 2715*d**2 - 2731*d**2 - 16*d**3 + 5*d**5.
4*d**2*(d - 2)*(d + 1)*(d + 2)
Let q(r) = -13*r**4 + 5*r**3 + 18*r**2 + 7*r - 7. Let w(n) = -6*n**4 + 3*n**3 + 9*n**2 + 3*n - 3. Let a(d) = -3*q(d) + 7*w(d). Find i such that a(i) = 0.
-1, 0, 3
Let r be (-1)/(-2 - -1)*5. Solve -4*c + 4*c**5 + 6*c**5 + 18*c**4 - 18*c**2 - 2*c**r - 4*c**3 = 0 for c.
-2, -1, -1/4, 0, 1
Let y(j) be the second derivative of -j**4/16 + 3*j**3/8 - 3*j**2/4 + 11*j. Factor y(n).
-3*(n - 2)*(n - 1)/4
Let a(s) be the second derivative of -s**5/30 + s**4/8 + s**3/3 + s**2/2 - 2*s. Let d(x) be the first derivative of a(x). Suppose d(z) = 0. Calculate z.
-1/2, 2
Let y(v) be the third derivative of -v**8/13440 + v**7/3360 - v**5/10 + 7*v**2. Let g(i) be the third derivative of y(i). Let g(u) = 0. Calculate u.
0, 1
Suppose 4 = -5*j + 29. Let f(i) be the third derivative of 0*i + 2*i**2 - 4/3*i**3 - 1/3*i**4 - 1/30*i**j + 0. What is r in f(r) = 0?
-2
Suppose -3*x = 26 - 8. Let r = x - -8. Factor 1 + 0 - 2*g - 1 + 2*g**r.
2*g*(g - 1)
Let q = 26 + -10. Suppose q - 6 = 2*i. Factor i*y**2 - 2*y**3 - 5*y**2.
-2*y**3
Factor -1/3*l**3 + 0 + 2/3*l**2 + l.
-l*(l - 3)*(l + 1)/3
Factor -4/7*f**3 - 2/7 - 4/7*f**2 + 6/7*f**4 - 2/7*f**5 + 6/7*f.
-2*(f - 1)**4*(f + 1)/7
Suppose -1 = 2*o + 4*k - 15, -5*o + 4*k = -7. Factor -32/7 + 48/7*d + 4/7*d**o - 24/7*d**2.
4*(d - 2)**3/7
Let l(c) be the third derivative of 1/105*c**7 + 0*c**3 + 0 + c**2 + 1/120*c**5 + 1/48*c**6 + 0*c**4 + 0*c. Factor l(w).
w**2*(w + 1)*(4*w + 1)/2
Suppose -6*g = -2*g - 24. Factor k + 3*k**2 - g*k**4 + 0*k + 5*k**4 - 3*k.
-k*(k - 1)**2*(k + 2)
Let l be 4*(-35)/(-60)*32/84. Determine k, given that -4/9*k**3 - l*k - 10/9*k**2 - 2/9 = 0.
-1, -1/2
Let r(w) = w**3 + 9*w**2 - 3*w - 1. Let v(y) = -2*y**3 - 10*y**2 + 2*y + 2. Let h(o) = -4*r(o) - 3*v(o). Factor h(c).
2*(c - 1)**3
Let u(b) be the second derivative of 0*b**3 - 1/10*b**5 + 1/15*b**6 - 3*b + 0*b**2 - 1/6*b**4 + 1/21*b**7 + 0. Factor u(v).
2*v**2*(v - 1)*(v + 1)**2
Let x(d) be the second derivative of d**5/190 - d**4/19 + 4*d**3/19 - 8*d**2/19 - 14*d. Find s, given that x(s) = 0.
2
Let o(x) = x**3 + 13*x**2 + 23*x + 13. Let t be o(-11). Let y(p) be the first derivative of 2/3*p**3 + 1/4*p**4 - 2 + 1/2*p**t + 0*p. Let y(d) = 0. Calculate d.
-1, 0
Factor 1/3*k**5 + k**3 - 1/3*k**2 - k**4 + 0*k + 0.
k**2*(k - 1)**3/3
Suppose -2*r = r - 39. Let k = -4 + r. Let -10*d**3 + 11*d**4 + 8*d + 2*d**3 + d + d**4 - 2 - k*d**2 = 0. Calculate d.
-1, 1/2, 2/3
Let c(z) be the first derivative of -5/3*z**2 - 20/9*z**3 - 5/3*z**4 - 2/3*z + 1 - 2/3*z**5 - 1/9*z**6. Factor c(u).
-2*(u + 1)**5/3
Let g be (-135)/6*(-22)/66. Factor -9/2*s + g*s**2 - 3.
3*(s - 1)*(5*s + 2)/2
Suppose b = -o + 7, -2*b + 2*o + 4 = -b. Determine q so that -5*q**3 - 2*q**3 + b*q**3 = 0.
0
Let b(m) be the second derivative of 2*m**5/15 + 7*m**4/18 + m**3/3 + 22*m. Factor b(k).
2*k*(k + 1)*(4*k + 3)/3
Let m(g) be the first derivative of -g**4/26 - 2*g**3/13 - 1. Factor m(w).
-2*w**2*(w + 3)/13
Let q(a) be the first derivative of 2*a**3/33 + 6*a**2/11 + 10*a/11 + 14. Solve q(i) = 0 for i.
-5, -1
Suppose -4*i - 1 = -3*o, 2*i - i = o - 1. Suppose -i*f = f. Factor 0 + 0*t**4 + 4/9*t**3 - 2/9*t + f*t**2 - 2/9*t**5.
-2*t*(t - 1)**2*(t + 1)**2/9
Let f(h) be the first derivative of 0*h**2 + 2 + 1/12*h**3 + 1/16*h**4 + 0*h. Factor f(x).
x**2*(x + 1)/4
Determine q, given that 20/7*q**2 - 4/7*q**5 + 0 + 12/7*q**3 - 4/7*q**4 + 8/7*q = 0.
-1, 0, 2
Factor -6/5*t**3 - 2/5*t**4 + 2/5*t**2 + 6/5*t + 0.
-2*t*(t - 1)*(t + 1)*(t + 3)/5
Factor x**2 + 0*x - 1/2*x**3 + 0.
-x**2*(x - 2)/2
Factor -3/4 - 3/4*r**2 + 3/2*r.
-3*(r - 1)**2/4
Let y(u) be the third derivative of -1/21*u**3 + 0 - 1/210*u**5 - 1/42*u**4 - u**2 + 0*u. What is z in y(z) = 0?
-1
Let g(w) = w**3 - 9*w**2 + 7*w - 3. Let z be g(9). Determine l so that 6*l + 28*l**2 + 47*l**3 - z*l**5 - 3*l + 0*l**2 - 19*l**4 + l = 0.
-2/3, -2/5, -1/4, 0, 1
Let m(d) = -6*d**2 + 6. Let r(y) be the third derivative of y**5/15 - 2*y**3/3 - y**2. Let u(s) = 5*m(s) + 8*r(s). Factor u(p).
2*(p - 1)*(p + 1)
Let n be (-2)/(-5) + 0*1/(-6). Suppose 0*s - n*s**2 + 0 = 0. Calculate s.
0
Let m(b) be the third derivative of -b**7/6 + 19*b**6/24 - 5*b**5/4 + 5*b**4/24 + 5*b**3/3 + b**2. Factor m(c).
-5*(c - 1)**3*(7*c + 2)
Factor x**2 + x**2 + 2*x**2 + 9*x - 13*x.
4*x*(x - 1)
Let l(z) = -z**2 - 2*z - 1. Let v be l(-1). Let r(q) be the second derivative of 1/6*q**4 + 3*q + q**2 + 2/3*q**3 + v. Factor r(m).
2*(m + 1)**2
Let p(s) be the third derivative of -s**7/6300 - s**6/600 - s**5/150 + s**4/24 - 2*s**2. Let m(v) be the second derivative of p(v). Factor m(h).
-2*(h + 1)*(h + 2)/5
Factor 15/2*l**3 - 2*l + 25*l**4 + 0 - 6*l**2.
l*(2*l - 1)*(5*l + 2)**2/2
Let i(j) be the first derivative of j**6/9 + 8*j**5/15 + 2*j**4/3 - 4*j**3/9 - 5*j**2/3 - 4*j/3 + 1. Factor i(u).
2*(u - 1)*(u + 1)**3*(u + 2)/3
Let a(c) be the third derivative of -c**6/80 - c**5/40 + c**4/16 + c**3/4 + 8*c**2. Determine r so that a(r) = 0.
-1, 1
Suppose 0 = -0*y - 4*y + r + 3, -3*y + 5*r = 19. Solve -s**3 - s**3 + 5*s**2 - y*s**2 - s**2 = 0.
0, 1
Let n be 35/(-5)*2/(-7). Suppose -6 = -s - n*s. Factor g**4 + 1/2*g**3 + 0*g**s + 1/2*g**5 + 0*g + 0.
g**3*(g + 1)**2/2
Suppose 0*y**3 + 3/5*y**5 + 0 + 0*y + 0*y**2 - 3/5*y**4 = 0. Calculate y.
0, 1
Let k(a) = -a**3 + 8*a**2 + 8*a + 9. Let l be k(9). Let m(h) be the second derivative of -1/48*h**4 - 1/24*h**3 + h + 0 + l*h**2. Factor m(i).
-i*(i + 1)/4
Let v(u) = -u**3 + 6*u**2 + u - 3. Let f be v(6). Factor 4*k + 2*k**f - 4*k - 2*k.
2*k*(k - 1)*(k + 1)
Suppose c - 3*j - 20 = 0, -c + 3*c = -4*j - 10. Find a such that 0*a**2 - 2/5*a**c + 1/5*a**4 + 0*a + 1/5*a**3 + 0 = 0.
-1/2, 0, 1
Let s(z) = z**3 - 10*z**2 - 11*z + 2. Let r be s(11). Let l be -2*1*r/(-10). Factor -l*b**2 + 8/5*b - 8/5.
-2*(b - 2)**2/5
Suppose 0 = 17*a + 24 - 92. Let -2/9*k**2 + 0*k**3 + 2/9*k**a + 0 + 0*k = 0. What is k?
-1, 0, 1
Suppose 3 = 3*m - 3. Find g such that -5*g**2 + 6*g - 5*g - 3*g + 4*g**m + g**3 = 0.
-1, 0, 2
Let z(s) be the third derivative of s**5/150 + 3*s**4/5 + 108*s**3/5 - 61*s**2. Solve z(m) = 0 for m.
-18