0 - 5*j**4/24 + 6*j**2. Let k(n) be the second derivative of h(n). Factor k(b).
-4*(b - 3)**2
Let h be 1/3 - 6/18. Factor r**4 + 3*r**3 + h*r**4 - 2*r**3.
r**3*(r + 1)
Suppose -m = -5 - 4. Find z, given that -3*z + 3*z**2 + 3*z + 3*z**2 + m*z**3 = 0.
-2/3, 0
What is c in -10*c**3 - 4*c**4 + 14*c + 2*c**4 - 6*c**2 - 1 - 4*c + 9 = 0?
-4, -1, 1
Let x be (-36)/(-8)*6/36. Find a such that -x*a + 1/2 + 1/4*a**2 = 0.
1, 2
Solve 0 - 2/5*w**3 + 2/5*w**2 + 4/5*w = 0.
-1, 0, 2
Let s = 33/14 - 6/7. Factor -9/4 + 3/4*g**2 - s*g.
3*(g - 3)*(g + 1)/4
Let k(t) be the third derivative of -t**5/20 + t**4/2 + 6*t**3 + 4*t**2 + 3*t. Factor k(w).
-3*(w - 6)*(w + 2)
Let c = 4 - 2. Let m(i) be the second derivative of c*i - 1/12*i**4 - 1/2*i**2 + 0 + 1/3*i**3. Determine w, given that m(w) = 0.
1
Let i = 2185/7 + -311. Determine m, given that 2/7 + 2/7*m**4 - i*m**3 - 8/7*m + 12/7*m**2 = 0.
1
Let y be ((-2)/(-28))/((-3)/240*-1). Factor 4*m**2 + 16/7 + y*m + 6/7*m**3.
2*(m + 2)**2*(3*m + 2)/7
Let g(b) be the second derivative of 7*b**6/10 + 57*b**5/20 + 15*b**4/4 + b**3/2 - 3*b**2 - 9*b. Find l such that g(l) = 0.
-1, 2/7
Let r be 8/(-10)*10/(-4). Suppose -r*m + 10 = -0*m + k, 2*m = 2*k - 2. Find t, given that 3*t**2 - 12*t**2 - t**4 + 3*t**4 + 4*t**4 + 3 + 3*t - m*t**3 = 0.
-1, -1/2, 1
Let p(b) be the second derivative of -b**5/10 + b**4/2 + b**3/3 - 3*b**2 - 9*b. Determine l, given that p(l) = 0.
-1, 1, 3
Factor 137*z**4 + 10*z**4 + 752*z**3 - 288*z + 264*z**2 - 248*z**3 + 48.
3*(z + 2)**2*(7*z - 2)**2
Let q(c) be the second derivative of -3*c**5/80 - c**4/4 - 5*c**3/8 - 3*c**2/4 + 3*c. Factor q(d).
-3*(d + 1)**2*(d + 2)/4
Let x be 26/6 + 1/(-3). Let a be -4 + -5*6/(-3). Solve 13*y + 0 + a + 4 - 5*y**2 - x = 0 for y.
-2/5, 3
Let j(t) = t**3 + 7*t**2 - 9*t - 5. Let k be j(-8). Suppose 0*c**3 - c**3 - c - 2 + k*c + c = 0. Calculate c.
-2, 1
Suppose -5*a - 2*w = -7, -3*w - 2 - 13 = -a. Factor -7*v**2 - a*v**3 + 2*v**2 + 12 - 4*v**2.
-3*(v - 1)*(v + 2)**2
Let s(u) = u + 6. Let p be s(-3). Suppose t - p*t + 16 = -4*i, -i - 5 = -t. What is c in -2*c**5 - 6*c**3 - 3*c**t - 6*c**4 - c**2 + c**2 + c**2 = 0?
-1, 0
Let i(r) = -r**2 + 3*r + 3. Let j(v) = v**3 - 5*v**2 - 6*v + 3. Let h be j(6). Let c be i(h). Find t such that 4*t**2 + 2*t**c - 6*t**2 + 0*t**3 = 0.
0, 1
Solve 5*w**4 - 2*w**3 - 6*w**3 + 8*w**2 - 6*w**4 - 5*w**4 = 0 for w.
-2, 0, 2/3
Let d(r) be the first derivative of 2*r**3/27 + r**2/9 - 4*r/9 + 6. Factor d(b).
2*(b - 1)*(b + 2)/9
Suppose 3*t - 21 - 6 = 0. Let u be 21/t*8/14. Factor u - 2*w + 2/3*w**2.
2*(w - 2)*(w - 1)/3
Let p be ((-10)/(-4) + -2)*6. Let w(d) be the third derivative of 0 - 7/60*d**5 + 4*d**2 + 0*d - 3/8*d**4 - 1/3*d**p. Factor w(g).
-(g + 1)*(7*g + 2)
Let r = -219 + 4600/21. Let a(y) be the third derivative of 0*y + 0*y**5 - r*y**3 - 1/42*y**4 + 0 + 1/210*y**6 + 2*y**2 + 1/735*y**7. Factor a(s).
2*(s - 1)*(s + 1)**3/7
Let z(k) = -30*k**5 - 21*k**4 + 39*k**3 + 21*k**2 - 30*k. Let r(t) = -3*t**5 - 2*t**4 + 4*t**3 + 2*t**2 - 3*t. Let g(f) = -21*r(f) + 2*z(f). Factor g(q).
3*q*(q - 1)**2*(q + 1)**2
Suppose 0 = 2*p - 3*p + 3*v + 13, -15 = 3*v. Let y = 6 + p. Solve 0 + a**4 - 2*a**y + 0 - 4*a**2 - 4*a**3 = 0 for a.
-2, 0
Let x(s) be the second derivative of s**6/50 + 3*s**5/50 - 4*s. Factor x(r).
3*r**3*(r + 2)/5
Let p(i) be the second derivative of -i**7/21 - 2*i**6/15 + 3*i**5/10 + 2*i**4/3 - 4*i**3/3 + 35*i. Factor p(m).
-2*m*(m - 1)**2*(m + 2)**2
Suppose 4*t = 5*t + 2*m - 2, 4*m + 4 = 0. Suppose -t*v + 2*c = -0*v - 6, 5*v + 5*c - 45 = 0. Determine a, given that -v*a + 2*a**2 - 3*a - a + 8 = 0.
2
Let q = 67 + -333/5. Let x be (-3 + 2)*(-1)/5. Determine c so that 0*c**4 + 1/5*c + x*c**5 - q*c**3 + 0*c**2 + 0 = 0.
-1, 0, 1
Suppose 0 = -4*h + 1 + 11. Let z(w) be the third derivative of w**2 + 0*w + 1/168*w**8 + 0 + 0*w**6 + 0*w**h + 0*w**5 + 0*w**4 - 1/105*w**7. Factor z(o).
2*o**4*(o - 1)
Factor 6/13*u - 2/13*u**2 - 4/13.
-2*(u - 2)*(u - 1)/13
Let b = -59/4 - -15. Let s be ((-2)/20)/((-4)/10). Factor 1/4*g**3 + 1/4*g**2 - b*g - s.
(g - 1)*(g + 1)**2/4
Let m(x) = 18*x**3 + 6*x**2 - x - 23. Let u(s) = 2*s**2 + 0*s + 6*s**3 - 3 - 5 + 0*s. Let a(p) = -6*m(p) + 17*u(p). What is v in a(v) = 0?
-1, -1/3, 1
Let k(p) be the second derivative of 3*p**5/10 + 7*p**4/6 + 2*p**3/3 + 8*p. Factor k(l).
2*l*(l + 2)*(3*l + 1)
Let f(c) be the second derivative of -c**7/189 + 2*c**6/135 - c**4/27 + c**3/27 - 4*c. Let f(x) = 0. What is x?
-1, 0, 1
Let i(k) be the first derivative of -1/16*k**4 + 0*k**2 + 0*k + 3 + 1/12*k**3. Suppose i(f) = 0. What is f?
0, 1
Suppose -75*a + 54 = -57*a. What is z in -2/3*z**a - 2/9*z**4 - 2/3*z**2 - 2/9*z + 0 = 0?
-1, 0
Let u(f) be the second derivative of -4*f + 4/3*f**3 - 2*f**2 + 0 + 1/20*f**5 - 5/12*f**4. What is c in u(c) = 0?
1, 2
Factor 0 + 16/11*h**4 + 48/11*h**2 - 4*h**3 - 18/11*h - 2/11*h**5.
-2*h*(h - 3)**2*(h - 1)**2/11
Suppose -4*c + 1 = -7. Factor -4*t + t**c + t - 2*t**2 + 4*t**2.
3*t*(t - 1)
Let x(w) be the second derivative of 1/55*w**5 + 3/55*w**6 + 0*w**3 + 0 - w + 0*w**2 + 0*w**4 + 1/33*w**7. Factor x(g).
2*g**3*(g + 1)*(7*g + 2)/11
Let k(x) = -x**2 + 1. Let t be k(1). Factor t + 2/3*c**2 - 2/3*c.
2*c*(c - 1)/3
Let n(x) = -6*x**3 - 24*x**2 + 3*x. Let g(a) = -3*a**3 - 11*a**2 + a. Let r(d) = -14*g(d) + 6*n(d). Factor r(j).
2*j*(j + 1)*(3*j + 2)
Let k(j) be the first derivative of -j**3/12 + j/4 + 7. Factor k(c).
-(c - 1)*(c + 1)/4
Let b(d) = d**3 - 19*d**2 + 33*d + 17. Let l be b(17). Solve x**4 + 0 + 1/3*x**2 + l*x - 1/3*x**5 - x**3 = 0 for x.
0, 1
Let c(l) = 13*l**5 + 11*l**4 + 40*l**3 + 49*l**2 + 20*l + 4. Let f(t) = -3*t**5 - 3*t**4 - 10*t**3 - 12*t**2 - 5*t - 1. Let u(w) = 2*c(w) + 9*f(w). Factor u(b).
-(b + 1)**5
Let f be (21/28)/((-9)/6)*-1. Factor -1/2*l - f*l**3 + l**2 + 0.
-l*(l - 1)**2/2
Let u = 14 - 14. Let d(x) be the second derivative of 0*x**5 + u*x**3 + 0*x**2 + 2*x + 0 + 1/15*x**6 - 1/6*x**4. Factor d(o).
2*o**2*(o - 1)*(o + 1)
Let y(s) be the first derivative of s**4/32 - s**3/6 + s**2/4 + 16. Factor y(b).
b*(b - 2)**2/8
Suppose 0*b = 2*d - b - 3, -9 = -3*d - 3*b. Factor -u**5 + 2*u**2 - 4*u**2 + 2*u**d + u**2 - 3*u**3 + 3*u**4.
-u**2*(u - 1)**3
Suppose -2*s + 4 = -0*s. Solve -x**4 + 6*x**2 - 4*x + 3*x**4 - 6*x**3 + s*x = 0.
0, 1
Let g(v) be the second derivative of -4*v + 1/30*v**4 + 0 - 1/5*v**3 + 2/5*v**2. Factor g(a).
2*(a - 2)*(a - 1)/5
Let z(t) be the second derivative of -t**7/42 + t**6/5 - t**5/4 - t. Factor z(i).
-i**3*(i - 5)*(i - 1)
Suppose 4/5*q**2 - 16/5*q + 12/5 = 0. Calculate q.
1, 3
Let w(b) be the first derivative of -3*b**4/4 + 9*b**2/2 + 6*b + 26. Suppose w(n) = 0. What is n?
-1, 2
Let k = 26 - 24. Let 1/2*w + 1/4*w**k + 1/4 = 0. What is w?
-1
Suppose 1 + 1/4*l**2 - 5/4*l = 0. What is l?
1, 4
Let o = 322/5 - 64. Suppose j + 20 = t + 5*j, 5*j = 3*t + 25. Factor -2/5*i - o*i**2 + t.
-2*i*(i + 1)/5
Let r be (-52)/39*(1 + -4). Let h(k) be the second derivative of 1/30*k**3 - 1/30*k**4 + 0 - r*k - 1/100*k**5 + 1/5*k**2. Determine o so that h(o) = 0.
-2, -1, 1
Let h(y) = -y + 8. Let c be h(8). Let u(k) be the third derivative of 0*k**5 - 1/24*k**4 + 0*k + k**2 + 1/120*k**6 + c + 0*k**3. Factor u(s).
s*(s - 1)*(s + 1)
Let r(y) be the first derivative of y**4/4 - 5*y**3/3 + 3*y**2/2 + 9*y + 50. Factor r(k).
(k - 3)**2*(k + 1)
Let x be 7/14 + 2/(-12). Factor -2/3*t**2 + 0 + 1/3*t + x*t**3.
t*(t - 1)**2/3
Let s = -37 + 41. Suppose 0 + y**s - 1/4*y + y**2 - 1/4*y**5 - 3/2*y**3 = 0. What is y?
0, 1
Let v(o) be the third derivative of -1/120*o**6 + 0*o**3 + 1/336*o**8 + 0*o + 0*o**4 - 1/210*o**7 + 10*o**2 + 1/60*o**5 + 0. Factor v(s).
s**2*(s - 1)**2*(s + 1)
Let d(i) be the second derivative of 1/12*i**3 + 6*i + 0*i**2 + 1/84*i**7 + 0*i**4 + 0*i**6 + 0 - 1/20*i**5. Factor d(u).
u*(u - 1)**2*(u + 1)**2/2
Factor 16*d - 6 + 5 - 11 - 4*d**2.
-4*(d - 3)*(d - 1)
Let a(d) = d**2 + 25*d + 24. Let k be a(-24). Suppose 3/2*l**5 + k - 9/2*l**3 + 3*l**2 + 0*l**4 + 0*l = 0. What is l?
-2, 0, 1
Let b = 0 + 4. Factor 4*v - 10*v**3 + 6*v**4 + b*v**4 + 2*v**2 - 6*v**3.
2*v*(v - 1)**2*(5*v + 2)
Solve -1/2*s**2 + 0 - 1/2*s = 0.
-1, 0
Factor -3/7*s**3 - 3/7*s + 6/7*s**2 + 0.
-3*s*(s - 1)**2/7
Let h(g) be the first derivative of -1 - 1/12*g**3 + 1/16*g**4 - 1/8*g**2 + 1/4*g. Suppose h(x) = 0. What is x?
-1, 1
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