rd derivative of 0 + 1/30*p**5 + 0*p - 2/15*p**3 - 5*p**2 + 1/20*p**4. Factor l(k).
2*(k + 1)*(5*k - 2)/5
Let i(d) = -3*d**5 - d**4 - 4*d**3 + 4*d**2 - 4*d - 4. Let t(k) = k**4 + k**3 - k**2 + k + 1. Let n(b) = i(b) + 4*t(b). Factor n(y).
-3*y**4*(y - 1)
Suppose 9/4*g + 0 - 3/4*g**2 = 0. Calculate g.
0, 3
Let 2/9*m**3 - 4/9 + 10/9*m - 8/9*m**2 = 0. What is m?
1, 2
Find l such that -9*l**2 + 6/5 - 39/5*l = 0.
-1, 2/15
Let f(h) = -h**2 + 5*h - 2. Let l be f(4). Suppose -2*m + 2 = -2. Solve -3*x - 3*x**2 + l*x**2 + 3*x**m + x = 0.
0, 1
Let z be 488/183 + (-2)/(-6). Let o be 2/((-1 - 2)*-3). Factor o*y**4 - 2/9*y**5 + 0 - 2/9*y**2 + 2/9*y**z + 0*y.
-2*y**2*(y - 1)**2*(y + 1)/9
Let q(r) be the third derivative of r**7/1365 + r**6/390 + r**5/390 - 16*r**2. Determine b so that q(b) = 0.
-1, 0
Let p(q) be the first derivative of q**5 - 15*q**4/2 + 20*q**3 - 25*q**2 + 15*q + 27. Factor p(b).
5*(b - 3)*(b - 1)**3
Let c = 133 + -133. Let q(g) be the second derivative of 0*g**4 + 0*g**3 + 0*g**2 + 1/75*g**6 + c*g**5 - 4*g + 0. Factor q(k).
2*k**4/5
Solve 4/3*n - 2 + 2/3*n**2 = 0.
-3, 1
Find w, given that 2*w**5 + 11*w - 9*w**4 - 9*w - 9*w**2 + 230*w**3 - 216*w**3 = 0.
0, 1/2, 1, 2
Suppose -4*a = 4, 2*z - 2*a = 5*z + 5. Let y be (5 - (2 - z)) + 1. Solve 0 - 2/3*l**y - 2/3*l - 4/3*l**2 = 0.
-1, 0
Let n(c) = c**4 - c**3 + c + 1. Let t(r) = r**4 - 10*r**3 - 3*r**2 + 4*r + 4. Let m(a) = 4*n(a) - t(a). Factor m(v).
3*v**2*(v + 1)**2
Let p(f) be the third derivative of -f**7/1680 + f**5/240 - 2*f**3/3 + 5*f**2. Let w(n) be the first derivative of p(n). Determine i so that w(i) = 0.
-1, 0, 1
Factor 0*c + 3/7*c**3 + 0 + 9/7*c**2.
3*c**2*(c + 3)/7
Let r(x) be the first derivative of -2*x**5/15 - x**4/6 + 4*x**3/9 + 1. Factor r(z).
-2*z**2*(z - 1)*(z + 2)/3
Let 9/7*c**4 - 3/7*c + 6/7*c**3 - 18/7*c**2 - 3/7*c**5 + 9/7 = 0. Calculate c.
-1, 1, 3
Let b(w) be the second derivative of -w**5/2 + 3*w**4/4 + w**3/6 + 20*w. Suppose b(v) = 0. Calculate v.
-1/10, 0, 1
Let c = -15 - -19. Factor -16*l - 23*l**3 - l**c + 3*l**3 - 3*l**4 - 32*l**2 + 0*l**4.
-4*l*(l + 1)*(l + 2)**2
Let z(d) be the second derivative of -d**6/40 + 3*d**5/20 - d**4/4 - 2*d**2 + 8*d. Let a(m) be the first derivative of z(m). Factor a(b).
-3*b*(b - 2)*(b - 1)
Suppose -s + 4*t = 18, -t + 1 = -4. Let p = 11 + -7. Solve -s - 2*n + 2*n**2 + p*n - 3*n**3 + n**3 = 0 for n.
-1, 1
Let x(c) be the first derivative of c**5/10 + c**4/2 + c**3/3 - c**2 - 3*c/2 - 7. Factor x(w).
(w - 1)*(w + 1)**2*(w + 3)/2
Let q(k) be the second derivative of 19*k**4/3 + 16*k**3/3 - 38*k**2 + 2*k. Let t(n) = 7*n**2 + 3*n - 7. Let a(x) = -3*q(x) + 32*t(x). Factor a(b).
-4*(b - 1)*(b + 1)
Factor -152 + 5*i**2 - 10*i + 152.
5*i*(i - 2)
Let m = -17 + 69/4. Factor 0 + 1/2*l**2 + 0*l - m*l**3.
-l**2*(l - 2)/4
Let n be 2232/(-66) - 4/22. Let s be (n/(-10) - 4)/(-1). Find y such that -3/5*y**3 - s*y**2 + 3/5*y**4 + 0 + 3/5*y = 0.
-1, 0, 1
Factor -5/4*k**2 - 13/4*k + 1/4*k**3 - 7/4.
(k - 7)*(k + 1)**2/4
Let f(u) be the second derivative of -u**6/420 + u**5/210 + u**4/84 - u**3/21 + 3*u**2/2 + u. Let l(n) be the first derivative of f(n). Solve l(v) = 0 for v.
-1, 1
Let t(w) = -6*w**2 + 2*w + 4. Let h(x) = -11*x**2 + 4*x + 7. Let v(s) = -4*h(s) + 7*t(s). Solve v(i) = 0.
0, 1
Suppose 85*l**2 - 95*l + 11 + 0 - 1 + 0 = 0. What is l?
2/17, 1
Let b be 33/(-100) - (-6)/18. Let g(t) be the third derivative of 0 - 1/150*t**5 + t**2 + 0*t + b*t**6 + 0*t**3 + 0*t**4. Determine r so that g(r) = 0.
0, 1
Suppose -2*c = 3*z - 13, z - 5 = -3*c + 4. Suppose -3*y + 4 = -2. Factor 0*r - 2*r**y + 2 - 2 + c*r.
-2*r*(r - 1)
Let t = -688 - -692. Factor 24/7*o**3 - 32/7*o**t + 0*o**2 + 12/7*o**5 - 4/7*o + 0.
4*o*(o - 1)**3*(3*o + 1)/7
Solve 6*y - 10*y**2 + 4*y**3 + 6*y - 7*y + y**3 = 0 for y.
0, 1
Suppose 72 = 5*r - 4*b, b + 25 - 70 = -4*r. Let v = -10 + r. Suppose 2/7 - 2/7*s**v + 0*s = 0. Calculate s.
-1, 1
Let z(w) be the first derivative of 9*w**4/14 - 22*w**3/21 + 2*w**2/7 + 5. Let z(d) = 0. Calculate d.
0, 2/9, 1
Let g(l) be the third derivative of l**7/420 - l**6/240 - l**5/60 - 2*l**2. Factor g(z).
z**2*(z - 2)*(z + 1)/2
Let y(q) be the first derivative of -9*q**4/8 - 7*q**3/2 - 15*q**2/4 - 3*q/2 + 9. Find g such that y(g) = 0.
-1, -1/3
Let d(m) = 2*m - 2*m - m - 1. Let y be d(-4). Factor 0 + 4/7*v**2 + 0*v + 2/7*v**y.
2*v**2*(v + 2)/7
Let x be 4 - 2 - (-196)/(-105). Let d(c) be the first derivative of 0*c**2 - 2/5*c + 2 + x*c**3. Find a such that d(a) = 0.
-1, 1
Suppose 0*r**3 - 2*r - 3*r**2 + 4*r**3 + 5*r**2 + 0*r**2 = 0. What is r?
-1, 0, 1/2
Let v(g) = -g**2 + 48*g - 3. Let t(q) = 4*q**2 - 144*q + 8. Let s(y) = -3*t(y) - 8*v(y). Let s(z) = 0. Calculate z.
0, 12
Suppose -2*q - 3*q + 2*r - 160 = 0, -3*q - 3*r - 75 = 0. Let i = q - -32. What is g in 0 + 2/7*g**i + 0*g = 0?
0
Let b(d) be the third derivative of d**5/240 - d**3/24 - 11*d**2. Factor b(g).
(g - 1)*(g + 1)/4
Let z(h) be the second derivative of -h**5/110 - h**4/33 + h**3/33 + 2*h**2/11 - 7*h. Solve z(n) = 0 for n.
-2, -1, 1
Let a be 0/((-3)/(-1))*(-15)/(-15). Factor 0*z + a + 2*z**3 + 1/3*z**4 + 3*z**2.
z**2*(z + 3)**2/3
Let r(b) be the third derivative of -8*b**2 + 0 + 1/15*b**6 - 1/84*b**8 + 0*b**5 + 0*b**4 + 0*b**3 + 0*b - 2/105*b**7. Factor r(j).
-4*j**3*(j - 1)*(j + 2)
Let z be ((15/10)/1)/3. Factor z*q - q**3 + 0*q**4 + 0 + 1/2*q**5 + 0*q**2.
q*(q - 1)**2*(q + 1)**2/2
Let b(a) be the third derivative of a**8/1848 - a**7/1155 - a**6/330 + a**5/165 + a**4/132 - a**3/33 + 28*a**2. Let b(d) = 0. What is d?
-1, 1
Let j(b) = -b + 14. Let m be j(12). Factor -1/4*o**m + 1/4 + 0*o.
-(o - 1)*(o + 1)/4
Suppose 0 = -n - 3*d, 0 = 3*n - 2*d + d - 10. Factor 0 - 1/2*c**n + 0*c**2 + 1/2*c.
-c*(c - 1)*(c + 1)/2
Let k(y) be the first derivative of -y**5/20 - y**4/16 + y**3/12 + y**2/8 + 17. Factor k(q).
-q*(q - 1)*(q + 1)**2/4
Let q(n) be the first derivative of -n**6/10 - 21*n**5/25 - 21*n**4/20 + 23*n**3/5 + 12*n**2/5 - 48*n/5 + 24. What is t in q(t) = 0?
-4, -1, 1
Suppose 3*z - 14*z = -22. Solve 8/7 + 42*b**3 + 80/7*b + 38*b**z = 0.
-1/3, -2/7
Let t(j) = -6*j**4 - 12*j**3 + 15*j**2 + 15*j - 15. Let g(c) = 5*c**4 + 12*c**3 - 16*c**2 - 14*c + 15. Let d(r) = 3*g(r) + 2*t(r). Factor d(a).
3*(a - 1)**2*(a + 1)*(a + 5)
Suppose 0 = 4*w + 3*q - 29, 2*q - 7*q + 35 = 4*w. Solve -2*g**2 - 3*g + 4*g - w*g = 0.
-2, 0
Suppose q + 0 = 5. Suppose -s + 11 = q*o - 0*s, 3*o = -2*s + 8. Factor -4/5*u + 4/5*u**3 + 1/5*u**o - 1/5.
(u - 1)*(u + 1)*(4*u + 1)/5
Let m(y) be the first derivative of 1/5*y**3 - 3/5*y**2 + 3/5*y - 3. Determine c so that m(c) = 0.
1
Let r = 11 + -13. Let t = r - -9/4. Factor 0 - t*b - 1/4*b**4 + 1/4*b**2 + 1/4*b**3.
-b*(b - 1)**2*(b + 1)/4
Let q(n) be the second derivative of n**5/30 - n**4/6 + n**3/3 - n**2/3 + 2*n. Determine k so that q(k) = 0.
1
Let g(w) = 2*w - 5. Let d be g(5). Suppose 0 = 2*i + x - 16, -3*i - 2*i + d*x + 10 = 0. Let 1 + i*o**3 - 2*o**3 + 2*o - 5*o = 0. What is o?
-1, 1/2
Let n be (-1)/(-2) - 9/(-2). Let c = n + -1. Factor w**3 - w**c - w**3 + 2*w**3 - w**5 + 2*w**4.
-w**3*(w - 2)*(w + 1)
Let m(n) be the third derivative of -1/24*n**4 + 0 + 1/60*n**5 + 0*n + 0*n**3 - n**2. Determine s so that m(s) = 0.
0, 1
Let d(g) = -g**3 + g**2 - 2*g + 2. Let j be d(2). Let y(w) = -w**3 - 7*w**2 - 7*w - 3. Let p be y(j). Factor -5*t**3 + 7*t**2 + t + 2 - 2 - p*t.
-t*(t - 1)*(5*t - 2)
Let r be ((-5)/(-2) - 2)*12. Find b, given that r - 2*b**2 - 2*b + 5*b**2 + 11*b = 0.
-2, -1
Let z(j) be the first derivative of 2*j**5/5 - 3*j**4 + 6*j**3 - 4*j**2 + 6. Factor z(x).
2*x*(x - 4)*(x - 1)**2
Let z be (-70)/(-8) - 3 - 5. Let x**3 - 2*x**2 - z - 11/4*x = 0. What is x?
-1/2, 3
Let v(k) be the third derivative of 3*k**2 + 0 + 0*k + 0*k**3 + 1/180*k**5 + 1/36*k**4. Factor v(j).
j*(j + 2)/3
Let m(i) be the first derivative of -1/3*i + 1/3*i**3 - 2 - 1/3*i**2. Factor m(t).
(t - 1)*(3*t + 1)/3
Suppose 3*s = 5*s - 10. Factor q**5 - q**4 - q**4 + s*q**3 - 4*q**3.
q**3*(q - 1)**2
Let u = 104/3 + -722/21. Let o be 36/15 - 4/10. Solve 4/7*s + 2/7 + u*s**o = 0.
-1
Suppose -4*o + 9 + 3 = 0. Suppose -o*r + 6 = -3. Factor -4/7*f**r - 2/7*f**4 + 0 - 2/7*f**2 + 0*f.
-2*f**2*(f + 1)**2/7
Let a = -191567/135 + 1419. Let t = a - -56/135. Factor 6/5*w**4 - 6/5*w**3 + 0*w + 2/5*w**2 + 0 - t*w**5.
-2*w**2*(w - 1)**3/5