).
-m*(m + 3)/4
Factor -13*g**5 + 6*g**2 + 3*g + 8*g**5 - 6*g**3 + 8*g**5 - 3 - 3*g**4.
3*(g - 1)**3*(g + 1)**2
Let j(b) be the second derivative of -4*b + 3 - 1/8*b**3 + 5/4*b**2 - 1/48*b**4. Factor j(a).
-(a - 2)*(a + 5)/4
Suppose 5*i = 2*t + 6, 2*t - 40 = -3*i - 14. Let j(s) be the first derivative of 4/9*s**3 + t + 1/6*s**2 + 0*s. Let j(v) = 0. What is v?
-1/4, 0
What is y in 14/3*y**4 + 0 + 24*y**2 + 20*y**3 + 1/3*y**5 + 0*y = 0?
-6, -2, 0
Let o(x) be the second derivative of 0*x**4 + 6*x - 2/35*x**5 + 2/147*x**7 + 0 + 2/21*x**3 + 0*x**6 + 0*x**2. Factor o(w).
4*w*(w - 1)**2*(w + 1)**2/7
Suppose -4*d + v = -33 + 23, d = 5*v + 12. What is l in 2/3*l**3 - d*l**2 + 0 - 8/3*l = 0?
-1, 0, 4
Let f(n) = -n**3 + 10*n**2 + 5*n - 10. Let i(j) = -9*j**2 - 6*j + 9. Let x(q) = -3*f(q) - 2*i(q). Factor x(b).
3*(b - 4)*(b - 1)*(b + 1)
Let c = -820/11 + 2900/33. Determine q so that c - 20/3*q + 5/6*q**2 = 0.
4
Suppose 2*k = -3*t, 4*t - 14 = 2*k - 0. Solve -1/2*z**t - 1/4*z**3 + 0 - 1/4*z = 0.
-1, 0
Let r = 22 + -20. Suppose 2*s**4 - 2*s**3 - 25*s**2 - 4*s**4 + 27*s**r + 2*s**5 = 0. Calculate s.
-1, 0, 1
Let q(a) = a**2 - 19*a + 6. Let s be q(19). Let 6 - s*l**2 - 3*l**3 - 12*l + 9*l + 6*l = 0. Calculate l.
-2, -1, 1
Determine v, given that -6/5*v - 3/5*v**2 + 9/5 = 0.
-3, 1
Let s = 18286/7 + -2612. Factor -2/7*y**4 + 0*y - s*y**2 + 0 - 4/7*y**3.
-2*y**2*(y + 1)**2/7
Let x(w) = 3*w + 24. Let l be x(0). Let u = -20 + l. Factor 1/6*g**u - 1/6*g**3 - 1/6*g**2 + 0 + 1/6*g.
g*(g - 1)**2*(g + 1)/6
Let h(k) be the second derivative of k**7/14 - 19*k**6/5 + 297*k**5/5 - 162*k**4 + 2*k + 20. Factor h(x).
3*x**2*(x - 18)**2*(x - 2)
Let y(v) = 5*v**2 - 2*v + 3. Suppose 0 = 4*w + 73 + 31. Let m(b) = -21*b**2 + 9*b - 13. Let j(a) = w*y(a) - 6*m(a). Factor j(d).
-2*d*(2*d + 1)
Let w(m) = 21*m + 0*m + 13*m**3 - 3*m**2 + 2*m**3 + 4*m**4 + 30*m**2. Let a(v) = v**3 + v**2 - v. Let j(l) = -5*a(l) - w(l). Factor j(n).
-4*n*(n + 1)*(n + 2)**2
Let x(w) be the third derivative of w**4/24 + 2*w**3/3 - w**2. Let l be x(-2). Solve 5*s**3 - 5*s**3 - l*s + 3*s**2 + 0*s - s**4 = 0.
-2, 0, 1
Let r(w) be the first derivative of -w**3/18 + 7*w**2/4 - 10*w/3 + 123. Factor r(p).
-(p - 20)*(p - 1)/6
Let k(d) be the second derivative of d**4/6 + 18*d**3 + 729*d**2 + 94*d. Suppose k(n) = 0. Calculate n.
-27
Find g, given that -12/7*g**2 + 0 - 15/7*g + 18/7*g**3 - 3/7*g**5 + 12/7*g**4 = 0.
-1, 0, 1, 5
Let q(n) be the third derivative of -n**7/35 + n**6/3 + 29*n**5/15 + 11*n**4/3 + 3*n**3 + 156*n**2. Solve q(g) = 0 for g.
-1, -1/3, 9
Let h(x) be the first derivative of x**5/25 + 3*x**4/2 + 28*x**3/15 - 3*x**2 - 29*x/5 - 121. Factor h(o).
(o - 1)*(o + 1)**2*(o + 29)/5
Let q(b) be the third derivative of 0 + 3*b**2 - 11*b + 1/20*b**4 + 0*b**3 + 1/150*b**5. What is x in q(x) = 0?
-3, 0
Suppose 0 = -7*b + 1 + 20. Let t(a) be the first derivative of 2/5*a - 2/15*a**3 + 1/5*a**2 - 1/10*a**4 - b. Factor t(v).
-2*(v - 1)*(v + 1)**2/5
Let l = 8 - 4. Let o be 63/28 - 1/l. Let 10*s**3 + 13*s**3 + 4*s**o + 5*s**3 - 4*s**5 - 4*s**4 - 24*s**3 = 0. Calculate s.
-1, 0, 1
Let y(v) be the first derivative of -v**6/24 + v**5/12 + 10*v**4/3 + 50*v**3/3 + 29*v**2/2 - 25. Let o(g) be the second derivative of y(g). Factor o(c).
-5*(c - 5)*(c + 2)**2
Suppose -q + 5*a - 101 = 0, 5*q = -5*a + 2*a - 449. Let i be 14/q + 6/39. What is b in 2/5*b**2 - 4/5*b + i = 0?
0, 2
Let w(y) be the third derivative of -y**7/42 - 5*y**6/24 + 7*y**5/4 - 115*y**4/24 + 20*y**3/3 - 148*y**2. Suppose w(u) = 0. Calculate u.
-8, 1
Suppose -30*k**2 + 18*k**3 - k - 2*k**4 - 103*k + 54*k = 0. Calculate k.
-1, 0, 5
Let v(f) be the first derivative of -18 - 1/3*f**3 + 0*f + 1/2*f**2. Find m, given that v(m) = 0.
0, 1
Let d(s) = -28*s**4 - 82*s**3 - 100*s**2 - 22*s + 46. Let c(m) = m**4 - m**2 - 1. Let v(x) = -44*c(x) - 2*d(x). Determine o, given that v(o) = 0.
-12, -1, 1/3
Let y(b) = b**4 + 25*b**3 + 3*b**2 + 3*b + 3. Let o(g) = -g**4 - g**3 + g**2 + g + 1. Let q = -23 + 22. Let w(h) = q*y(h) + 3*o(h). Solve w(k) = 0 for k.
-7, 0
Let u(v) be the first derivative of 2*v**6/15 + 8*v**5/25 - 4*v**4/5 - 8*v**3/15 + 6*v**2/5 + 655. Let u(l) = 0. What is l?
-3, -1, 0, 1
Suppose 0 = 3*v + 4*f + f + 8, 0 = -3*v - 2*f + 4. Suppose 0 = 3*z - 2*s + v, 2*z - 3*s - 7 = -18. Solve m - z + 2*m**4 + 2 + m**5 - 2*m**2 - 2*m = 0.
-1, 0, 1
Let t(m) = -43*m + 991. Let a be t(23). Factor -2/5*h**5 + 0 - 2/5*h**3 + 0*h**a - 4/5*h**4 + 0*h.
-2*h**3*(h + 1)**2/5
Let s(f) be the first derivative of 3*f**5/230 - 4*f**4/69 + 7*f**3/69 - 2*f**2/23 - 9*f - 16. Let q(i) be the first derivative of s(i). Factor q(c).
2*(c - 1)**2*(3*c - 2)/23
Let z(y) = -y**2 + 3*y - 3. Let f be z(1). Let v be 0/f - (-2 + (-21)/(-12)). Factor 0 - v*k**2 + 1/2*k.
-k*(k - 2)/4
Let u(a) be the first derivative of -7/6*a**6 + 33/14*a**4 + 11/5*a**5 + 0*a - 52/21*a**3 + 4 + 4/7*a**2. Let u(w) = 0. Calculate w.
-1, 0, 2/7, 2
Let b = 31 - 15. Factor -b*q**4 + q**3 + 3*q**2 - 13*q**3 + q**2.
-4*q**2*(q + 1)*(4*q - 1)
Determine r so that -1418*r**2 - 4*r + 8*r + 1466*r**2 = 0.
-1/12, 0
Determine o, given that -120000/13*o**2 + 8000000/13*o - 200000000/13 - 2/13*o**4 + 800/13*o**3 = 0.
100
Let t(u) be the first derivative of u**7/378 - u**5/60 - u**4/54 - 22*u + 26. Let q(l) be the first derivative of t(l). Factor q(o).
o**2*(o - 2)*(o + 1)**2/9
Factor 2/9*t**4 + 0*t**2 + 0*t + 4/3*t**3 + 0.
2*t**3*(t + 6)/9
Let x = -215/68 + 58/17. Let u(c) be the second derivative of 5*c - 3*c**3 + 0 + x*c**4 + 27/2*c**2. Factor u(r).
3*(r - 3)**2
Let s be (-36423)/(-24495) + (-14)/10. Factor -6/23*y**3 - 8/23*y**2 + s*y + 4/23.
-2*(y + 1)**2*(3*y - 2)/23
Let p = 34 + -31. Suppose 3 = -2*u + 9. Factor 4*c + u - 8*c**4 + 31*c**5 - 35*c**5 + 8*c**2 - p.
-4*c*(c - 1)*(c + 1)**3
Let w(u) be the third derivative of 0*u**3 + 0 + 0*u - 1/100*u**5 + 1/100*u**6 - 1/20*u**4 - 12*u**2 + 1/350*u**7. Find y such that w(y) = 0.
-2, -1, 0, 1
Let b = 31 + -46. Let x(q) = 3*q**2 + 27*q + 24. Let r(u) = -u**2 - 7*u - 6. Let p(i) = b*r(i) - 4*x(i). Suppose p(w) = 0. What is w?
-1, 2
Let l(a) be the third derivative of -26*a**2 + 4/3*a**3 - 7/90*a**5 - 1/180*a**6 + 0 - 1/9*a**4 + 0*a. Solve l(k) = 0 for k.
-6, -2, 1
Find n such that -1817023 + 99*n**3 + 1817023 + 3*n**5 - 33*n**4 - 111*n**2 + 42*n = 0.
0, 1, 2, 7
Let p = -19 + 36. Let s(a) = p*a - 8*a**2 - a**2 - 13*a - 4*a**3. Let n(g) = 2*g**3 + 4*g**2 - 2*g. Let z(q) = 9*n(q) + 4*s(q). Suppose z(u) = 0. What is u?
-1, 0, 1
Suppose -4*s = 3*s - 133. Find r such that -s*r**2 + 2*r**3 + 6*r**2 + 7*r**2 = 0.
0, 3
Let a(y) = y**2 - 30*y - 172. Let v be a(35). Let n(r) be the third derivative of 0 + 0*r + 4/27*r**v - 2*r**2 + 1/90*r**5 - 2/27*r**4. What is p in n(p) = 0?
2/3, 2
Let z = -5 - -7. Determine q so that -4*q**z - 4*q**4 + 3*q + q - 8*q**2 + 12*q**3 = 0.
0, 1
Let j be (-144)/168 + 69/56 + 0. Factor -18*i - j*i**3 - 24 - 9/2*i**2.
-3*(i + 4)**3/8
Let n(f) be the first derivative of f**4 + 16*f**3 - 2*f**2 - 48*f - 123. Factor n(p).
4*(p - 1)*(p + 1)*(p + 12)
Let i = -21 + 26. Suppose i*t - 20 = -0*t. Solve -3*x**t - 87*x + 9*x**3 + 3*x**2 - 12*x**2 + 90*x = 0 for x.
0, 1
Factor -2/15*d**4 + 38/15*d**2 - 4/3*d - 16/15*d**3 + 0.
-2*d*(d - 1)**2*(d + 10)/15
Let d = -24 + 22. Let r(y) = 5*y + 8*y - 2*y - y - 10*y**2 + 3*y**3. Let k(m) = -30*m**3 + 99*m**2 - 99*m. Let g(v) = d*k(v) - 21*r(v). Let g(x) = 0. What is x?
0, 2
Suppose 22*i - 66 = -20*i + 20*i. Factor 24/11*d - 54/11*d**2 - 108/11*d**i + 162/11*d**4 + 8/11.
2*(3*d - 2)**2*(3*d + 1)**2/11
Factor 44/3*k**3 - 16*k**2 + 0*k + 0 + 4/3*k**4.
4*k**2*(k - 1)*(k + 12)/3
Let v = 23 + -21. Let h(g) be the second derivative of -1/33*g**3 - v*g - 1/66*g**4 + 2/11*g**2 + 0. Factor h(w).
-2*(w - 1)*(w + 2)/11
Let x = -20307 + 20307. Factor -3/2*p + x - 2*p**2.
-p*(4*p + 3)/2
Let p be (33/(-6))/(21/(-6) - -3). Factor -p*u**2 + u**2 - 27*u - 8*u**3 + 23*u - 2*u**4.
-2*u*(u + 1)**2*(u + 2)
Let b be 8*1 + (-4 - 6 - -7). Let r(m) be the first derivative of -b + 0*m - 2/15*m**3 + 0*m**2. Solve r(x) = 0.
0
Let i(q) be the first derivative of 12 + 1/10*q**4 - 2/15*q**3 + 0*q + 0*q**2. Solve i(k) = 0.
0, 1
Let p(c) be the second derivative of c**7/5040 + c**6/360 + c**5/60 - 23*c**4/12 + 13*c. Let r(y) be the third derivative of p(y). Factor r(n