
-w**3*(w - 1)
Let 5*d**4 - 25*d**3 + 34*d + 61*d**2 - 21*d**2 - 54*d = 0. Calculate d.
0, 1, 2
Let p be ((-22)/(-5))/(14/10). Suppose 3 = -3*s + 18. Determine d so that 24/7*d + 52/7*d**2 - 16/7 - p*d**3 - 24/7*d**4 + 10/7*d**s = 0.
-1, 2/5, 2
Let u(l) be the third derivative of -l**5/20 - 4*l**4 - 128*l**3 - l**2 + 25*l. Factor u(o).
-3*(o + 16)**2
Let s(k) be the first derivative of 2*k - 2/9*k**3 + 1/18*k**4 - 2 + 1/3*k**2. Let h(r) be the first derivative of s(r). Solve h(d) = 0 for d.
1
Suppose 5*c = 4*c + 10. Let p be 2/4*c*1. Factor 1 - q + 2*q**5 + 2*q**3 + 2*q**p - 5*q**5 + q**4 - 2*q**2.
-(q - 1)**3*(q + 1)**2
Let u(d) be the second derivative of 7*d**5/10 - 43*d**4/24 + 17*d**3/12 - d**2/2 + 6*d. Determine a, given that u(a) = 0.
1/4, 2/7, 1
Let r(v) be the first derivative of 0*v**2 - 2/21*v**3 + 0*v - 1 - 1/14*v**4. Factor r(p).
-2*p**2*(p + 1)/7
Let r(w) be the second derivative of -7*w**6/10 + 87*w**5/20 - 8*w**4 + 2*w**3 - 2*w - 8. Find q such that r(q) = 0.
0, 1/7, 2
Let j = 1305/2 - 651. What is t in j - 3/2*t**2 + 0*t = 0?
-1, 1
Suppose u + 0 = d - 1, -4*d = -12. Factor -9*c**2 + 10*c**u - c**3 + 0*c**3.
-c**2*(c - 1)
Let n(l) = -32*l**2 - 20*l + 200. Let y(f) = f**3. Let p(d) = -n(d) + 4*y(d). Factor p(h).
4*(h - 2)*(h + 5)**2
Factor 2/5*f**3 + 0 + 8/5*f**2 + 8/5*f.
2*f*(f + 2)**2/5
Let u be 0/(-3) - (-1 - 1). Factor -2 - 4*n + 2*n - u*n**2 + 6*n.
-2*(n - 1)**2
Let h(a) be the second derivative of 0 + 0*a**3 + 7*a + 1/48*a**4 + 3/80*a**5 + 1/60*a**6 + 0*a**2. Determine q, given that h(q) = 0.
-1, -1/2, 0
Solve -2*n**2 - 2*n + 4*n**2 + 2 + 0*n**2 - 2*n = 0.
1
Let i(x) be the first derivative of x**8/3360 - x**7/420 + x**6/144 - x**5/120 + x**3/3 + 2. Let w(r) be the third derivative of i(r). What is p in w(p) = 0?
0, 1, 2
Let t(f) = f**4 - f**2 + f. Let b(i) = -7*i**4 - i**3 + 11*i**2 - 9*i. Let r(m) = b(m) + 6*t(m). Factor r(q).
-q*(q - 1)**2*(q + 3)
Let n(w) be the first derivative of -3*w**4/4 - w**3 + 12. Factor n(z).
-3*z**2*(z + 1)
Let t(x) be the first derivative of 0*x + 8/3*x**3 - 3 + 0*x**2 + 8*x**4 + 3*x**6 + 42/5*x**5. Factor t(m).
2*m**2*(m + 1)*(3*m + 2)**2
Let u(y) be the second derivative of -7*y**7/3 + 1736*y**6/195 - 1669*y**5/130 + 343*y**4/39 - 124*y**3/39 + 8*y**2/13 + y. Find t, given that u(t) = 0.
2/13, 2/7, 1
Let q(y) be the first derivative of 3 + 1/3*y**4 - 16/9*y**3 - 1/9*y**6 + 4/15*y**5 - 4/3*y + 7/3*y**2. Factor q(b).
-2*(b - 1)**4*(b + 2)/3
Suppose 3*h + 312 = -h. Let x be h/(-30) + (-4)/(-10). Factor x*t**2 - t**2 - 6*t**2 - 12 + t**2 - 12*t.
-3*(t + 2)**2
Let r(w) be the third derivative of -w**7/1260 + w**6/360 - 5*w**4/12 + 3*w**2. Let b(x) be the second derivative of r(x). Find c such that b(c) = 0.
0, 1
Let q(t) be the second derivative of -t**4/32 - 3*t**3/8 - 3*t**2/2 + 2*t - 2. Find j, given that q(j) = 0.
-4, -2
Let m(k) = -k**3 - 6*k**2 - k - 1. Let b be m(-6). What is s in -2/3*s**3 + 2/9*s**2 + 0*s + 0 + 2/3*s**4 - 2/9*s**b = 0?
0, 1
Let i(z) be the third derivative of 1/240*z**5 - 3*z**2 + 0*z + 0 + 0*z**3 + 1/96*z**4. Determine a so that i(a) = 0.
-1, 0
Let g(d) = 5*d**3 + 20*d**2 + 14*d - 1. Let f(s) = s**3 + 4*s**2 + 3*s. Let i(b) = 11*f(b) - 2*g(b). Determine t so that i(t) = 0.
-2, -1
Let i(x) be the first derivative of 4*x**5/25 - 4*x**3/15 - 15. Find l, given that i(l) = 0.
-1, 0, 1
Let f(l) be the first derivative of 49*l**6/90 + 35*l**5/12 + 31*l**4/6 + 34*l**3/9 + 4*l**2/3 - 3*l + 1. Let p(q) be the first derivative of f(q). Factor p(w).
(w + 1)*(w + 2)*(7*w + 2)**2/3
Let q = 14 + -12. Let 2/3 - 10/3*u + 14/3*u**q - 2*u**3 = 0. Calculate u.
1/3, 1
Let r(d) be the second derivative of d**5/20 - d**4/12 - 2*d + 16. Factor r(n).
n**2*(n - 1)
Let g(k) be the second derivative of -k**7/105 + k**6/15 - 3*k**5/25 - k**4/15 + 7*k**3/15 - 3*k**2/5 + 13*k. Solve g(f) = 0 for f.
-1, 1, 3
Let r = 38 - 303/8. Let m(k) be the second derivative of 3/80*k**5 + 1/8*k**2 + k - 1/48*k**4 - r*k**3 + 0. Factor m(h).
(h - 1)*(h + 1)*(3*h - 1)/4
Let y(o) be the first derivative of 2*o**7/105 + o**6/10 + 2*o**5/15 - o**2 + 6. Let c(q) be the second derivative of y(q). What is x in c(x) = 0?
-2, -1, 0
Let q = 4 + -1. Suppose -2 = t - c, -q*c + 18 = t + 2*t. Factor 4*g - 3*g + 0*g + g**t.
g*(g + 1)
Suppose -2 - 5 = u. Let a be (u - -1)*5/(-10). Factor -30*f**a + 3*f**4 + 3*f**5 + 30*f**3.
3*f**4*(f + 1)
Let h(f) be the second derivative of -f**4/138 + 16*f**3/69 - 15*f**2/23 - 9*f. Factor h(n).
-2*(n - 15)*(n - 1)/23
Find v such that 0 - 1/6*v**5 - 1/3*v**2 + 1/6*v + 0*v**3 + 1/3*v**4 = 0.
-1, 0, 1
Let i(k) be the third derivative of 7*k**6/40 - k**5/4 - k**4/4 - 8*k**2. Factor i(o).
3*o*(o - 1)*(7*o + 2)
Let h = 33/62 + -1/31. Let s(a) be the first derivative of -2 + 1/2*a - 7/6*a**3 + 1/2*a**4 + h*a**2. Factor s(i).
(i - 1)**2*(4*i + 1)/2
Let l(b) be the first derivative of 5*b**6/69 - 54*b**5/115 + 20*b**4/23 + 16*b**3/69 - 48*b**2/23 + 32*b/23 + 13. Find x such that l(x) = 0.
-1, 2/5, 2
Let n(w) be the first derivative of -2/7*w**2 + 1/7*w**4 + 2/7*w**3 + 1 + 0*w - 6/35*w**5. Suppose n(q) = 0. What is q?
-1, 0, 2/3, 1
Let d(b) = -3*b**2 - 6*b + 11. Let v(m) = 3*m**2 + 6*m - 12. Let c(n) = -3*d(n) - 2*v(n). Let c(r) = 0. What is r?
-3, 1
Let x = 2/69 - -59/345. Factor 4/5*b**2 - x - 3/5*b.
(b - 1)*(4*b + 1)/5
Let x be (1/6)/((-16)/(-32)). Let w(l) be the third derivative of 2*l**2 + 4/15*l**5 - x*l**4 + 1/6*l**3 + 0 + 0*l. Factor w(t).
(4*t - 1)**2
Let x be 3 + 18/(1 + -4). Let b be 0*(15/(-6) - x). Factor b + 1/3*n**2 + 1/3*n.
n*(n + 1)/3
Let i(f) be the second derivative of 2*f - 1/40*f**5 - 1/6*f**3 - 1/8*f**4 + 0*f**2 + 0. Factor i(c).
-c*(c + 1)*(c + 2)/2
Let i(f) be the first derivative of f**7/3360 - f**6/720 + f**5/480 - 2*f**3/3 - 9. Let c(u) be the third derivative of i(u). Solve c(x) = 0 for x.
0, 1
Let z(n) be the third derivative of n**7/1050 - n**6/600 - n**5/100 + n**4/120 + n**3/15 + 7*n**2. Determine d, given that z(d) = 0.
-1, 1, 2
Let c(k) be the third derivative of -k**6/1260 + k**4/252 + 42*k**2. Factor c(s).
-2*s*(s - 1)*(s + 1)/21
Let f be 6/4 - 59/2. Let w = 141/5 + f. Find i such that 16/5*i**5 + 43/5*i**2 + w + 11/5*i + 56/5*i**4 + 73/5*i**3 = 0.
-1, -1/4
Let n(s) = -s**2 + 10*s - 7. Let u be n(9). Determine b so that 1/3*b**3 - 1/3*b**u + 1/3*b**4 + 0 - 1/3*b = 0.
-1, 0, 1
Let o(c) be the third derivative of 2*c**7/735 - 13*c**6/420 + 3*c**5/70 + 10*c**4/21 + 16*c**3/21 + 26*c**2. Solve o(w) = 0.
-1, -1/2, 4
Let r(n) be the first derivative of -5*n**6/6 + n**5 + 5*n**4/4 - 5*n**3/3 + 13. Factor r(s).
-5*s**2*(s - 1)**2*(s + 1)
Let 4/3 + 2/3*g**2 - 2*g = 0. What is g?
1, 2
Let s(z) be the third derivative of z**6/210 - z**4/6 - 4*z**3/7 - 10*z**2. Factor s(b).
4*(b - 3)*(b + 1)*(b + 2)/7
Let n(s) be the first derivative of 8*s**6/9 + 64*s**5/15 + 79*s**4/12 + 28*s**3/9 - 5*s**2/6 - 2*s/3 + 26. Find m, given that n(m) = 0.
-2, -1, -1/4, 1/4
Factor -7/3 + 1/3*d**2 - 2*d.
(d - 7)*(d + 1)/3
Let r(j) = 6*j**3 + j**2 + 8*j - 8. Let h(g) = -5*g**3 - g**2 - 7*g + 7. Let n(w) = 7*h(w) + 6*r(w). Let n(q) = 0. Calculate q.
-1, 1
Let a be 1/3 - (15/(-63))/(-5). Factor -6/7*s + 4/7 + a*s**2.
2*(s - 2)*(s - 1)/7
Let p = 19 + -14. Suppose 2*a + 0*a = p*v - 14, 0 = 2*v + 5*a + 6. Find i such that 0*i**v - 1/3*i**5 + 0*i**4 + 2/3*i**3 - 1/3*i + 0 = 0.
-1, 0, 1
Factor 16*g**2 + 0 + 8/3*g + 50/3*g**4 + 30*g**3.
2*g*(g + 1)*(5*g + 2)**2/3
Let w be 4/2 + 11 + (-225)/18. Let w*p - 1/2*p**3 - 1 + p**2 = 0. Calculate p.
-1, 1, 2
Let u = -21 - -28. Factor 0 + 6 - u + r**2.
(r - 1)*(r + 1)
Let r be -4 + (-34)/(-9) - (-14)/21. Factor r*p**2 - 2/3*p**3 - 4/9 + 2/3*p.
-2*(p - 1)*(p + 1)*(3*p - 2)/9
Let b be 624/(-130) - (1 - 6). Factor b*z**2 + 1/5 - 2/5*z.
(z - 1)**2/5
Let h(q) be the first derivative of q**4/14 - 4*q**3/21 + q**2/7 + 10. Suppose h(l) = 0. What is l?
0, 1
Let q(o) = -5*o**2 - 5 - 2*o**2 + o - 2. Let d(c) = -6*c**2 - 6. Suppose 3 = 2*r + 13. Let l(m) = r*d(m) + 4*q(m). Factor l(p).
2*(p + 1)**2
Let x(t) be the second derivative of -t**4/8 - t**3/4 + 3*t**2/2 + 4*t. Factor x(w).
-3*(w - 1)*(w + 2)/2
Find o, given that -12/13 - 2/13*o**2 + 14/13*o = 0.
1, 6
Let q(f) be the first derivative of 1/18*f**6 - 2/15*f**5 + 0*f**3 - 3 + 1/12*f**4 + 0*f**2 + 0*f. Factor q(y).
y**3*(y