5
Let b(r) be the third derivative of r**8/1008 + r**7/126 + r**6/40 + 7*r**5/180 + r**4/36 - 11*r**2. Let b(o) = 0. What is o?
-2, -1, 0
Suppose -9*f + 30 = -4*f. Let r(o) be the second derivative of 0 - 1/42*o**7 + 2*o + 1/15*o**f + 0*o**5 + 1/6*o**3 + 0*o**2 - 1/6*o**4. Factor r(t).
-t*(t - 1)**3*(t + 1)
Suppose 0 = f - 1 - 30. Let o = 63/2 - f. Let -o*x - 1/4*x**2 - 1/4 = 0. Calculate x.
-1
Let y(m) be the third derivative of -2*m**7/1365 - 7*m**6/780 - 3*m**5/130 - 5*m**4/156 - m**3/39 + 7*m**2. Factor y(o).
-2*(o + 1)**3*(2*o + 1)/13
Let r(d) = -8*d**2 - 11*d - 14. Let b(j) = 3*j**2 + 4*j + 5. Let o(h) = -11*b(h) - 4*r(h). Let o(w) = 0. Calculate w.
-1, 1
Let n(r) = 5*r - 1. Let x be n(1). Let -z**5 - 6*z**3 - z**2 + 3*z**3 + z**4 - x*z**4 = 0. Calculate z.
-1, 0
Let h = 59/32 - -1013/32. Let i = h - 33. Factor i*t**2 + 0 + 1/2*t.
t*(t + 1)/2
Let l(n) be the third derivative of n**7/840 + n**6/240 - n**5/60 - n**4/48 + n**3/8 + 27*n**2. Factor l(t).
(t - 1)**2*(t + 1)*(t + 3)/4
Suppose -3*w = 5*z - 32, w + 15 = 2*z - 0*z. Suppose 5*q - 4*g = z, 0*q = -2*q - 5*g + 16. Factor 0*b + 0*b**2 - 2/3*b**q + 0.
-2*b**3/3
Let g(t) be the first derivative of 1/15*t**5 - 1 - 2/9*t**3 + 1/3*t + 0*t**2 + 0*t**4. Find s, given that g(s) = 0.
-1, 1
Determine k so that -4/3*k - 4/3 - 1/3*k**2 = 0.
-2
Let j(w) be the first derivative of 4*w**3/3 - 6*w**2 + 8*w + 2. Find g, given that j(g) = 0.
1, 2
Let d be 12/(-138)*2/1. Let q = d - -66/115. Factor 2/5*u - q*u**2 + 0.
-2*u*(u - 1)/5
Suppose -4*q = 7 - 27. Let d(x) be the second derivative of 3/25*x**6 + 0 - x - 12/25*x**q + 1/5*x**2 - 8/15*x**3 + 11/15*x**4. Find v, given that d(v) = 0.
1/3, 1
Let f(l) be the second derivative of -l**5/60 + l**4/18 - l**3/18 - 8*l. Find t, given that f(t) = 0.
0, 1
Let b(s) be the second derivative of -s**9/5040 + s**8/3360 + 5*s**4/12 + 3*s. Let i(l) be the third derivative of b(l). Factor i(y).
-y**3*(3*y - 2)
Factor 112*w**5 + w**4 + 3*w**2 + 4*w**4 - 7*w**3 - 113*w**5.
-w**2*(w - 3)*(w - 1)**2
Let h(w) be the first derivative of 128*w**4 - 512/5*w**5 - 64*w**3 - 3 - 2*w + 16*w**2. Factor h(b).
-2*(4*b - 1)**4
Let -32/5*x**5 - 2/5*x**2 + 0 - 48/5*x**4 + 0*x - 18/5*x**3 = 0. What is x?
-1, -1/4, 0
Let k be (6/60)/((24/(-15))/(-4)). Factor 1/2*j + 1/4*j**2 + k.
(j + 1)**2/4
Find i such that -3 + 9/2*i - 3/2*i**2 = 0.
1, 2
Suppose 0 = 3*h + 5*i + 28, 3*h - 12 = -0*h + 3*i. Let z be h/(-2) + 3/18. Factor 2/3*o**5 + 4/3*o**4 - z*o + 0*o**3 + 0 - 4/3*o**2.
2*o*(o - 1)*(o + 1)**3/3
Factor -24*o**3 + 0*o**2 + 4/3*o**4 + 0 + 0*o.
4*o**3*(o - 18)/3
Let y be -4 + (-2 - (-6 + 0)). Let u(w) be the first derivative of y*w**4 - 4/15*w**3 + 0*w + 4/25*w**5 + 1/5*w**2 + 1 - 1/15*w**6. Factor u(i).
-2*i*(i - 1)**3*(i + 1)/5
Solve -4 + 0*j**3 + 2 - 5*j + 3*j + 2*j**2 + 2*j**3 = 0 for j.
-1, 1
Suppose 3*u = -2*p - 10, 5*p - 4*u + 12 = -5*u. Let q be (4/(-24))/(p/4). Factor -1/3*x**2 + 0*x + q.
-(x - 1)*(x + 1)/3
Factor -a + 1/4*a**2 + 3/4.
(a - 3)*(a - 1)/4
Let x = -53/10 - -11/2. Solve 3/5*f**3 + 1/5*f**2 + x*f**5 + 0*f + 0 + 3/5*f**4 = 0 for f.
-1, 0
Let z(h) be the second derivative of h**7/10080 - h**6/960 + h**5/240 - 5*h**4/12 + 3*h. Let v(l) be the third derivative of z(l). Factor v(d).
(d - 2)*(d - 1)/4
Suppose -h + 4*s = 6, -5*h + s + 16 = 4*s. Let o(u) be the first derivative of u - 4 - 1/2*u**h + 1/12*u**3. Find w such that o(w) = 0.
2
Let b be 10/3 + 12/18. Let l be -1*(-3)/(-5) + 1. Determine d so that -2/5*d**5 - l*d**2 + 0*d - 6/5*d**b - 6/5*d**3 + 0 = 0.
-1, 0
Let i be ((-5)/(-10))/((-1)/(-6)). Let m = 13 + -9. Suppose 0*w**2 - 2/3*w**i + 2/3*w - 1/3 + 1/3*w**m = 0. Calculate w.
-1, 1
Let v(g) = g**2 + 6*g - 10. Let y be v(-7). Let f = -1 - y. Suppose 4*t**3 + 2*t**4 + 4*t**2 + 0*t**f - t**4 = 0. Calculate t.
-2, 0
Let -2/19*x - 2/19*x**2 + 0 = 0. What is x?
-1, 0
Let c(l) = l**3 - l**2 - l + 3. Let i be c(0). Let n be i - ((-2)/1)/2. Factor 0 - 1/2*q**2 - 7/4*q**5 - 11/4*q**3 + 0*q - n*q**4.
-q**2*(q + 1)**2*(7*q + 2)/4
Let a be (((-3)/48)/((-7)/42))/15. Let b(s) be the third derivative of 1/18*s**3 - 3*s**2 + 0 + 1/60*s**5 + 5/72*s**4 - a*s**6 + 0*s. Factor b(q).
-(q - 1)*(3*q + 1)**2/3
Let k(d) = d**3 - 3*d**2 - 3*d - 3. Let h be k(4). Factor -h - 8 - 12*t + 24*t - 3*t**2.
-3*(t - 3)*(t - 1)
Let a(y) be the third derivative of -y**5/120 - y**4/16 - y**3/6 + 5*y**2. Determine l, given that a(l) = 0.
-2, -1
Let z(g) be the first derivative of -3 + 0*g - 1/4*g**2 + 1/6*g**3. Solve z(u) = 0.
0, 1
Let h(z) be the third derivative of -z**5/210 + z**4/21 - 4*z**3/21 + 4*z**2. Factor h(l).
-2*(l - 2)**2/7
Let k(x) = -5*x**4 + x**3 + 9*x**2 - x - 11. Let w(r) = -r**4 + r**3 + r**2 - r - 1. Let m(i) = 2*k(i) - 14*w(i). Determine s, given that m(s) = 0.
-1, 1, 2
Suppose 1 + 7 = 2*o + 2*r, 4*r = -3*o + 15. Let x be o/8 + 9/120. Factor 0 + 2/5*q**2 + x*q**3 + 0*q.
q**2*(q + 2)/5
Let w(a) be the third derivative of 1/24*a**3 + 5/96*a**4 + 1/120*a**6 + a**2 + 1/30*a**5 + 0*a + 0. What is x in w(x) = 0?
-1, -1/2
Suppose 0 = -2*r + 6*r + 2*d - 76, -3*d = 4*r - 72. Find z, given that 9*z**4 - 21*z**4 - 6 - r*z - 2*z**2 + 21*z**3 + 5*z**2 + 15*z**2 = 0.
-1, -1/4, 1, 2
Let d(q) be the third derivative of q**7/420 + q**6/45 + q**5/12 + q**4/6 + q**3/6 - 2*q**2. Let r(w) be the first derivative of d(w). Factor r(j).
2*(j + 1)**2*(j + 2)
Let v = 11 + -17. Let j be v/15*(-3 - 7). Factor -2*o**4 + o**2 + o**j - o**4 + o**4.
-o**2*(o - 1)*(o + 1)
Let d(n) = 2*n**2 - 3*n + 3. Let z be d(2). Let q(v) be the second derivative of v + 4/5*v**z + 0 - 7/6*v**3 - 2/3*v**4 - 1/2*v**2. Factor q(o).
(o - 1)*(4*o + 1)**2
Let m be (1 + 20/(-8))*-2. Let h(s) be the first derivative of s - 1/3*s**m + 0*s**2 + 1. Factor h(t).
-(t - 1)*(t + 1)
Suppose -9/8*q - 27/8 + 15/8*q**2 - 3/8*q**3 = 0. Calculate q.
-1, 3
Let q(j) = j + 1. Let p = -2 + 5. Suppose -p*u + 0*u = -15. Let l(r) = 2*r**3 + 3*r + 5. Let i(s) = u*q(s) - l(s). Factor i(w).
-2*w*(w - 1)*(w + 1)
Let r(w) be the first derivative of 2*w**3/33 + 2*w**2/11 + 15. Let r(b) = 0. What is b?
-2, 0
Let c(j) be the third derivative of -j**6/300 - j**5/50 + 3*j**4/20 - j**3/3 + 35*j**2. Determine z, given that c(z) = 0.
-5, 1
Let n(s) be the first derivative of -s**5/270 + 3*s**2/2 - 3. Let m(b) be the second derivative of n(b). Suppose m(y) = 0. Calculate y.
0
Let i(w) be the second derivative of -w**5/70 + w**4/42 + w**3/21 - w**2/7 + w. Factor i(k).
-2*(k - 1)**2*(k + 1)/7
Solve -2*k - 1/3*k**2 - 3 = 0.
-3
Let n = 61/52 - 12/13. Find a, given that -n*a**2 - 1/4 + 1/2*a = 0.
1
Let h = 54 + -54. Let w(y) be the third derivative of 0*y + h - 2/15*y**5 + 31/120*y**6 + 0*y**3 - 1/6*y**4 + 1/6*y**7 - 3*y**2. Factor w(i).
i*(i + 1)*(5*i - 2)*(7*i + 2)
Let t(h) be the first derivative of -3*h**4/16 + 5*h**3/4 - 3*h**2 + 3*h + 6. Factor t(k).
-3*(k - 2)**2*(k - 1)/4
Let r(k) be the second derivative of k**4/30 - 2*k**3/15 + 6*k. Solve r(h) = 0.
0, 2
Let a be (4/14)/(108/21). Let v(b) be the first derivative of -1/6*b**2 - 3 + a*b**6 + 2/9*b**3 + 0*b**4 + 0*b - 2/15*b**5. Factor v(g).
g*(g - 1)**3*(g + 1)/3
Let z(o) be the first derivative of -3 - 2*o - o**2 - 1/6*o**3. Solve z(h) = 0.
-2
Let z = -76573/20 - -3831. Let k = 13/5 - z. Factor 1/4*b**5 + 0*b**2 + 0*b**4 + 0*b - k*b**3 + 0.
b**3*(b - 1)*(b + 1)/4
Solve 3/2*i**3 + 0*i**2 - 2*i + 0 - 1/2*i**4 = 0.
-1, 0, 2
Let t(f) be the first derivative of -5*f**6/27 + 34*f**5/45 + 2*f**4/9 - 128*f**3/27 + 64*f**2/9 - 32*f/9 + 29. Solve t(n) = 0.
-2, 2/5, 1, 2
Let d be ((0 - -3)*2)/(-1). Let t be 1 + 3 + 20/d. Suppose 8/3*k - 4*k**2 - t + 8/3*k**3 - 2/3*k**4 = 0. Calculate k.
1
Let x(r) be the first derivative of -r**7/4200 - r**6/1800 + 4*r**3/3 + 1. Let i(b) be the third derivative of x(b). Find v, given that i(v) = 0.
-1, 0
Let v(m) be the third derivative of m**6/6 + m**5/15 - 5*m**4/6 - 2*m**3/3 + m**2. Factor v(a).
4*(a - 1)*(a + 1)*(5*a + 1)
Let y(a) be the first derivative of -a**3/7 - 15*a**2/14 - 18*a/7 + 25. Factor y(f).
-3*(f + 2)*(f + 3)/7
Let l(k) = k**4 - 4*k**3 + 5*k**2 + k + 3. Let a(v) = 0*v + 11 + v**3 - 12 - v**4 - v. Let q(t) = 3*a(t) + l(t). Factor q(u).
-u*(u - 1)*(u + 2)*(2*u - 1)
Let p(y) be the third derivative of y**8/1344 - y**7/168 + 7*y**6/480 + y**5/240 - y**4/12 + y**3/6 - 9*y**2. Deter