Let i(l) be the third derivative of -1/2*l**3 + 1/32*l**4 + 0*l + 3/80*l**5 + 5*l**2 + 0. Determine j so that i(j) = 0.
-4/3, 1
Let a(w) be the third derivative of w**7/210 - 3*w**6/10 + 179*w**5/30 - 51*w**4/2 + 289*w**3/6 + 21*w**2 + w. Suppose a(y) = 0. What is y?
1, 17
Let l(m) = -16*m - 13. Let k be l(-1). Let o(u) be the first derivative of 2/3*u**k + 4*u + 3*u**2 + 4. Factor o(c).
2*(c + 1)*(c + 2)
Let s be (11 + -10)*0*(-1)/(-2). Suppose 10 = -2*p - w + 16, 0 = 2*p - 5*w - 18. Determine c so that 1/2*c**3 + p*c**5 + 0 + 1/2*c**2 + s*c - 5*c**4 = 0.
-1/4, 0, 1/2, 1
Let i(g) = 11*g**2 + 182*g - 1961. Let c(p) = 4*p**2 + 60*p - 654. Let t(h) = -17*c(h) + 6*i(h). Suppose t(f) = 0. What is f?
18
Suppose -2*a - 2*o - 120 = -128, o = -3*a + 10. Determine p, given that 4/7*p**5 + 24/7*p**2 - 8/7*p**a + 4/7*p - 12/7 - 12/7*p**4 = 0.
-1, 1, 3
Let f(n) = n**4 - 21*n**3 + 28*n**2 - 18*n + 1. Let q(z) = 3*z**4 - 41*z**3 + 56*z**2 - 36*z + 3. Let v(o) = 5*f(o) - 3*q(o). Let v(c) = 0. Calculate c.
1/2, 1, 2
Suppose 0 = b - 9*b + 40. Let y(p) be the third derivative of 1/300*p**5 - 1/40*p**4 + 0 - b*p**2 + 1/15*p**3 + 0*p. Let y(t) = 0. Calculate t.
1, 2
Solve -22*y + 2*y**3 - 200/7*y**2 + 60/7 = 0 for y.
-1, 2/7, 15
Let t(l) be the third derivative of -l**5/60 + 7*l**4/24 - 2*l**3 - 433*l**2. Factor t(m).
-(m - 4)*(m - 3)
Let x(p) = p**4 + 5*p**3 - 9*p**2 + 6*p - 3. Let n(q) = -3*q**4 - 15*q**3 + 26*q**2 - 16*q + 8. Let h(j) = 3*n(j) + 8*x(j). Factor h(g).
-g**2*(g - 1)*(g + 6)
Let x be (-2)/7 - (-1181)/140. Let g = x - 31/4. What is v in -g*v**2 - 4/5 + 6/5*v = 0?
1, 2
Let l be 8/(-1) - 6/(-2). Let q be 5 - -2 - (-2 - l). Suppose q + 2*g - 8*g + 14*g**3 - 12*g**3 = 0. What is g?
-2, 1
Let s(q) be the first derivative of -1/12*q**4 - 1/18*q**3 - 1/30*q**5 + 0*q - 14 + 0*q**2. Find d, given that s(d) = 0.
-1, 0
Factor -121*o + 5*o**3 + 120*o - 216 - 2*o**3 + 172*o - 42*o**2.
3*(o - 8)*(o - 3)**2
Let a(r) = -10*r**4 - 10*r**3 - 4*r - 4. Let s(q) = q**4 - q**2 + q + 1. Let w(k) = -a(k) - 4*s(k). Factor w(n).
2*n**2*(n + 1)*(3*n + 2)
Find z, given that -16 + 20*z**3 + 220/3*z**2 - 28/3*z**5 - 92/3*z**4 - 112/3*z = 0.
-3, -2, -2/7, 1
Let b(p) be the second derivative of -p**4/48 - 7*p**3/24 - 3*p**2/4 - 43*p. Factor b(d).
-(d + 1)*(d + 6)/4
Suppose 2*n - 4*p + 17 = -99, 3*n + 154 = -4*p. Let k = -52 - n. Solve 1/4*w + 1/4*w**k + 0 = 0 for w.
-1, 0
Let k = 199 + -191. Suppose k*n = 18*n - 20. Factor 2*w + 2 + 1/2*w**n.
(w + 2)**2/2
Let u(o) be the second derivative of o**6/540 + o**5/10 + 9*o**4/4 - 37*o**3/6 - 23*o. Let a(r) be the second derivative of u(r). Factor a(f).
2*(f + 9)**2/3
Suppose 0 = 4*q + 12, 432 = 2*s - s - 5*q. Suppose s - 5 = 4*g. Find u, given that 99*u - 5*u**3 - g*u + 8*u**2 + u**3 = 0.
0, 1
Let o be (1 - (-3)/(36/(-14))) + 23837/1182. Suppose -12 - 25/3*s**2 + o*s = 0. What is s?
6/5
Let h be 5*3/105 + (-250)/(-14). Let g be (28/3)/((-1)/(-3)). Factor -g*l - 19*l - 11*l - 80 + h*l - 5*l**2.
-5*(l + 4)**2
Let g(c) = -c**5 + c**4 - c**3 + c + 1. Let f(y) = y**5 + 2*y**4 + 25*y**3 - 162*y**2 + 322*y - 218. Let s(z) = -f(z) - 2*g(z). Factor s(d).
(d - 3)**2*(d - 2)**2*(d + 6)
Suppose -3*o = 2*b - 13, b = -0*b + 5. Let s be (-12)/(-27)*o/2. Solve 4/9*m**2 - s*m + 0 - 2/9*m**3 = 0 for m.
0, 1
Let q(p) be the third derivative of p**6/60 - 3*p**5/10 + 9*p**4/4 - 9*p**3 + 16*p**2 + 6*p. Suppose q(d) = 0. What is d?
3
Let t(x) be the second derivative of x**8/2240 + x**7/1680 - x**6/480 + 37*x**4/12 - x. Let z(h) be the third derivative of t(h). Factor z(c).
3*c*(c + 1)*(2*c - 1)/2
Suppose -6 = -3*y, 0*s = s - y - 5. Determine p, given that -7 + s + 6*p + 2*p**2 + 0*p**2 = 0.
-3, 0
Solve f**3 + 23*f**3 - 24*f - 3*f**3 - 3*f**3 - 14*f**4 + 80*f**2 = 0 for f.
-2, 0, 2/7, 3
Determine d so that -7/4*d**3 - 5/4*d - 3/2 + 9/2*d**2 = 0.
-3/7, 1, 2
Factor -5*p**4 - 359*p**5 - 196*p**2 + 358*p**5 + 7*p**3 + 15*p**4.
-p**2*(p - 7)**2*(p + 4)
Let k(r) be the second derivative of -1/6*r**2 + 1/12*r**4 + 0 + 1/9*r**3 + 21*r. Let k(x) = 0. What is x?
-1, 1/3
Let v(o) = -3*o. Suppose 5*j + 19 = -41. Let r be 33/9 - 4/j. Let c(i) = -i**3 + i**2 + 4*i. Let y(g) = r*v(g) + 3*c(g). Factor y(t).
-3*t**2*(t - 1)
Let p be (120/(-27))/((-6)/18*6). Factor -p*z - 2/3*z**2 - 2/3.
-2*(z + 3)*(3*z + 1)/9
Factor -7/2*a**3 + 1/2*a**5 + 3*a + 0 + 5/2*a**4 - 5/2*a**2.
a*(a - 1)**2*(a + 1)*(a + 6)/2
Let s = -8813 + 8817. Factor 4/11*k**3 - 2/11*k**s + 0*k**2 + 0 + 0*k.
-2*k**3*(k - 2)/11
Let m(c) be the second derivative of -3*c**6/280 + c**5/70 - 13*c**2/2 + 4*c. Let s(y) be the first derivative of m(y). Factor s(o).
-3*o**2*(3*o - 2)/7
Solve 1/5*l**4 + 28/5*l**2 - 9/5*l**3 - 36/5*l + 16/5 = 0.
1, 2, 4
Let b(o) be the third derivative of 0*o + 2/15*o**5 + 0*o**7 + 22*o**2 + 1/10*o**6 + 0 + 0*o**3 + 0*o**4 - 1/84*o**8. Solve b(r) = 0.
-1, 0, 2
Suppose 7*d - 467 + 103 = 0. Let t = d - 155/3. Let 2/3*v + 0 + t*v**2 = 0. Calculate v.
-2, 0
Let n be 19803/(-165) + (6/10)/3. Let i = 120 + n. Determine h so that -2/11*h + 0*h**2 + i*h**3 + 0 = 0.
-1, 0, 1
Let i(s) be the second derivative of s**8/16800 - s**7/1575 + s**6/360 - s**5/150 - 5*s**4/6 - 2*s. Let d(q) be the third derivative of i(q). Factor d(g).
2*(g - 2)*(g - 1)**2/5
Let b(r) = -r**2 + 4*r + 25. Let q be b(7). Factor 6 - 19*o + 35*o + o**2 - q*o**2 - 13*o.
-3*(o - 2)*(o + 1)
Let q be ((-8)/2)/((-2)/1). Suppose q + 6 = 2*m. Factor m*o**2 + 2 + 3*o**2 - 21*o - 20 + 2*o**2.
3*(o - 3)*(3*o + 2)
Let h(v) = v + 6. Let p be (1 + 1)*(-15)/6. Let t be h(p). Factor 21*m + 21*m**2 + 9 - t + 6*m**3 - 2.
3*(m + 1)*(m + 2)*(2*m + 1)
Factor 3/2*w**4 + 759/2*w**2 + 486 + 918*w - 51*w**3.
3*(w - 18)**2*(w + 1)**2/2
Let n(f) = -5*f**3 - 4*f**2 + 12*f + 12. Let u(q) = -4*q**3 - 2*q**2 + 12*q + 15. Let g(s) = -5*n(s) + 4*u(s). Find l such that g(l) = 0.
-2, 0, 2/3
Let s(h) be the first derivative of -h**4/4 - 2*h**3 + h**2/2 + 6*h + 3. Let t be s(-6). Factor t*l**2 + 2*l**2 + 0*l**2.
2*l**2
Suppose 0 = 2*x + 12, -x = -c - 0 + 8. Find b, given that 6/7*b**3 + 12/7*b**5 + 3*b**4 + 0 - 3/7*b**c + 0*b = 0.
-1, 0, 1/4
Suppose -8*y + 2*y + 204 = 0. Suppose u + 34 = y. Factor 0 + 0*p**2 - 7/3*p**4 + u*p - 2/3*p**3.
-p**3*(7*p + 2)/3
Let n(i) be the first derivative of -6*i**5/5 + i**4/2 + 6*i**3 + 3*i**2 - 4*i - 137. Find w such that n(w) = 0.
-1, 1/3, 2
What is t in 0 - 2/19*t + 4/19*t**2 + 0*t**3 - 4/19*t**4 + 2/19*t**5 = 0?
-1, 0, 1
Suppose -1 = 4*j + 3, 4*j = -2*q + 28. What is v in -q*v + 24*v**2 - 2*v - 1 - 10*v**2 + 5 = 0?
2/7, 1
Solve -2*s + 56/3 + 2/3*s**4 - 58/3*s**2 + 2*s**3 = 0.
-7, -1, 1, 4
Let d(r) be the second derivative of 5*r**4/66 - 18*r**3/11 - r**2 - 13*r + 8. Solve d(q) = 0.
-1/5, 11
Let t be (-2 + 32/21)*15*22/(-550). Factor 8/7*w**5 + 0*w + 2*w**4 - t*w**2 + 4/7*w**3 + 0.
2*w**2*(w + 1)**2*(4*w - 1)/7
Let u = -41726 + 542462/13. Factor 8/13*o - 14/13*o**2 + 2/13*o**3 + u.
2*(o - 6)*(o - 2)*(o + 1)/13
Let w be 7/2 - (170/20 - 8). Let g(j) be the third derivative of 0*j**4 + 0*j + w*j**2 + 0 - 1/30*j**5 + 0*j**3 + 1/60*j**6. Factor g(c).
2*c**2*(c - 1)
Find d, given that -3 - 3/2*d + 3/2*d**3 + 3*d**2 = 0.
-2, -1, 1
Let g(k) be the first derivative of -3*k**4/4 + k**3 + 6*k**2 - 12*k - 29. Factor g(q).
-3*(q - 2)*(q - 1)*(q + 2)
Let g = 14 - 12. Suppose -b - g*b = -6. Find a such that -2*a**2 - 2*a + b*a**3 - 3*a + 3*a + 2*a**4 = 0.
-1, 0, 1
Let g be 1/(-2) + 24/(-80)*-5. What is d in 2/3*d - g - 1/9*d**2 = 0?
3
Factor 105*r**3 + 5/3*r**4 + 2300*r**2 + 58000/3*r + 40000.
5*(r + 3)*(r + 20)**3/3
Determine q, given that 15*q**2 + 60*q + 60*q**3 - 25*q**3 + 48*q**2 - 32*q**3 = 0.
-20, -1, 0
Let a = -37 - -41. Let t(f) be the first derivative of -1/3*f**2 + 3 + 0*f + 1/3*f**3 - 1/5*f**5 + 1/6*f**a. Determine j so that t(j) = 0.
-1, 0, 2/3, 1
Let l be (1 - (1 + -3)) + -1. Let m be -4 + (l - 3/(9/(-6))). Factor m*y**2 + 1/3*y**5 - 2/3*y**4 + 1/3*y**3 + 0 + 0*y.
y**3*(y - 1)**2/3
Suppose -15 = -r - 6. Suppose r*t = 10*t - 4. Factor -t*o**3 - 2 - 2*o**2 + 4*o**2 + 4*o + 6 - 6*o**2.
-4*(o - 1)*(o + 1)**2
Factor -5*y**4 + 150*y**2 - 5*y**3 - 150*y**2.
-5*y**3*(y + 1)
Let f(m) be the third derivative of 16*m**9/945 + 4*m**8/175 + 2*m**7/175 + m**6/450 + 4*m**3/3 - m**2. Let y(i) be the first derivative of f(i). Factor y(s).
4*s**