1 - 2528/33. Determine l so that 10/3 + 25/3*l + p*l**2 + 5/3*l**3 = 0.
-2, -1
Let n be -3*(6 + (-22)/4)*-2. Let 0*d**2 + 0 + 4/5*d**n - 4/5*d = 0. What is d?
-1, 0, 1
Let -6/11*k**5 - 2/11*k + 0 - 24/11*k**3 - 20/11*k**4 - 12/11*k**2 = 0. Calculate k.
-1, -1/3, 0
Let f = 11958 + -11954. Suppose 0 + 0*m - 2/9*m**f + 2/9*m**3 + 0*m**2 = 0. What is m?
0, 1
Let h(n) be the first derivative of n**6/3 + 11*n**5/5 + 21*n**4/4 + 16*n**3/3 + 2*n**2 + 172. Factor h(p).
p*(p + 1)*(p + 2)**2*(2*p + 1)
Factor 3/8 - 1/4*z - 1/8*z**2.
-(z - 1)*(z + 3)/8
Let h = 113 - 70. Factor 8 - 8*k**2 - h*k**2 + 7*k**2 - 28*k**3 + 48*k**4 - 12*k**4 + 28*k.
4*(k - 1)**2*(k + 1)*(9*k + 2)
Let y(m) be the third derivative of m**8/840 + m**7/140 - m**6/180 - m**5/20 - m**3/3 + 4*m**2. Let k(h) be the first derivative of y(h). Factor k(a).
2*a*(a - 1)*(a + 1)*(a + 3)
Suppose -y + 6 = -7. Let k = -8 + y. Factor 3*p**3 - p**5 - p**k - 7*p**4 + p**4 + 5*p**5.
3*p**3*(p - 1)**2
Let f(y) be the third derivative of y**5/90 + 29*y**4/18 + 841*y**3/9 + 3*y**2. Solve f(k) = 0.
-29
Solve -4/3*l**2 + 1/6*l**4 - 1/6*l**3 + 0 + 2*l = 0.
-3, 0, 2
Suppose -1216 = -791*n + 183*n. Factor -2/15*m**n + 0*m + 0.
-2*m**2/15
Factor -3*q**5 - q**5 - 1002*q**2 + 994*q**2 + 0*q**5 + 12*q**3.
-4*q**2*(q - 1)**2*(q + 2)
Let n = 12722/3 - 4240. Factor 2/3*u**2 + 0*u + 0 + n*u**3.
2*u**2*(u + 1)/3
Factor 2*s**2 + 0*s**3 + 0 + 0*s - 1/2*s**4.
-s**2*(s - 2)*(s + 2)/2
Let o = 125 - 53. Suppose 5*x - 23 - o = 0. Factor -u**2 - 4*u**3 + 15*u + 9*u**2 - x*u.
-4*u*(u - 1)**2
Determine m, given that 156865/2*m - 455/2*m**4 + 52441/2 + 25535*m**3 + 77975*m**2 + 1/2*m**5 = 0.
-1, 229
Let g(i) be the third derivative of -i**6/360 + i**5/18 - 19*i**4/72 - 5*i**3/3 - 6*i**2 - 45*i. Find r such that g(r) = 0.
-1, 5, 6
Let y(p) = -9*p**2 - 25*p + 8. Let k(s) = 17*s**2 + 50*s - 14. Let o(b) = 4*k(b) + 7*y(b). Factor o(q).
5*q*(q + 5)
Let o(k) be the first derivative of k**3/12 + 35*k**2/8 + 92. Determine y so that o(y) = 0.
-35, 0
Suppose 0*j - 3 = -j - 7*c, -2*c + 3 = j. Solve -6/7*q**j + 2/7*q**4 - 2/7*q**2 + 4/7*q + 2/7*q**5 + 0 = 0.
-2, -1, 0, 1
Let g(p) be the second derivative of p**6/40 + p**5/20 + 6*p**2 - 16*p. Let b(m) be the first derivative of g(m). Suppose b(f) = 0. Calculate f.
-1, 0
Let b(g) be the third derivative of -32/3*g**3 - 7*g**2 - 2/105*g**7 + 0*g - 16/3*g**4 - 8/5*g**5 + 0 - 4/15*g**6. Find v such that b(v) = 0.
-2
Factor -7*k**3 - 51*k**2 + 12*k**3 + 31*k**2 + 30*k**2 - 75*k.
5*k*(k - 3)*(k + 5)
Factor -1/7*n**4 - 195/7*n**2 - 169/7*n + 0 - 27/7*n**3.
-n*(n + 1)*(n + 13)**2/7
Let u(p) = -p**4 + 10*p**2 + 8*p - 1. Let n(d) = d**3 + d**2 + d + 1. Let h(j) = -12*n(j) + 3*u(j). Factor h(x).
-3*(x - 1)**2*(x + 1)*(x + 5)
Let u be (-40)/12*(-42)/28. Factor 0*f + 2/5*f**4 - 2/5*f**2 + 0 - 2/5*f**u + 2/5*f**3.
-2*f**2*(f - 1)**2*(f + 1)/5
Let a(t) be the second derivative of 0 + 1/48*t**4 + 0*t**2 - 3/80*t**5 + 21*t + 1/168*t**7 - 1/120*t**6 + 1/12*t**3. Factor a(v).
v*(v - 2)*(v - 1)*(v + 1)**2/4
Let q = -11 + 13. Factor -4*h**3 - h + h**2 + 7*h**q - 12*h**2 + 0*h**2.
-h*(2*h + 1)**2
Let n(d) be the second derivative of -d**7/21 - 2*d**6/15 - d**5/8 - d**4/24 + 2*d + 2. Factor n(r).
-r**2*(r + 1)*(2*r + 1)**2/2
Let b(y) be the second derivative of 1/2*y**3 - 3/20*y**5 - 3/4*y**4 - 34*y + 0 + 9/2*y**2. Suppose b(u) = 0. What is u?
-3, -1, 1
Let x = 7 - 3. Suppose 0 = 3*y - x*u - 35, -y - 5*u - 12 = 8. Let 2*j + 40 - 40 - 5*j + 6*j**3 - 3*j**y = 0. Calculate j.
-1, 0, 1
Let l(m) be the first derivative of m**8/336 - m**7/105 - m**6/40 + 23*m**2/2 - 21. Let x(t) be the second derivative of l(t). Factor x(p).
p**3*(p - 3)*(p + 1)
Suppose -322*l**2 - 2*l + 96 + 302*l**2 + 136*l + 141*l - 43*l = 0. Calculate l.
-2/5, 12
Let q(m) = 12*m - 3*m - 10*m. Let h(g) = g**3 + 10*g**2 + 32*g. Let o(v) = 2*h(v) + 14*q(v). Determine x, given that o(x) = 0.
-5, 0
Solve 16/7*r**4 - 92/7*r**3 + 24/7 + 92/7*r - 40/7*r**2 = 0 for r.
-1, -1/4, 1, 6
Let g(d) be the first derivative of -d**3 - 138*d**2 - 6348*d + 184. Factor g(h).
-3*(h + 46)**2
Let -2*u**4 - u**4 + 23 + 12*u**3 - 12*u**2 + 0*u**3 - 23 = 0. Calculate u.
0, 2
Factor 851*a - 3*a**2 - 156 + 823*a - 1833*a.
-3*(a + 1)*(a + 52)
Let u = -9 - -3. Let v(h) = h**2 + 8*h + 15. Let i be v(u). Suppose 0 + 0*n + 2/5*n**2 - 2/5*n**i = 0. What is n?
0, 1
Determine s, given that 4*s**3 - 4 + 4*s**2 + 45*s - 49*s + 0*s**3 = 0.
-1, 1
Let z be 6 + (2/(-1) - -1). Suppose z*y - 6 = 2*y. Find n such that -20*n**y + 3 + 1 + 1 - 35*n + 5 = 0.
-2, 1/4
Let f(c) be the second derivative of -c + 0*c**3 + 0*c**2 + 1/36*c**4 + 39. Suppose f(q) = 0. What is q?
0
Let h(m) be the first derivative of m**6/2 + 9*m**5/20 - m**4/2 - 9*m - 8. Let k(v) be the first derivative of h(v). Factor k(q).
3*q**2*(q + 1)*(5*q - 2)
Let c(i) be the first derivative of i**3/9 - 5*i**2/6 - 14*i/3 + 4. Factor c(o).
(o - 7)*(o + 2)/3
Let q(a) be the third derivative of -a**8/1512 - 2*a**7/315 + 4*a**6/45 - 37*a**5/135 + 11*a**4/36 + 2*a**2 - 76. Find f, given that q(f) = 0.
-11, 0, 1, 3
Let -210*h + 14*h**2 + 2205 - 5*h**2 - 4*h**2 = 0. Calculate h.
21
Let g(q) be the second derivative of 0 - 1/140*q**5 + 1/42*q**3 - 20*q + 1/84*q**4 - 1/14*q**2. Determine r, given that g(r) = 0.
-1, 1
Let g(c) be the second derivative of -c**4/78 + 16*c**3/39 - 15*c**2/13 - 2*c - 11. Factor g(x).
-2*(x - 15)*(x - 1)/13
Suppose 18 = 25*p - 19*p. Factor 19*t + p*t**5 + 24*t**4 - 68*t + 25*t - 57*t + 54*t**3.
3*t*(t - 1)*(t + 3)**3
Let m = -65 + 53. Let n be m/1*3/(-12). Solve -2/7*a**n - 2/7*a**4 + 0 + 2/7*a + 2/7*a**2 = 0.
-1, 0, 1
Let -173552*l**2 + 173552*l**2 - 3*l**3 + 21*l - 18 = 0. What is l?
-3, 1, 2
Let j = -9 + 13. Suppose s = -j*f + 15, -4*f - s - 2*s = -13. Factor 8*l**2 + 4*l**3 + l**4 - l + l - 5*l**f.
-4*l**2*(l - 2)*(l + 1)
Let c(l) = -l**3 - l**2 - l + 3. Let b be c(0). What is t in -4*t**5 + t**4 + 0*t**b + 3*t**4 + 4*t**3 - 4*t**2 = 0?
-1, 0, 1
Solve 8*k**2 + 4/3*k**5 + 0 - 2*k**4 - 8/3*k - 14/3*k**3 = 0 for k.
-2, 0, 1/2, 1, 2
Suppose -o - 3 = 5. Let i(p) = -11*p**2 + 5*p + 8. Let n(v) = 7*v**2 - 3*v - 5. Let j be (-1)/(3*(-2)/(-30)). Let g(x) = j*i(x) + o*n(x). Factor g(u).
-u*(u + 1)
Let w be (-630)/49*(-7 + 0). Let f = w - 48. Factor -3*n**2 + f*n - 2 - 1 - 48*n.
-3*(n + 1)**2
Suppose 4 - 2 = -2*i. Let u(c) = 25*c**4 + 36*c**3 - 23*c**2 - 36*c - 11. Let x(w) = w**4 + w**2 + 1. Let y(t) = i*u(t) - 3*x(t). Find r, given that y(r) = 0.
-1, -2/7, 1
Find v such that 35/6*v + 37/3 - 1/6*v**2 = 0.
-2, 37
Suppose -2*d + 3*d = -1. Let v be 4*d*(-4)/8. Determine k, given that -k**2 + 34*k + 4*k**v - 37*k = 0.
0, 1
Let u(r) be the second derivative of -r**8/112 + r**7/35 - 17*r**2/2 - 15*r. Let q(f) be the first derivative of u(f). Factor q(y).
-3*y**4*(y - 2)
Let h(a) be the second derivative of a**6/195 - a**5/65 - 3*a**4/26 + 2*a**3/39 + 8*a**2/13 + 258*a. Let h(s) = 0. What is s?
-2, -1, 1, 4
Let g = 185 + -170. Suppose -2*w = g*w - 68. Factor -8/3*x + 0 + 20/3*x**w - 12*x**3 + 28/3*x**2 - 4/3*x**5.
-4*x*(x - 2)*(x - 1)**3/3
Let d(t) = -2 + 5*t**2 - 2 - 1 - 2 + 2*t. Let h(f) be the first derivative of 2*f**3 + f**2 - 8*f + 1. Let w(l) = -4*d(l) + 3*h(l). What is x in w(x) = 0?
-2, 1
Let f = 29 - 14. Suppose 5*a - 6 = -2*n, -2*a = -5*n - 5*a + f. Factor -4 + m - 5*m + 4*m**2 - 18*m**n + 22*m**3.
4*(m - 1)*(m + 1)**2
Factor 11/3*l**5 - 56/3*l**2 - 2/3 + 19/3*l + 74/3*l**3 - 46/3*l**4.
(l - 1)**4*(11*l - 2)/3
Let m = 1914 - 1910. Factor 2/13*d**5 + 4/13*d**m + 0 - 2/13*d + 0*d**3 - 4/13*d**2.
2*d*(d - 1)*(d + 1)**3/13
Let r be 56/(-21)*(-63)/(-6). Let u be r/(-494) + (48/104)/3. Let 2/19*m + 0*m**4 - u*m**3 + 2/19*m**5 + 0 + 0*m**2 = 0. Calculate m.
-1, 0, 1
Let f(l) = -5*l**2 + 4*l - 11. Let g(m) be the second derivative of -m**4/3 + m**3 - 5*m**2 + 2*m - 3. Let y(x) = -2*f(x) + 3*g(x). Suppose y(a) = 0. What is a?
1, 4
Let x(b) be the first derivative of 1/8*b**4 - 2 - 2/15*b**5 - 1/3*b**2 + 1/36*b**6 + 0*b + 2/9*b**3. Determine q so that x(q) = 0.
-1, 0, 1, 2
Let m(s) be the third derivative of s**3/6 - 5*s**2. Let c(v) = -3*v**2 + 7. Let x(b) = c(b) - 4*m(b). Factor x(h).
-3*(h - 1)*(h + 1)
Let y(z) be the second derivative of -z**7/273 + 47*z**6/195 + z**5/65 - 47*z**4/39 - z**3/39 + 47*z**2/13 - 425*z. Sup