 -a**5/180 + a**4/36 + a**3/6 - 7*a**2/2 + 3*a. Let w(k) be the first derivative of h(k). Determine r, given that w(r) = 0.
-1, 3
Let a(l) be the second derivative of 5*l**4/12 - 10*l**3/3 + 6*l. Find s, given that a(s) = 0.
0, 4
Let q(d) be the first derivative of d**4/8 - 2*d**3/3 + 3*d**2/4 - 20. Factor q(u).
u*(u - 3)*(u - 1)/2
Let f(n) be the third derivative of -n**6/660 + n**4/132 + 8*n**2. Solve f(h) = 0 for h.
-1, 0, 1
Let n(v) be the third derivative of -v**5/15 + v**4/6 + 4*v**3/3 - 23*v**2. Factor n(p).
-4*(p - 2)*(p + 1)
Let q be 1230/(-1107)*(-6)/5. Factor 0*o**4 - 1/3*o**2 + 0*o + q*o**5 + 0 - o**3.
o**2*(o - 1)*(2*o + 1)**2/3
Let v(i) be the third derivative of -i**8/3696 + 2*i**7/1155 - i**6/264 + i**5/330 + 57*i**2. Suppose v(n) = 0. Calculate n.
0, 1, 2
Let n(i) = i**2 + 3*i - 4. Let l be n(-4). Suppose -3*f - 2 - 4 = 0, l = -5*s + 5*f + 20. Suppose 2*j + 3*j**2 - 2 + 1 + 0*j**s = 0. What is j?
-1, 1/3
Let h = 4/5 + -19/30. Let -h*r**3 + 1/6*r + 0*r**2 + 0 = 0. Calculate r.
-1, 0, 1
Suppose 334*n = 333*n. Factor n*r**2 + 0 - 1/4*r + 1/4*r**3.
r*(r - 1)*(r + 1)/4
Let z(v) be the third derivative of -v**8/840 + v**7/525 + v**6/300 - v**5/150 + 11*v**2. Factor z(r).
-2*r**2*(r - 1)**2*(r + 1)/5
Let z(j) be the third derivative of -j**6/120 + j**3/6 + 2*j**2. Let g(p) = 8*p**3 + 2*p**2 + p - 7. Let d(q) = -2*g(q) - 14*z(q). Factor d(h).
-2*h*(h + 1)**2
Let p(q) be the first derivative of -q**5/180 - q**4/36 - q**3/18 - q**2 + 3. Let l(n) be the second derivative of p(n). Solve l(k) = 0 for k.
-1
Let d be (17/(-459))/((-4)/6). Let j(x) be the second derivative of 1/30*x**5 - 1/9*x**3 - x + d*x**4 + 0 - 1/3*x**2. Determine z so that j(z) = 0.
-1, 1
Let k(c) be the third derivative of -c**6/360 - c**5/60 - c**4/36 - 6*c**2. Factor k(t).
-t*(t + 1)*(t + 2)/3
Factor -3/2 - a + 1/2*a**2.
(a - 3)*(a + 1)/2
Suppose 5*o + x = 13, o - 3*x = 10 - 1. What is j in 14/3*j**2 - 4/3*j + 4/3*j**o - 14/3*j**4 + 0 = 0?
-1, 0, 2/7, 1
Factor 0*l + 0 - 4/5*l**2.
-4*l**2/5
Let d = -117 - -235/2. Let -d*p**2 + p - 1/2 = 0. What is p?
1
Suppose -3*a = -3*c - 5*a, 0 = 5*a + 15. Let g(w) = -4*w**3 - 3*w + 2. Let x(s) = s**3. Let q be (-4)/6 - 32/(-3). Let h(k) = c*g(k) + q*x(k). Factor h(f).
2*(f - 1)**2*(f + 2)
Let k(h) be the second derivative of -h**7/840 + h**6/120 - h**5/40 + h**4/24 + h**3/3 - h. Let o(a) be the second derivative of k(a). Factor o(n).
-(n - 1)**3
Factor 2/3*s + 0 + 2/9*s**3 - 8/9*s**2.
2*s*(s - 3)*(s - 1)/9
Factor 4/9*d**2 + 0*d - 2/9*d**3 + 0.
-2*d**2*(d - 2)/9
Find y such that -3/8*y + 1/4 + 1/8*y**2 = 0.
1, 2
Let i(w) = -w + 2. Let g = -9 + 9. Let o be i(g). Determine l, given that -1/2 + 0*l + 1/2*l**o = 0.
-1, 1
Let i(n) be the first derivative of n**7/560 + n**6/720 - n**5/120 - 2*n**3/3 + 2. Let j(p) be the third derivative of i(p). Determine v, given that j(v) = 0.
-1, 0, 2/3
Let b(g) be the first derivative of 1/30*g**4 + 1/5*g**3 - 3*g - 2 + 2/5*g**2. Let m(f) be the first derivative of b(f). Factor m(c).
2*(c + 1)*(c + 2)/5
Let c(m) be the first derivative of 2*m**6/3 + 16*m**5/5 + 6*m**4 + 16*m**3/3 + 2*m**2 - 26. Factor c(w).
4*w*(w + 1)**4
Let l = 12 + -10. Solve f**5 + f**5 - f**5 - l*f**5 = 0 for f.
0
Let h be (-5 + 5/2)*(-6)/5. Determine j so that -2/5*j**4 + 0*j + 0 + 0*j**h + 2/5*j**2 = 0.
-1, 0, 1
Let k = -214/3 + 72. Let s(x) be the first derivative of -4*x + 1 + k*x**3 - x**2. Factor s(t).
2*(t - 2)*(t + 1)
Let j(t) = -t**3 + 5*t**2 + 13*t + 2. Let m(q) = q**3 + q**2 - q. Let g(o) = j(o) + 5*m(o). Factor g(x).
2*(x + 1)**2*(2*x + 1)
Let o(q) be the second derivative of q**4/4 - 12*q**3 + 216*q**2 + 14*q. Determine d so that o(d) = 0.
12
Let x be 1 + (0 - -1) + -8. Let k(w) = 6*w**3 + 11*w**2 + 11*w + 6. Let b(d) = 1 - 2*d + 3*d + d**3 + d + 2*d**2. Let i(a) = x*k(a) + 34*b(a). Solve i(n) = 0.
-1, 1
Let j(q) = -q**4 - q**3 - q. Let y(a) = 7*a**4 + 11*a**3 + 2*a**2 - a - 4. Let d(g) = -5*j(g) - y(g). Find x such that d(x) = 0.
-2, -1, 1
Determine h, given that -1/3*h**2 + 2/3*h + 8/3 = 0.
-2, 4
Let o(n) = -2*n - 8. Let c be o(-5). Let v(t) be the first derivative of 4*t**2 - 8*t - 2/3*t**3 - c. Let v(a) = 0. What is a?
2
Suppose 29 = 5*u + l, 3*l = 5*l - 8. Factor -6*z**3 + 3*z**5 - 3 - 3*z**4 - 2*z**2 + u*z**2 + 3*z**2 + 3*z + 0*z**5.
3*(z - 1)**3*(z + 1)**2
Factor 4*q**2 + 0*q**2 - q + 6*q - 7*q - 2*q**3.
-2*q*(q - 1)**2
Let s(v) = -v**2 - v - 1. Let z(p) = -6*p**2 - 9*p - 7. Let b(c) = 14*s(c) - 2*z(c). Let b(h) = 0. What is h?
0, 2
Let x be 1 + 2/(-1) + 3. Let 10 - 5 - 16*f + x*f**2 + 27 = 0. What is f?
4
Find h, given that -36/5*h**2 - 6 - 3/5*h**3 - 63/5*h = 0.
-10, -1
Let j(p) be the second derivative of p**5/60 - 2*p**3/9 + 2*p - 1. Suppose j(t) = 0. What is t?
-2, 0, 2
Let g(s) = 7*s - 89. Let z be g(13). Factor 3 - 3/2*f - 3/2*f**z.
-3*(f - 1)*(f + 2)/2
Solve 1/3*g**2 + 0 - g = 0.
0, 3
Let q be (-12)/(-6) - (0 - -1). Suppose -1 = -0*k - k, 0 = 5*r - k + q. Determine j, given that 0*j**2 + 2/5*j**3 + 2/5*j**5 - 4/5*j**4 + r*j + 0 = 0.
0, 1
Let h = 11 + -8. Factor -x**2 + x**4 - x**5 + 9*x**3 + 2*x**5 - 10*x**h.
x**2*(x - 1)*(x + 1)**2
Let l(n) = 59*n**5 + 181*n**4 + 113*n**3 + 25*n**2 + 7*n + 5. Let j(m) = -m**5 + m**4 + m**3 + m + 1. Let r(z) = -20*j(z) + 4*l(z). Factor r(s).
4*s*(s + 2)*(4*s + 1)**3
Suppose -90 = 11*d - 90. Find n such that d*n - 2/7*n**2 + 0 - 2/7*n**3 = 0.
-1, 0
Find o, given that 4*o**2 + 5*o**3 + 4*o**5 + 12*o**4 - 2*o**3 + 9*o**3 = 0.
-1, 0
Let v(o) be the third derivative of o**7/525 + o**6/60 - o**5/25 + 15*o**2. Factor v(d).
2*d**2*(d - 1)*(d + 6)/5
Let 8*m - 5*m**2 + 2*m**4 - 23*m - 7*m**4 - 16 + 15*m**3 + 26 = 0. Calculate m.
-1, 1, 2
Let f(b) be the third derivative of 0*b**3 - 1/70*b**7 + 0*b + 10*b**2 + 1/40*b**6 + 0 - 1/60*b**5 + 0*b**4 + 1/336*b**8. Find s such that f(s) = 0.
0, 1
Let k(j) = -j**3 - j + 3*j + 2*j**3 - 3*j. Let p(t) = 4*t**3 - 3*t**2 - 8*t - 1. Let l(i) = -5*k(i) + p(i). Factor l(g).
-(g + 1)**3
Let m(j) = j**2 + 6*j + 4. Let d be m(-6). Suppose n + 10 = 5*a - 8, d*a = -n + 18. Let 2/9 - 2/9*x**4 - 4/9*x + 0*x**n + 4/9*x**3 = 0. What is x?
-1, 1
Let f(r) be the third derivative of r**5/180 + r**4/18 + 5*r**2. Factor f(z).
z*(z + 4)/3
Solve -2/7*b**4 + 16/7*b + 0 - 24/7*b**2 + 12/7*b**3 = 0.
0, 2
Suppose -2/5*x**2 + 19/5*x - 9/5 = 0. What is x?
1/2, 9
Let k(w) be the second derivative of -w**4/12 + w**3/3 - w**2/2 + 19*w. Factor k(t).
-(t - 1)**2
Let a be 6/15 + 2/(-5). Factor -1/2*d**2 + 1/2*d + 1/2*d**4 + a - 1/2*d**3.
d*(d - 1)**2*(d + 1)/2
Let c(d) be the third derivative of 0*d + 3/80*d**6 + 0 + 0*d**3 - d**2 - 1/140*d**7 + 1/16*d**4 - 3/40*d**5. Suppose c(l) = 0. Calculate l.
0, 1
Suppose 6*z - 2 + 31*z**2 - 3*z**4 + 2 - 6*z**3 - 28*z**2 = 0. What is z?
-2, -1, 0, 1
Let d(s) = s - 2. Let o be d(2). Let y = 82 - 78. Find a, given that -2/5*a - 6/5*a**3 + 6/5*a**2 + o + 2/5*a**y = 0.
0, 1
Let b be 350/56 - ((-14)/8 - -2). Let a(x) be the first derivative of 2 - 1/7*x**2 + 0*x - 1/21*x**b + 0*x**5 + 0*x**3 + 1/7*x**4. Factor a(n).
-2*n*(n - 1)**2*(n + 1)**2/7
Let o be 10*1*(2 + 39/(-26)). Solve 0 - 2*k**o + 11/2*k**4 + 0*k - 5/2*k**3 - k**2 = 0 for k.
-1/4, 0, 1, 2
Determine m so that 34*m + 512 - 147*m - 79*m + 24*m**2 - 2*m**3 + m**3 = 0.
8
Let g(u) be the third derivative of -u**6/200 + u**5/100 + u**4/20 + 38*u**2. Factor g(k).
-3*k*(k - 2)*(k + 1)/5
Let v(s) = 10*s + 1. Let q be v(-1). Let y = q + 11. Solve -1/2*c - c**y - 1/2*c**3 + 0 = 0 for c.
-1, 0
Let k(d) be the second derivative of d**5/140 + 11*d**4/84 + 4*d**3/7 - 18*d**2/7 - 17*d. Factor k(y).
(y - 1)*(y + 6)**2/7
Let p be (-40)/12*(-6)/2. Factor k**5 - 3*k**5 - 6*k**2 + 4*k**5 + p*k**2 - 2*k - 4*k**4.
2*k*(k - 1)**3*(k + 1)
Suppose 2*b + 3*p - 7 = 15, 3*p = 5*b - 13. Factor 11*h + 15*h + 6 + 3*h**3 + 3 + 15*h**2 - b*h.
3*(h + 1)**2*(h + 3)
Let d(o) = o**3 + 2*o**2 - 4*o - 1. Let f be d(-3). Solve -v**4 - 3*v**3 + v**3 - f*v**2 - v**4 + 6*v**3 = 0 for v.
0, 1
Let l be 2/12 + 34/12. Let p(x) be the third derivative of 1/240*x**6 + 0 + 0*x**l + 0*x**4 + 0*x**5 - x**2 - 1/210*x**7 + 0*x + 1/672*x**8. Factor p(s).
s**3*(s - 1)**2/2
Let d(w) = -w**3 - 11*w**2 - 29*w - 2. Let z be d(-7). Determine k, given that 2/9*k**3 + 0*k**4 + 0*k + 0*k**2 - 2/9*k**z + 0 = 0.
-1, 0, 1
Let p = -35 + 37.