*b + 1. Let s(f) be the first derivative of k(f). Suppose s(x) = 0. What is x?
-1, 0
Suppose -4*m = -9 + 1. Let l(f) be the second derivative of 0 - m*f + 0*f**3 - 1/24*f**4 + 1/4*f**2. Factor l(x).
-(x - 1)*(x + 1)/2
Suppose 4*d + 18 = 5*w, 2*w - 4*w + 6 = -d. Let k be w*8/20*5. Determine c, given that 0*c + 1/3*c**3 - 1/6*c**2 - 1/6*c**k + 0 = 0.
0, 1
Let l(h) be the third derivative of 1/24*h**4 + 0*h**3 + 0 + 1/120*h**5 - 4*h**2 + 0*h. Let l(f) = 0. What is f?
-2, 0
Let u(o) be the second derivative of -1/6*o**6 + 1/42*o**7 + 9/20*o**5 + 1/3*o**3 + 0 - 7/12*o**4 + 4*o + 0*o**2. Find z, given that u(z) = 0.
0, 1, 2
Let b(j) be the third derivative of 0*j**3 + 0*j - 8*j**2 - 1/140*j**7 + 0 + 0*j**4 - 1/672*j**8 - 1/120*j**5 - 1/80*j**6. Find t, given that b(t) = 0.
-1, 0
Let d(v) = -15*v - 6. Let f be d(-7). Let o be (f/55)/((-4)/(-5)). Factor -o*b**3 - 1/2*b**2 + 0*b - 7/4*b**4 + 0.
-b**2*(b + 1)*(7*b + 2)/4
Let y(c) be the second derivative of c**5/20 + 5*c**4/12 + 7*c**3/6 + 3*c**2/2 - 2*c. Factor y(b).
(b + 1)**2*(b + 3)
Let o(v) be the first derivative of v**5/210 + v**4/84 - 2*v**3/21 - v**2/2 - 8. Let d(r) be the second derivative of o(r). Find f, given that d(f) = 0.
-2, 1
Let z = -8 - -13. Suppose z*j + 2 = -2*v + 11, -9 = 3*v. Factor 6*s - s**2 - 3*s**4 + s**5 + 3*s**j - 6*s.
s**2*(s - 1)**3
Let w(p) be the first derivative of -2*p**9/189 - p**8/105 + p**7/60 - p**6/180 + p**3 + 1. Let v(o) be the third derivative of w(o). Factor v(h).
-2*h**2*(h + 1)*(4*h - 1)**2
Factor -g - g - g - 21*g**2 + 24*g**2.
3*g*(g - 1)
Let a(b) be the first derivative of -b**6/75 + b**5/30 - b**4/60 + b**2 - 2. Let t(n) be the second derivative of a(n). Find f, given that t(f) = 0.
0, 1/4, 1
Let v(l) be the first derivative of -l**5 + 15*l**4/4 - 5*l**3/3 - 15*l**2/2 + 10*l + 3. Factor v(n).
-5*(n - 2)*(n - 1)**2*(n + 1)
Let q be (-1)/6 + 169/78. Let 2*l + 2 + l**q + 0*l - 5*l = 0. Calculate l.
1, 2
Let c(s) = -8*s**5 + 12*s**4 - 18*s**3 + 5*s**2 + 3. Let o(n) = 15*n**5 - 25*n**4 + 35*n**3 - 10*n**2 - 5. Let r(h) = 5*c(h) + 3*o(h). What is x in r(x) = 0?
0, 1
Let d(j) = j**2 - 5*j + 3. Let a be d(5). Let x be (a/27)/((-2)/(-6)). Suppose 1/3 + n**2 + x*n**3 + n = 0. Calculate n.
-1
Let a = -15 - -9. Let w(i) = -12*i**3 + 9*i**2 - 4*i - 15. Let d(z) = -3*z**3 + 2*z**2 - z - 4. Let q(m) = a*w(m) + 22*d(m). Determine j so that q(j) = 0.
-1/3, 1
Let x(l) = 3*l**2 - l + 1. Let w be (-2 - 4/(-4))*1. Let c be x(w). Determine a so that -1/4*a**3 + 0*a**2 - 5/4*a**4 - a**c + 0*a + 0 = 0.
-1, -1/4, 0
Let h(j) be the second derivative of -j**6/2 - j**5 - 5*j**4/9 + 14*j. Let h(q) = 0. Calculate q.
-2/3, 0
Let l(i) be the second derivative of i**4/6 + 2*i**3 + 5*i**2 + 5*i. Factor l(v).
2*(v + 1)*(v + 5)
Let j(x) be the third derivative of x**9/25200 - x**8/11200 - x**7/2100 + 5*x**4/24 + 3*x**2. Let z(s) be the second derivative of j(s). Factor z(k).
3*k**2*(k - 2)*(k + 1)/5
Factor -20*u + 60 + 5/3*u**2.
5*(u - 6)**2/3
Let i(l) be the third derivative of l**6/1980 - l**4/132 + l**3/3 + 2*l**2. Let j(k) be the first derivative of i(k). Factor j(q).
2*(q - 1)*(q + 1)/11
Let l(a) = a**3. Let h(b) = b**2. Let t(s) = s**3 - 6*s**2 - 7*s + 1. Let j be t(7). Let o(g) = j*h(g) - l(g). Suppose o(r) = 0. What is r?
0, 1
Suppose -2*b - 3*b - 3*f - 19 = 0, 2*b = f - 1. Let y be (-8)/16*1/b. Determine l so that y*l**2 - 1/4*l**3 + 1/4*l - 1/4 = 0.
-1, 1
Let u be (2/(-15))/((-68)/85). Let o(c) be the third derivative of u*c**3 + 1/48*c**4 + 0*c + 0 - 1/240*c**6 - 1/60*c**5 + 3*c**2. Factor o(x).
-(x - 1)*(x + 1)*(x + 2)/2
Factor -32*x + 5*x**2 + 4*x**3 + 9*x**2 - 14*x**4 + 0*x**4 + 28*x.
-2*x*(x - 1)*(x + 1)*(7*x - 2)
Let f(m) be the second derivative of 0*m**3 + 0*m**4 - 2*m + 1/126*m**7 + 0*m**2 + 0*m**5 + 0 + 1/45*m**6. Factor f(r).
r**4*(r + 2)/3
Let q(a) = -a. Let d(j) = j**4 + 2*j**3 - 3*j**2 + 7*j. Let b(y) = -2*d(y) - 14*q(y). Let b(g) = 0. Calculate g.
-3, 0, 1
Let p(l) be the second derivative of -l**5/4 - 3*l**4/8 + l**3 + l**2/2 + l. Let t(a) be the first derivative of p(a). Factor t(n).
-3*(n + 1)*(5*n - 2)
Let t(y) be the third derivative of -1/36*y**4 + 0*y**3 + 0 + y**2 + 0*y - 1/45*y**5 - 1/180*y**6. Let t(f) = 0. What is f?
-1, 0
Let b(q) be the first derivative of q**6/30 + 2*q**5/25 + q**4/20 - 33. Solve b(s) = 0.
-1, 0
Let r(d) be the first derivative of d**4 + d**3 - d**2/2 - 3. Factor r(y).
y*(y + 1)*(4*y - 1)
Let x(w) be the third derivative of w**5/540 + w**4/216 + 3*w**2. Suppose x(l) = 0. What is l?
-1, 0
Let s(x) be the third derivative of x**7/210 + x**6/30 + x**5/12 + x**4/12 - 10*x**2. Let s(v) = 0. Calculate v.
-2, -1, 0
Let g(b) = -47*b**3 + 73*b**2 - 37*b + 5. Let z(i) = 142*i**3 - 218*i**2 + 112*i - 15. Let j(w) = -7*g(w) - 2*z(w). Find s such that j(s) = 0.
1/3, 1
Find v, given that 5/2*v - 1/2*v**5 - 2*v**3 + 1 - 2*v**4 + v**2 = 0.
-2, -1, 1
Let j(v) be the second derivative of -v**4/4 + 3*v**2/2 - 10*v. Factor j(u).
-3*(u - 1)*(u + 1)
Let o be (5 - 1736/360)*(-15)/(-6). Suppose -14/9*q**5 - 6*q**3 - 46/9*q**4 - 26/9*q**2 + 0 - o*q = 0. Calculate q.
-1, -2/7, 0
Suppose -5*g = -3*g. Let f = -28 - -57/2. Factor -f*n**4 + 1/2*n**2 + 0 - 1/2*n**5 + g*n + 1/2*n**3.
-n**2*(n - 1)*(n + 1)**2/2
Let q = 91/62 - -1/31. Factor -2 + 9/2*x**3 + q*x**2 - 4*x.
(x - 1)*(3*x + 2)**2/2
Let t be 5*(-54)/225*1/(-2). Factor -1/5*u**2 + t*u - 2/5.
-(u - 2)*(u - 1)/5
Determine f so that 4 + 6 - 3 + 5*f**3 + 16*f - 3 + 17*f**2 = 0.
-2, -1, -2/5
Let q(f) be the third derivative of -f**7/70 + 3*f**5/10 + f**4 + 3*f**3/2 + 16*f**2. Factor q(g).
-3*(g - 3)*(g + 1)**3
Let m(w) be the first derivative of 15*w**5 + 5*w**4/4 - 10*w**3/3 + 16. Find r such that m(r) = 0.
-2/5, 0, 1/3
Let k(a) be the third derivative of -4*a**2 + 0 - 1/840*a**8 + 4/75*a**5 + 0*a**4 + 2/175*a**7 - 1/25*a**6 + 0*a**3 + 0*a. Determine x so that k(x) = 0.
0, 2
Let d(q) be the third derivative of q**8/141120 + q**7/17640 - q**5/20 - q**2. Let z(v) be the third derivative of d(v). Factor z(r).
r*(r + 2)/7
Let v(f) be the first derivative of 2/9*f**2 - 3 + 2/45*f**5 + 0*f**4 - 2/9*f**3 + 0*f. Solve v(j) = 0 for j.
-2, 0, 1
Let l(f) = -12*f**2 + 8*f. Let z(u) = -u**3 - 25*u**2 + 17*u. Let t(v) = 9*l(v) - 4*z(v). Factor t(y).
4*y*(y - 1)**2
Let d(n) be the second derivative of -2*n**7/21 - 2*n**6/15 + 13*n. Factor d(c).
-4*c**4*(c + 1)
Let c(a) = -a**2 - 9*a - 6. Let l be c(-8). Suppose 5*i = 2*i. Find q, given that 3/4*q**3 - 1/2*q**l + 0 + i*q - 1/4*q**4 = 0.
0, 1, 2
Let x = -3599/120 + 30. Let a(z) be the second derivative of z + 1/8*z**2 + x*z**6 + 1/8*z**4 + 1/20*z**5 + 0 + 1/6*z**3. Factor a(y).
(y + 1)**4/4
Find i, given that 1/3*i**2 - 1/3*i - 2/3 = 0.
-1, 2
Let m(n) be the second derivative of n**6/165 - n**5/22 + 7*n**4/66 - n**3/11 + 21*n. Factor m(w).
2*w*(w - 3)*(w - 1)**2/11
Let l(n) = -n**3 - 6*n**2 - n - 2. Let d be l(-6). Let w = 7 - d. Factor t**4 - 3*t**3 + 2*t**3 + 2*t**w - t**2 - t.
t*(t - 1)*(t + 1)**2
Suppose h - 2 = -2*m, -2*m = -h - 2*h - 34. Let o(t) = t**2 + 8*t + 2. Let y be o(h). Factor -y*j**2 + 4 + 5*j - 2 + 0*j**2 - 5*j**3.
-(j - 1)*(j + 1)*(5*j + 2)
Let z be -1*18/(-48)*2. Let -3/2*f + z + 3/4*f**2 = 0. What is f?
1
Let k(c) be the second derivative of -c**10/70560 - c**9/11760 + c**7/1470 - 5*c**4/12 - c. Let u(f) be the third derivative of k(f). Factor u(b).
-3*b**2*(b - 1)*(b + 2)**2/7
Let f(v) be the second derivative of 3/2*v**2 + 0 - 1/360*v**6 + 0*v**3 + 0*v**4 + 3*v + 1/180*v**5. Let q(s) be the first derivative of f(s). Factor q(o).
-o**2*(o - 1)/3
Let q(f) = f**3 + 3*f**2 + f + 1. Let k be q(-2). What is m in -4 - 2*m**k + 2 + 2 + 2*m = 0?
-1, 0, 1
Solve 21/4*m**3 + 3/2*m + 0 - 45/4*m**2 = 0 for m.
0, 1/7, 2
Let v(d) be the third derivative of -d**7/1260 - d**6/360 + d**5/120 + 21*d**2. Suppose v(n) = 0. What is n?
-3, 0, 1
Let t(k) be the second derivative of -k**8/7560 + k**7/3780 + k**6/1620 - k**5/540 - 2*k**3/3 + k. Let f(h) be the second derivative of t(h). Factor f(w).
-2*w*(w - 1)**2*(w + 1)/9
Let u be 253/(-66) + 2*2. Let n(j) be the first derivative of -1/4*j - 1/8*j**2 + u*j**3 + 1/8*j**4 + 3 - 1/20*j**5 - 1/24*j**6. Factor n(x).
-(x - 1)**2*(x + 1)**3/4
Let z(k) be the third derivative of -3*k**2 - 1/270*k**5 + 1/54*k**4 + 0 + 0*k - 1/27*k**3.