(v) be the first derivative of 1/3*v**6 + 0*v - 4 + 0*v**2 + 0*v**5 - 1/2*v**4 + 0*v**3. Suppose g(n) = 0. What is n?
-1, 0, 1
Let m be (-5 - 0/5) + 4 + 4. Let x(i) be the first derivative of m - 2/21*i**3 - 3/7*i**2 - 4/7*i. Factor x(f).
-2*(f + 1)*(f + 2)/7
Let x(s) be the first derivative of 84*s**5/25 + 61*s**4/10 + 28*s**3/15 - 7*s**2/5 - 4*s/5 - 2. What is q in x(q) = 0?
-1, -1/2, -2/7, 1/3
Let p(r) = 11*r + 1. Let x be p(1). Factor -12 + 2*f**2 + x - 2*f.
2*f*(f - 1)
Let o(m) be the first derivative of m**6/540 + m**5/90 - m**4/12 + 10*m**3/3 - 8. Let l(x) be the third derivative of o(x). Let l(y) = 0. Calculate y.
-3, 1
Let b(u) = -7*u**2 + 29. Let g(z) = -4*z**2 + 15. Let s(j) = 3*b(j) - 5*g(j). Let n(d) = 2. Let k(o) = 11*n(o) - 2*s(o). Find m, given that k(m) = 0.
-1, 1
Let k(h) be the second derivative of h**6/45 - h**5/30 - 14*h. Suppose k(j) = 0. What is j?
0, 1
Suppose h = 3*h. Let g(q) be the third derivative of 0*q + 0 + 1/120*q**6 + 1/60*q**5 + h*q**3 + 0*q**4 - q**2. Let g(m) = 0. What is m?
-1, 0
Let o(k) be the first derivative of 4*k**5/15 - k**4 + 4*k**3/9 + 2*k**2 - 8*k/3 - 13. Solve o(a) = 0 for a.
-1, 1, 2
Suppose 11*b - 15*b = 0. Let a(i) be the first derivative of b*i - 1/20*i**4 - 1/15*i**3 + 1 + 0*i**2. Factor a(m).
-m**2*(m + 1)/5
Factor 0*b + 8/7*b**2 + 0 + 2/7*b**3.
2*b**2*(b + 4)/7
Let c be 1*(-2)/(-9)*6. Factor 2/3 - c*x + 2/3*x**2.
2*(x - 1)**2/3
Let q(p) be the third derivative of p**8/420 + 2*p**7/525 - p**6/150 - p**5/75 + 23*p**2. Factor q(v).
4*v**2*(v - 1)*(v + 1)**2/5
Suppose -4*b = 2*t - 22, -5*b + 2*t + 25 = 4*t. What is r in 0 - 4/5*r**2 + 0*r + 4/5*r**4 - 2/5*r**5 + 2/5*r**b = 0?
-1, 0, 1, 2
Suppose -2*j - 11 = -3. Let r(c) = -36*c**2 + 66*c - 9. Let l(g) = 7*g**2 - 13*g + 2. Let u(w) = j*r(w) - 21*l(w). What is a in u(a) = 0?
1, 2
Let r be (24/18)/4*(6 + 0). Factor 0 - 1/3*x**5 - r*x**4 - 8/3*x**2 + 0*x - 4*x**3.
-x**2*(x + 2)**3/3
Let v(n) be the first derivative of -n**9/108 - n**8/84 + n**7/840 + n**6/180 + 5*n**3/3 + 6. Let r(l) be the third derivative of v(l). What is s in r(s) = 0?
-1/2, 0, 2/7
Let t be (6/21)/(3/21). Factor -6*h**2 + 9*h**2 - 3*h**2 + 2*h**t.
2*h**2
Suppose 0 = -4*o - s + 7, -9*o = -8*o + 2*s. Factor 10/3*c**o - 16/3*c - 8/3.
2*(c - 2)*(5*c + 2)/3
Let k(d) = d**2 + 2*d - 2. Let o be k(-4). Suppose 5*a = -3*z, 0 = 3*z + 2*a - o*a. Factor -2*s**2 - 4 + 4*s + 2 + z.
-2*(s - 1)**2
Let f(m) = m**5 - 37*m**4 - 48*m**3 - 24*m**2 - 7*m + 7. Let y(b) = b**5 - 19*b**4 - 24*b**3 - 12*b**2 - 4*b + 4. Let j(p) = 4*f(p) - 7*y(p). Factor j(r).
-3*r**2*(r + 1)*(r + 2)**2
Suppose 0*r + r - 2 = 0. Suppose -r*i = -4*i + 6. Determine w so that 2*w**2 + 2*w**3 - 3*w - 3*w**2 + w**i + 3 - 2 = 0.
-1, 1/3, 1
Let u be 7/2 - 2/(-4). Solve 3*p**2 + 34*p**4 + p - p - 37*p**u = 0.
-1, 0, 1
Let x be (0 + 4/12)*-98. Let t = x - -33. Factor b**2 - 2/3 + t*b - 1/3*b**4 - 1/3*b**3.
-(b - 1)**2*(b + 1)*(b + 2)/3
Let k = 869/2 + -433. Solve 3*r - k - 3/2*r**2 = 0 for r.
1
Let x = -1/16770 + 16468147/117390. Let r = x + -140. Solve 4/7 - r*c**3 - 2/7*c**4 + 6/7*c**2 + 10/7*c = 0 for c.
-1, 2
Let h(d) be the second derivative of -3/20*d**5 + 0 + 1/42*d**7 + 1/30*d**6 - 1/12*d**4 + 1/3*d**3 + 0*d**2 - d. Factor h(l).
l*(l - 1)**2*(l + 1)*(l + 2)
Let k(i) be the second derivative of 2*i**6/15 - i**5/5 - i**4/3 + 2*i**3/3 + 11*i. What is g in k(g) = 0?
-1, 0, 1
Let p = 12 + -10. Suppose -2/9*k**p + 0*k + 2/9 = 0. Calculate k.
-1, 1
Suppose -15*f**2 + 29*f**3 - 41*f**3 + f**4 - 4*f**4 - 6*f = 0. Calculate f.
-2, -1, 0
Let n(j) = 11*j**3 - 11*j. Let b(l) be the third derivative of l**6/30 - l**4/6 - l**2. Let t = 25 + -17. Let u(k) = t*b(k) - 3*n(k). Factor u(d).
-d*(d - 1)*(d + 1)
Let r(d) be the second derivative of -d**6/105 + d**5/14 - 3*d**4/14 + d**3/3 - 2*d**2/7 + 46*d. Solve r(t) = 0 for t.
1, 2
Let z(h) = -h**2 - 3*h. Let s be z(0). Let p(i) be the second derivative of -1/10*i**6 + 4*i**2 - 7/6*i**4 - 13/20*i**5 - i + s + 2/3*i**3. Solve p(b) = 0.
-2, -1, 2/3
Let g(m) be the second derivative of 0 + 5/9*m**3 - m - 1/45*m**6 + 1/6*m**4 - 1/30*m**5 + 2/3*m**2. Solve g(v) = 0 for v.
-1, 2
Let k be 18/8 + 1/(-4). Let 5*t**3 + 3*t**3 + t**k - 9*t**3 = 0. Calculate t.
0, 1
Let u(z) be the first derivative of 0*z**5 + 1/3*z**2 + 0*z**3 - 8 - 1/3*z**4 + 1/9*z**6 + 0*z. Solve u(d) = 0.
-1, 0, 1
Solve -1/3*v**2 + 0 + 1/3*v = 0 for v.
0, 1
Let a = -48 - -89/2. Let n = a - -39/10. Solve -8/5*r - n*r**2 - 8/5 = 0 for r.
-2
Suppose -66 = -i + 4*i - 3*t, 3*t + 67 = -4*i. Let s = i - -23. Determine n so that 10/3*n + 2/3 - 10/3*n**3 - 8/3*n**s + 2*n**2 = 0.
-1, -1/4, 1
Let z(h) be the first derivative of -h**4/18 + 8*h**3/27 - h**2/3 - 14. Let z(f) = 0. Calculate f.
0, 1, 3
Let a = -40 - -27. Let v = -13 - a. Find q, given that 0*q**4 + 0*q**2 + 1/4*q**5 + 0*q**3 + v*q + 0 = 0.
0
Let b(c) be the second derivative of -c**7/119 + 4*c**6/255 + 2*c**5/85 - c**4/17 - c**3/51 + 2*c**2/17 - 33*c. Find f, given that b(f) = 0.
-1, -2/3, 1
Let z(o) = -o**2 - 2*o - 4. Let c(h) = -h**2 - h - 3. Let a(b) = 4*c(b) - 3*z(b). Find f, given that a(f) = 0.
0, 2
Let p = -7 + 9. Let i = 0 + p. Determine j, given that -2/5*j**4 + 0*j**i + 2/5 + 4/5*j - 4/5*j**3 = 0.
-1, 1
Suppose 16 = g + 13. Let 33*v**4 - 4*v**2 + 2*v**5 - 2*v**g - 19*v**4 - 10*v**4 = 0. Calculate v.
-2, -1, 0, 1
Let r(x) be the third derivative of 0*x**3 + 0 - 1/200*x**6 + 0*x**4 - 1/100*x**5 + 0*x + 4*x**2 + 1/70*x**7 - 3/560*x**8. Factor r(b).
-3*b**2*(b - 1)**2*(3*b + 1)/5
Let p be (7/21*(-9)/4)/(-1). Let a = 21/4 - 5. Factor 0*m - 1/2*m**3 - p*m**2 + a.
-(m + 1)**2*(2*m - 1)/4
Let x(g) = -g**3 + 17*g**2 - g + 24. Let s be x(17). Suppose s*y + 0 - 21 = 0. Suppose 0*o + 0 + 2/7*o**2 - 2/7*o**y = 0. What is o?
0, 1
Suppose 0 = 4*i + i - 25. Let l be (2/(-7))/((-7)/63). Factor -2/7*x - l*x**i + 24/7*x**4 + 0 + 4/7*x**3 - 8/7*x**2.
-2*x*(x - 1)**2*(3*x + 1)**2/7
Let o(q) be the second derivative of 5*q**7/42 + 5*q**6/6 + q**5/2 - 35*q**4/6 - 5*q**3/2 + 45*q**2/2 + 6*q. Find v such that o(v) = 0.
-3, -1, 1
Factor -2/5*x**3 + 84/5*x**2 + 5488/5 - 1176/5*x.
-2*(x - 14)**3/5
Suppose 14 = 4*t + 6. Suppose -4*d + t*d + 2 = 3*r, -r = 5*d - 5. Let -1/2*s + 1/2*s**2 + r = 0. What is s?
0, 1
Factor -1/2*j**2 - 5/2*j**3 - 2 + 1/2*j**4 + 1/2*j**5 + 4*j.
(j - 1)**3*(j + 2)**2/2
Let s(y) be the second derivative of y**6/6 - y**5/2 - 5*y**4/12 + 5*y**3/3 + 9*y. Factor s(j).
5*j*(j - 2)*(j - 1)*(j + 1)
Let b be 212/18 + 6/27. Suppose b = 2*o + 4. Determine j so that -j**2 + o*j**2 - j**2 + j**3 - 2 + j - 2*j**3 = 0.
-1, 1, 2
Let z be 115/35 + 2/(-7). Let r(t) be the third derivative of -1/180*t**5 + 0 + 0*t**z + 2*t**2 + 1/210*t**7 + 0*t + 1/90*t**6 - 1/36*t**4. Factor r(u).
u*(u + 1)**2*(3*u - 2)/3
Factor 5 + 2*j + 1/5*j**2.
(j + 5)**2/5
Let n = 167 + -1167/7. Find p, given that 4/7 + 2/7*p - n*p**2 = 0.
-1, 2
Let v(s) be the second derivative of s**7/336 - s**5/80 + s**3/48 + 11*s. What is u in v(u) = 0?
-1, 0, 1
Factor -9 - 2 + 27*u + 5 - 18*u**2 + 3*u**3 - 6.
3*(u - 4)*(u - 1)**2
Let q(p) be the third derivative of 1/10*p**5 - 1/280*p**7 + 0 + 0*p - 2*p**3 + 1/4*p**4 + 10*p**2 + 1/896*p**8 - 1/40*p**6. Factor q(x).
3*(x - 2)**3*(x + 2)**2/8
Let d(y) = -y**2. Let z(k) = k**4 - k**3 + 1. Let w(o) = -o**5 + o**4 - o**3 + 7*o**2 - o + 1. Let t(g) = w(g) - 3*z(g). Let c(u) = -3*d(u) - t(u). Factor c(n).
(n - 1)**2*(n + 1)**2*(n + 2)
Let f(d) be the first derivative of 2*d**3/3 - 7*d**2 + 12*d + 19. Determine n, given that f(n) = 0.
1, 6
Let t = 21030/19 + -222406/171. Let j = t - -194. Find s such that 8/9*s**2 - 10/9*s + j = 0.
1/4, 1
Factor -10 - 30 - 145*t**3 - 190*t**2 - 140*t - 8*t**5 + 20*t**3 - 40*t**4 + 3*t**5.
-5*(t + 1)**2*(t + 2)**3
Let s = 49/342 + 3/38. Let j(n) be the first derivative of -4/27*n**3 + 0*n**2 + 0*n**4 + 2 + 2/45*n**5 + s*n. Factor j(p).
2*(p - 1)**2*(p + 1)**2/9
Let b(t) be the first derivative of 0*t - 2 + 1/21*t**3 - 1/21*t**4 + 1/70*t**5 - 1/2*t**2. Let x(l) be the second derivative of b(l). Let x(i) = 0. What is i?
1/3, 1
Let x(w) be the second derivative of 1/3*w**3 + 0 + 4*w - 1/6*w**4 + 1/15*w**6 + 0*w**2 - 1/10*w**5. Suppose x(t) = 0. Calculate t.
-1, 0, 1
Let u(l) be the third derivative of l**5/4 - 3*l**4/2 + 2*l**3 - 8*l**2. Factor u(i).
3*(i - 2)