hird derivative of -j**5/60 + j**4/2 - 6*j**3 + 26*j**2. Factor v(o).
-(o - 6)**2
Solve 0*j**3 + 1/3*j**4 + 1/3 + 0*j - 2/3*j**2 = 0.
-1, 1
Let n(o) be the second derivative of 0 - 4*o + 0*o**2 + 0*o**3 - 1/12*o**4. Find y such that n(y) = 0.
0
Let j(s) be the second derivative of 0 + 4/13*s**2 - 1/26*s**4 + 0*s**3 + 4*s + 1/130*s**5. Factor j(y).
2*(y - 2)**2*(y + 1)/13
Let w(p) be the third derivative of 0*p + 0*p**6 + 0*p**3 - 1/45*p**5 + 0 + 2/315*p**7 + 1/504*p**8 - 1/36*p**4 - 3*p**2. Find v, given that w(v) = 0.
-1, 0, 1
Suppose 3*q - 2*r - r = 6, 5*r = 4*q - 10. Let x be ((-8)/6)/((-4)/6). Factor b**2 + 0*b + b - 2 + q*b**2 - x*b.
(b - 2)*(b + 1)
Let u be 4 - 3/((-21)/(-20)). Factor -u*z**3 + 4/7 + 24/7*z**2 - 18/7*z.
-2*(z - 2)*(2*z - 1)**2/7
Let u(v) be the second derivative of v**7/4200 + v**6/900 - v**3/3 - 7*v. Let x(h) be the second derivative of u(h). Determine j, given that x(j) = 0.
-2, 0
Let m(l) be the third derivative of l**9/6048 - l**8/4480 - l**7/2520 + l**4/3 + 8*l**2. Let f(v) be the second derivative of m(v). What is k in f(k) = 0?
-2/5, 0, 1
Let s = 17 + -15. What is i in 19*i**s - 6*i**5 + 13*i + 18*i**3 + 0*i**4 + 5*i**2 - 4*i**4 - 5*i = 0?
-1, -2/3, 0, 2
Let p(j) be the first derivative of -7/3*j**6 - 2*j**2 + 26/3*j**3 + 0*j - 27/2*j**4 + 46/5*j**5 - 3. Suppose p(x) = 0. Calculate x.
0, 2/7, 1
Let s(a) = -a**2 + a. Let v(f) = -2*f**4 + 2*f**3 + f**2 - 5*f + 4. Let c(d) = 5*s(d) - v(d). Factor c(t).
2*(t - 1)**3*(t + 2)
Let i(u) be the second derivative of -u**6/20 + u**4/8 + 6*u. Solve i(j) = 0.
-1, 0, 1
Factor -4*n**2 + 8*n - 645*n**4 + 0*n**2 + 649*n**4 - 8*n**3.
4*n*(n - 2)*(n - 1)*(n + 1)
Let x(a) be the third derivative of 0*a**4 + 2/3*a**3 + 0 + a**2 + 0*a - 1/60*a**5. Factor x(m).
-(m - 2)*(m + 2)
Let t = -30 - -34. Let b(i) be the first derivative of 1/21*i**6 + 8/21*i**3 + 0*i + 1/7*i**2 + 3/7*i**t - 1 + 8/35*i**5. Factor b(p).
2*p*(p + 1)**4/7
Let x = -65 + 67. Let a(l) be the second derivative of 0 - l - 2/21*l**4 + 1/21*l**3 + 0*l**x. Suppose a(r) = 0. What is r?
0, 1/4
Let a(j) be the second derivative of -3*j**5/140 - 3*j**4/28 + 2*j**3/7 - 3*j. Suppose a(d) = 0. What is d?
-4, 0, 1
Let a(y) = -5*y**3 + 9*y**2 + 5*y + 5. Let o(i) = -4*i**3 + 8*i**2 + 4*i + 4. Let q(r) = -5*a(r) + 6*o(r). Let h be q(-3). Factor h*z + 3*z + z**2 - 5*z - z.
z*(z - 1)
Let a(t) be the third derivative of -t**6/660 + t**5/110 - 4*t**3/33 + 14*t**2. Factor a(h).
-2*(h - 2)**2*(h + 1)/11
Let v(j) be the third derivative of j**7/280 - 7*j**6/240 + 23*j**5/240 - j**4/6 + j**3/6 + 31*j**2. Factor v(p).
(p - 2)*(p - 1)**2*(3*p - 2)/4
Let t be -2*(1 - (-21)/(-6)). Suppose -14 = -t*i + 6. Let -6*n**5 + i*n**4 + 1 + 12*n**3 + 1 - 8*n**2 - 1 + 3 - 6*n = 0. What is n?
-1, 2/3, 1
Let b(c) = 5*c**4 - 15*c**3 + 5*c**2 + 9*c - 4. Let s(r) = -20*r**4 + 60*r**3 - 20*r**2 - 35*r + 15. Let n(d) = 25*b(d) + 6*s(d). Factor n(f).
5*(f - 2)*(f - 1)**2*(f + 1)
Let q = -3/71 - -83/284. Factor -1/2*n**3 + q*n - 1/4*n**2 + 0.
-n*(n + 1)*(2*n - 1)/4
Suppose -3*o = 9, -3*m + 15 = -3*o - 6. Suppose 0 = 4*i + 5*s + 15, s = -5*i + m*s + 9. Solve i + 0*d + 1/2*d**2 = 0.
0
Let y(s) be the third derivative of s**5/12 + 5*s**4/12 + 5*s**3/6 + 8*s**2. Factor y(i).
5*(i + 1)**2
Let c(f) be the second derivative of -5/27*f**4 + 8/9*f**2 + 1/90*f**5 - f + 0 + 4/135*f**6 - 4/27*f**3 + 1/189*f**7. Solve c(j) = 0 for j.
-2, 1
Let x(j) be the second derivative of j**5/5 + 5*j**4/3 + 14*j**3/3 + 6*j**2 + j. Factor x(m).
4*(m + 1)**2*(m + 3)
Let j(u) be the first derivative of -3*u**4/16 + u**3/4 + 3*u**2/4 - 34. Factor j(d).
-3*d*(d - 2)*(d + 1)/4
Let t(x) = x**3 - 8*x**2 + 6*x + 9. Let j be t(7). Let -4/3*s**2 + 2/3 + 4*s**3 - 2*s**5 + 2/3*s**4 - j*s = 0. What is s?
-1, 1/3, 1
Let k(a) be the first derivative of 0*a**2 + 0*a + 3 + 2/15*a**3. Determine u, given that k(u) = 0.
0
Let c(i) be the first derivative of -i**7/150 + i**6/300 - i**2/2 - 4. Let p(o) be the second derivative of c(o). Let p(m) = 0. What is m?
0, 2/7
Let k(h) be the third derivative of 3*h**5/20 - h**4/4 - h**3/2 - h**2. Let o(a) = -18*a**2 + 13*a + 5. Let r(i) = 7*k(i) + 3*o(i). Solve r(f) = 0.
-2/3, 1
Suppose -4*z = -2*b + 14, 27*z = 22*z - 10. Factor 2/5*i**2 - 2/5*i**b - 2/5*i**4 + 0 + 2/5*i.
-2*i*(i - 1)*(i + 1)**2/5
Let c(r) be the first derivative of 2*r**3/15 - 2*r**2/5 + 2*r/5 - 4. Factor c(p).
2*(p - 1)**2/5
Factor x + 1/2*x**2 - 3/2.
(x - 1)*(x + 3)/2
Let x(i) be the first derivative of i**6/1080 - i**4/72 + i**3/3 - 2. Let t(u) be the third derivative of x(u). Suppose t(b) = 0. What is b?
-1, 1
Let r(z) = 4*z**5 - 2*z**4 - 8*z**3 - 6*z**2 - 6*z + 6. Let x(k) = 3*k**5 - k**4 - 7*k**3 - 5*k**2 - 5*k + 5. Let g(p) = 5*r(p) - 6*x(p). Factor g(j).
2*j**3*(j - 1)**2
Let p(l) be the first derivative of -2*l**3 + 2*l**2 + 8. Factor p(c).
-2*c*(3*c - 2)
Let f = 643 + -7067/11. Factor -2/11 - 4/11*r**2 - f*r.
-2*(r + 1)*(2*r + 1)/11
Let z(t) = -t + 4. Let c be z(4). Let 0*w - 4/3*w**2 + w**4 - 1/3*w**5 + 0*w**3 + c = 0. Calculate w.
-1, 0, 2
Let o be 32*3/189 + (-2)/7. Suppose 0 - 2/9*k + o*k**2 = 0. Calculate k.
0, 1
Determine b so that 0 - 24/11*b**3 + 6/11*b**4 - 6*b**2 - 36/11*b = 0.
-1, 0, 6
Let r(p) = 2*p**3 + 3*p**2 + 3*p - 3. Let n(i) = 6*i**3 + 10*i**2 + 8*i - 8. Let h(v) = -3*n(v) + 8*r(v). Factor h(o).
-2*o**2*(o + 3)
Let v(q) be the second derivative of -q**7/10080 - q**4/12 + 3*q. Let s(u) be the third derivative of v(u). Let s(o) = 0. What is o?
0
Factor u**2 + 4*u**2 - 3431*u - 40 + 3396*u.
5*(u - 8)*(u + 1)
Let c be (-3)/6*(2 + -2). Let k(l) be the third derivative of l**2 + 0 - 1/200*l**6 + 1/100*l**5 - 1/120*l**4 + c*l**3 + 0*l + 1/1050*l**7. Factor k(g).
g*(g - 1)**3/5
Let o(f) be the second derivative of -f**6/240 - f**5/24 - f**4/6 - f**3/3 + 3*f**2 + 5*f. Let r(w) be the first derivative of o(w). Solve r(y) = 0.
-2, -1
Let b(t) = -5*t**3 - 9*t**2 + 5*t. Let a(r) = -r**3 - 2*r**2 + r. Let h(f) = -18*a(f) + 4*b(f). Factor h(q).
-2*q*(q - 1)*(q + 1)
Let v be 0*(-2 + 6/4). Let m be 1 - ((-1 - 1) + v). Let -g + 0*g**2 + g**2 + 2*g**m - g**4 - g**3 = 0. Calculate g.
-1, 0, 1
Let c = 409 - 2038/5. Let v = 9/5 - c. Let 8/5*y**3 + 4/5*y + 14/5*y**2 - v = 0. Calculate y.
-1, 1/4
Let p = 66 + -66. Let d(s) be the third derivative of 1/180*s**5 + s**2 + 0*s**3 + p + 0*s + 0*s**4. Factor d(z).
z**2/3
Let n(w) = -w**3 + 1. Let z(u) = -2*u**2 + 2. Let p(m) = 4*n(m) - 2*z(m). Find d, given that p(d) = 0.
0, 1
Suppose 8*l + 6 = 11*l. Let v(k) be the first derivative of 0*k + 0*k**3 - 3 + 1/18*k**4 - 1/9*k**l. Determine x, given that v(x) = 0.
-1, 0, 1
Factor 0 + 2/23*x**5 + 0*x**4 - 4/23*x**2 + 0*x - 6/23*x**3.
2*x**2*(x - 2)*(x + 1)**2/23
Let f(v) be the second derivative of 1/12*v**4 + 9/2*v**2 - v**3 + 0 - v. Determine g, given that f(g) = 0.
3
Let s = -125/18 + 43/6. Let h(w) be the first derivative of -4/9*w**2 + 2/9*w + 2/45*w**5 + 4/9*w**3 + 2 - s*w**4. Let h(c) = 0. What is c?
1
Let r(b) be the third derivative of 0*b - 1/9*b**7 - 13/45*b**5 - 1/9*b**4 + 0 + 8/27*b**3 + 187/540*b**6 + 4*b**2. Suppose r(f) = 0. What is f?
-2/7, 2/5, 2/3, 1
Let r(i) be the third derivative of -i**5/20 + i**4/2 + 3*i**3/2 - 3*i**2. Let l(b) = -b**2 + 3*b + 2. Let n(w) = 9*l(w) - 2*r(w). What is h in n(h) = 0?
0, 1
Solve 4/13*z**3 + 0 - 2/13*z**4 + 0*z**2 + 0*z = 0 for z.
0, 2
Let r(a) = a**2 - a - 3. Let q be r(3). Factor 0 + 2/5*s**q + 0*s + 2/5*s**2.
2*s**2*(s + 1)/5
Let o = 14 - 22. Let v = o + 10. Let -1/5*w**v + 3/5*w - 2/5 = 0. What is w?
1, 2
Let h(z) be the second derivative of -4*z**6/45 - z**5/3 + z**4/3 + 16*z**3/9 - 8*z**2/3 + 8*z. Solve h(j) = 0.
-2, 1/2, 1
Let a(u) be the third derivative of -u**5/105 - u**4/14 - 4*u**3/21 + u**2. Factor a(j).
-4*(j + 1)*(j + 2)/7
Solve 5/3 - 1/3*s**2 - 4/3*s = 0 for s.
-5, 1
Let f(b) be the second derivative of 1/126*b**7 + 0 + 0*b**4 - 5*b + 0*b**5 + 0*b**3 + 0*b**2 + 1/45*b**6. Find w such that f(w) = 0.
-2, 0
Let x(g) = -g**3 + 5*g**2 - 5*g + 1. Let p be x(4). Let y = p + 6. Find i such that 0*i + 0 - 2/5*i**y - 2/5*i**2 = 0.
-1, 0
Let q(c) be the first derivative of -6*c**2 + 6 - 6/5*c**5 + 9/4*c**4 - 1/2*c**6 + 0*c + 4*c**3. Find h, given that q(h) = 0.
-2, 0, 1
Let v = 4 - 0. Let w(x) be the third derivative of 4/3*x**3 - x**v + 3/10*x**5 + 