3*f**4.
2*f*(f - 1)**2*(f + 2)/3
Let g(l) be the first derivative of 3 + 1/21*l**6 + 12/35*l**5 + 0*l + 0*l**2 + 16/21*l**3 + 6/7*l**4. Factor g(p).
2*p**2*(p + 2)**3/7
Let u(i) be the first derivative of i**5/15 + i**4/2 + 13*i**3/9 + 2*i**2 + 4*i/3 + 14. Determine t so that u(t) = 0.
-2, -1
Let o(m) be the second derivative of m**9/10080 - m**7/560 - m**6/240 + 7*m**4/12 - 7*m. Let y(r) be the third derivative of o(r). Factor y(h).
3*h*(h - 2)*(h + 1)**2/2
Let l = -5210/93 + -51/31. Let z = -57 - l. Factor -r**2 + z - 1/3*r.
-(r + 1)*(3*r - 2)/3
Suppose 4*h**4 - 4*h**2 - 8*h**3 + 32*h**3 - 4*h**5 - 20*h**3 = 0. Calculate h.
-1, 0, 1
What is g in -2/13*g**4 + 0*g**2 + 0 + 0*g**3 + 0*g - 2/13*g**5 = 0?
-1, 0
Let b(h) be the third derivative of h**9/211680 + h**8/70560 - h**5/12 - 2*h**2. Let a(w) be the third derivative of b(w). Determine k, given that a(k) = 0.
-1, 0
Let l(h) be the second derivative of 2*h**7/21 + 2*h**6/5 - 4*h**5/5 - 16*h**4/3 + 32*h**2 - 2*h. Find a, given that l(a) = 0.
-2, 1, 2
Let y(h) be the second derivative of 0*h**2 - 1/189*h**7 - 1/54*h**4 + h + 0 - 1/45*h**6 - 1/30*h**5 + 0*h**3. What is z in y(z) = 0?
-1, 0
Let a be (98/18)/(74/6). Let x = a - 4/37. Factor 0 - x*q - 1/3*q**2.
-q*(q + 1)/3
Let n(a) be the third derivative of -a**8/1848 - 4*a**7/1155 - a**6/220 - 3*a**2 - 1. Determine x so that n(x) = 0.
-3, -1, 0
Let d(v) = v**3 + 3*v**2 - 26*v - 44. Let z be d(-6). Factor 0 + 1/3*b**3 - 1/3*b**z + 1/3*b**2 - 1/3*b.
-b*(b - 1)**2*(b + 1)/3
Factor 0*l - 700*l**4 - 3*l**2 - 24*l**3 + 685*l**4 + 6*l.
-3*l*(l + 1)**2*(5*l - 2)
Let y(z) be the third derivative of 0*z**6 + 1/15*z**5 - 1/105*z**7 + 0*z**4 + 2*z**2 - 1/3*z**3 + 0*z + 0. Find c such that y(c) = 0.
-1, 1
Let l be ((-2)/(-58))/(1/2). Let o = l + 23/87. Factor -1/3*k**2 + 2/3*k - o.
-(k - 1)**2/3
Let y be ((-4)/10*-2)/((-44)/(-10)). Solve -4/11*m**2 + 2/11*m**4 + 0*m + y + 0*m**3 = 0.
-1, 1
Let d(t) be the first derivative of -2*t**5/25 + 3*t**4/10 - 2*t**3/15 - 3*t**2/5 + 4*t/5 + 3. Let d(y) = 0. Calculate y.
-1, 1, 2
Let o(j) = 7*j - 4. Let v be o(4). Let 6*u**2 + v*u**4 + 3 - 21*u**4 + 12*u**2 - 12*u - 12*u**3 = 0. What is u?
1
Let g(z) be the third derivative of z**7/840 + z**6/240 + z**4/24 - 6*z**2. Let b(d) be the second derivative of g(d). Let b(a) = 0. What is a?
-1, 0
Let f(q) = q**4 + q**2 + 1. Let r(m) = -3*m**4 - 2*m**2 - 3. Let z(d) = -8*f(d) - 3*r(d). Suppose z(n) = 0. What is n?
-1, 1
Let w be 65/20 - 1/4. Factor -2*x**w + 3*x**4 - 7*x**5 + 3*x**5 + 3*x**5.
-x**3*(x - 2)*(x - 1)
Let u(h) be the first derivative of 2*h**4 - 10*h**3/3 + h**2 - 2. Find l such that u(l) = 0.
0, 1/4, 1
Let f(o) be the first derivative of 2*o**6/3 + 8*o**5/5 - 8*o**3/3 - 2*o**2 - 5. Solve f(l) = 0 for l.
-1, 0, 1
Let k be 3 + 0 - (-7 + 10). Let z(y) be the third derivative of 0*y**4 + 0*y - 2*y**2 + 1/40*y**6 + 1/70*y**7 + k*y**3 + 0*y**5 + 0. Let z(f) = 0. Calculate f.
-1, 0
Let f(j) be the first derivative of j**6/9 + 8*j**5/15 + j**4 + 8*j**3/9 + j**2/3 - 8. Let f(l) = 0. What is l?
-1, 0
Let m(q) be the second derivative of 0 + 1/66*q**4 - 2/11*q**2 - 1/11*q**3 + 3/110*q**5 + 1/165*q**6 - 4*q. Suppose m(v) = 0. What is v?
-2, -1, 1
Let j(z) be the first derivative of z**6/3 - 74*z**5/35 + 73*z**4/14 - 134*z**3/21 + 4*z**2 - 8*z/7 - 5. Let j(q) = 0. What is q?
2/7, 1, 2
Let i = -6 + 8. Factor 2*x**4 - 5*x**i + x - x**4 + 3*x**2 + x**5 - 2*x**3 + 1.
(x - 1)**2*(x + 1)**3
Let p(q) be the third derivative of -q**5/240 + q**4/96 + q**2. Solve p(l) = 0.
0, 1
Let z(r) = 2*r**3 + 7*r**2 + 6*r + 9. Let c be z(-3). Factor 2/7*n + 2/7*n**5 + 0*n**2 - 4/7*n**3 + 0 + c*n**4.
2*n*(n - 1)**2*(n + 1)**2/7
Let i(q) be the third derivative of q**5/12 + 5*q**4/12 + 5*q**3/6 + 30*q**2. Let i(j) = 0. What is j?
-1
Let l(a) be the first derivative of -a**5/15 + 3*a**4/4 - 7*a**3/3 + 19*a**2/6 - 2*a + 16. Factor l(f).
-(f - 6)*(f - 1)**3/3
Let d(r) = r. Let h be d(3). Solve 5*q**3 + 8*q**2 - 2*q**h + 5*q**3 + 2*q = 0.
-1/2, 0
Let o be ((-60)/40)/(-1 + (-1)/(-4)). Factor -5/2*v**o - 2*v - v**3 - 1/2.
-(v + 1)**2*(2*v + 1)/2
Let d = 11 - -10. Let s = d - 83/4. Suppose 0 - s*m**2 + 0*m**3 + 1/4*m**4 + 0*m = 0. What is m?
-1, 0, 1
Let q = -11 - -23. Let p be 102/180 + (-2)/q. Suppose 2/5*r**3 - 2/5*r + 0 - 2/5*r**2 + p*r**4 = 0. Calculate r.
-1, 0, 1
Suppose 1 = l - 1. Let f be (35/(-14))/(l/(-4)). Factor -5*q + f*q - q**3 - q**2 + 0*q + 2*q.
-q*(q - 1)*(q + 2)
Let o(y) be the third derivative of -y**7/125 + 17*y**6/750 + 9*y**5/250 - 2*y**4/25 + 4*y**3/75 - y**2. Determine t so that o(t) = 0.
-1, 2/7, 1/3, 2
Let z = 8 - 11. Let b(s) = -s**2 - 5*s - 1. Let o(i) = 2*i**2 + 14*i + 4. Let g(c) = z*o(c) - 8*b(c). Find w, given that g(w) = 0.
-1, 2
Let s(z) = -12*z**3 + 22*z**2 + 2*z - 8. Let j(y) = -12*y**3 + 22*y**2 + y - 9. Let l be 1 - (-2)/(-2)*-3. Let f(g) = l*j(g) - 5*s(g). Solve f(h) = 0.
-1/2, 1/3, 2
Factor -2*q**4 + 10*q**3 - 3*q**4 + 8*q + q**4 + 4*q**2 - 18*q**3.
-4*q*(q - 1)*(q + 1)*(q + 2)
Suppose 0 = g - 3 + 2. Let x(m) = 2*m + 2*m**2 - 5*m**2 + 0*m**2 - g. Let p(i) = -7*i**2 + 4*i - 2. Let r(s) = 2*p(s) - 5*x(s). Solve r(n) = 0 for n.
1
Let b be 1/2*0/(-38). Determine f, given that -4/9*f**2 + b*f - 2/9*f**4 + 2/3*f**3 + 0 = 0.
0, 1, 2
Let y(z) = 2*z**2 - 3*z. Let d be y(2). Let 0*r**2 - 4*r**d + 2*r + 3*r**2 - r = 0. What is r?
0, 1
Let r(a) be the second derivative of 1/6*a**3 + 7*a + 1/6*a**4 + 0*a**2 + 0 + 1/20*a**5. Factor r(d).
d*(d + 1)**2
Let t(q) = -3*q**2 + 5*q + 3. Let j(x) = -2*x**2 + 3*x + 2. Let o(m) = -5*j(m) + 3*t(m). Factor o(k).
(k - 1)*(k + 1)
Suppose 2*x - 5 = -3. Let r = 2 - 0. Factor 3 + 0 - 4*d + 2*d**r - x.
2*(d - 1)**2
Let x be (-2)/8 - (-26)/8. What is z in 0*z**x + 0*z**2 + 0*z + 0 - 2/5*z**4 = 0?
0
Let p(n) be the third derivative of n**5/12 - 5*n**4/12 + 5*n**3/6 + 9*n**2. Factor p(x).
5*(x - 1)**2
Let m = 2 + 0. Factor -5*g + 3*g + 0*g**4 - 2*g**4 + 0*g + 2*g**3 + 2*g**m.
-2*g*(g - 1)**2*(g + 1)
Determine b so that -10*b - 2*b**2 - 3*b**2 - 15 + 30*b = 0.
1, 3
Let o be 11 - (6/(-2) + 2). Let 6*v - 4 - 8*v**2 - o*v**3 + 4*v**4 + 6*v**5 + 6 + 2 + 0 = 0. Calculate v.
-1, -2/3, 1
Let b(s) be the first derivative of -s**6/2 + 9*s**5/5 - 3*s**4/2 - 2*s**3 + 9*s**2/2 - 3*s - 4. Solve b(z) = 0.
-1, 1
Find l such that 4/7*l**3 + 0 - 4/7*l + 2/7*l**4 - 2/7*l**2 = 0.
-2, -1, 0, 1
Let c be (3 - 1/1) + -1. Find s such that -4 + 4 - c - 5 - 9*s**2 + 15*s = 0.
2/3, 1
Let f(t) = -t**3 + 7*t**2 - t + 12. Let a be f(7). Let i(d) be the first derivative of 1 - 1/9*d**3 + 0*d**2 + 0*d + 1/6*d**4 - 1/15*d**a. Factor i(g).
-g**2*(g - 1)**2/3
Let j(c) be the first derivative of -6/11*c**2 + 18/11*c + 2/33*c**3 + 5. Factor j(d).
2*(d - 3)**2/11
Let v(s) be the third derivative of -4*s**7/105 + 2*s**6/15 - 3*s**5/20 + s**4/12 + s**3/2 - 2*s**2. Let k(h) be the first derivative of v(h). Factor k(a).
-2*(a - 1)*(4*a - 1)**2
Let l(w) be the first derivative of w**5/20 - 3*w**4/16 + w**3/6 + 6. What is c in l(c) = 0?
0, 1, 2
Suppose -5*l = -w - 3*l - 6, 4*w - 3*l = -4. Factor 2/7*y + 1/7*y**4 - 1/7 + 0*y**w - 2/7*y**3.
(y - 1)**3*(y + 1)/7
Let p(n) be the first derivative of n**7/49 + 4*n**6/105 - n**5/70 - n**4/21 + 5*n - 4. Let h(q) be the first derivative of p(q). Factor h(w).
2*w**2*(w + 1)**2*(3*w - 2)/7
Let d(f) be the third derivative of f**6/120 + f**5/24 - f**4/12 - f**3/6 + 3*f**2. Let u(y) be the first derivative of d(y). Let u(s) = 0. What is s?
-2, 1/3
Let r(d) be the second derivative of d**5/30 + 5*d**4/18 + 7*d**3/9 + d**2 + 5*d. Suppose r(c) = 0. What is c?
-3, -1
Factor 7*q**3 + 4*q**2 + 7*q**2 + 3*q**4 - 3*q**5 - 2*q**2 + 8*q**3.
-3*q**2*(q - 3)*(q + 1)**2
Factor 10/3*g**3 + 2/3*g**4 - 16/3*g - 2/3*g**5 - 2/3*g**2 - 8/3.
-2*(g - 2)**2*(g + 1)**3/3
Suppose 0 = -2*f + 3*p + 21, -f + 4*p = 6*p + 7. Suppose -f*w + b = 4*b - 3, -4*w = -5*b + 5. Let -63/2*v**3 + w + 16*v**2 - 2*v = 0. What is v?
0, 2/9, 2/7
Let g = 36 - 539/15. Let b(n) be the first derivative of -g*n**5 + 1/9*n**3 + 1 + 0*n**2 + 0*n**4 + 0*n. Suppose b(h) = 0. Calculate h.
-1, 0, 1
Factor -3/7*c**2 + 9/7 - 6/7*c.
-3*(c - 1)*(c + 3)/7
Let a(v) be the second derivative of v**5/70 + v**4/42 - 5*v. Factor a(p).
2*p**2*(p + 1)/7
Let u(b) be the second derivative of -5/3*b**3 + 4*b - 2*b**2 + 0 +