p**3 - 2/3*p**5 + 0.
-2*p**3*(p - 1)*(p + 1)/3
Let h(f) be the third derivative of -f**8/36960 - f**7/27720 - f**5/15 - 3*f**2. Let y(u) be the third derivative of h(u). Let y(n) = 0. Calculate n.
-1/3, 0
Let c(h) be the third derivative of h**6/480 - 7*h**5/240 - h**4/96 + 7*h**3/24 + 18*h**2. Find j, given that c(j) = 0.
-1, 1, 7
Let k(m) be the second derivative of 3*m**8/560 - m**7/140 - m**6/40 + m**5/20 - m**3/6 + 3*m. Let h(a) be the second derivative of k(a). Factor h(v).
3*v*(v - 1)*(v + 1)*(3*v - 2)
Let t(h) be the third derivative of 1/1512*h**8 + 0*h**4 - 5*h**2 - 1/945*h**7 + 0*h + 1/270*h**5 + 0*h**3 + 0 - 1/540*h**6. Let t(p) = 0. What is p?
-1, 0, 1
Suppose 3*o = -2*d + 7, o - 2*o + 4 = -d. Let j(t) be the first derivative of 1/5*t**6 + 4/15*t**o + 0*t**2 + 0*t - 1/10*t**4 + 2 - 8/25*t**5. Factor j(y).
2*y**2*(y - 1)**2*(3*y + 2)/5
Let w(b) be the second derivative of 1/60*b**4 + 0 + 1/30*b**3 + 0*b**2 - 1/100*b**5 - 1/150*b**6 - b. Solve w(p) = 0 for p.
-1, 0, 1
Let a(h) be the third derivative of -h**7/2940 - h**6/1260 + h**5/210 + h**3/2 - 5*h**2. Let l(x) be the first derivative of a(x). Let l(f) = 0. What is f?
-2, 0, 1
Let g = -30 + 61/2. Solve 0*s**2 + s**4 - g*s**5 - 1/2*s**3 + 0 + 0*s = 0 for s.
0, 1
Let i = 1861/12 + -155. Let q(x) be the second derivative of 1/3*x**3 + i*x**4 + 1/2*x**2 - x + 0. Let q(k) = 0. What is k?
-1
Suppose 3*k = -2*k. Suppose 4*d - 2*d - 14 = k. Factor -40*r**3 + 72*r**2 + d*r**4 - 32*r - 6 - 5 - 5.
(r - 2)**3*(7*r + 2)
Factor -4*u**3 + 10*u - 4*u**2 + 4*u**4 + 0 - 6*u + 0.
4*u*(u - 1)**2*(u + 1)
Let 11/2*g**2 - 9/2*g**3 - g + 0 = 0. Calculate g.
0, 2/9, 1
Let u(c) = -10*c**2 + 10*c + 5. Let l(j) = -9*j**2 + 11*j + 4. Let x(b) = -5*l(b) + 4*u(b). Factor x(g).
5*g*(g - 3)
Let 1/3*i**5 - i**4 + 0 - 1/3*i**2 + i**3 + 0*i = 0. What is i?
0, 1
Let o(z) be the first derivative of -z**5/240 + z**4/96 + z**3/12 + 7*z**2/2 - 1. Let b(k) be the second derivative of o(k). Factor b(v).
-(v - 2)*(v + 1)/4
Suppose -2*z - 18 = -4*z. Factor 15*j**2 + z*j**2 + 21*j**3 + 16*j**4 - 8*j**2 + 4*j - 7*j**4.
j*(j + 1)*(3*j + 2)**2
Let o(y) be the third derivative of -y**2 + 1/300*y**5 + 0*y**3 + 0 + 1/60*y**4 + 0*y - 1/600*y**6. Factor o(h).
-h*(h - 2)*(h + 1)/5
Let s(m) = 8*m**4 - 7*m**2 + 5. Let b(f) = f**4 - f**3 + f + 1. Let c(x) = -6*b(x) + 2*s(x). Factor c(n).
2*(n - 1)*(n + 1)**2*(5*n - 2)
Find c such that -1/3*c**2 + 0 + 1/3*c**5 + 2/3*c - c**3 + 1/3*c**4 = 0.
-2, -1, 0, 1
Factor -6/5*j + 2/5*j**2 + 0.
2*j*(j - 3)/5
Let v be (156/16)/(-13) + 1. Factor 0*i + 0 + v*i**4 - 1/2*i**3 + 1/4*i**2.
i**2*(i - 1)**2/4
Suppose -2*w + 5*w + 5*f - 21 = 0, -3*f + 1 = -4*w. Suppose -2*g - 3*c = -7*g + 6, -w*g + c = -3. Factor 4/5 + 6/5*k**2 + 2/5*k**g - 2/5*k**4 - 2*k.
-2*(k - 1)**3*(k + 2)/5
Let i(v) be the third derivative of -v**5/120 - v**4/8 + 7*v**3/12 + 2*v**2 - 27*v. Factor i(m).
-(m - 1)*(m + 7)/2
What is j in -6/11*j**3 - 2/11*j**4 - 2/11*j**2 + 4/11 + 6/11*j = 0?
-2, -1, 1
Suppose 9*f**3 + 9*f**3 + 62*f**2 - 110*f**2 + 32*f = 0. What is f?
0, 4/3
Suppose 5*n = 3*q - 27, -4*n - q - 20 = -3*q. Let p = n + 6. Suppose 2*j**4 + 4*j**p + 4*j**2 - 4*j - 6*j**4 - j**3 + j**5 + 0*j**5 = 0. What is j?
-1, 0, 1, 2
Let 0*s + 0 - 1/2*s**2 - 1/2*s**3 = 0. Calculate s.
-1, 0
Let j(n) be the third derivative of -n**5/12 + 5*n**4/72 + 5*n**3/9 + 10*n**2. Determine f so that j(f) = 0.
-2/3, 1
Let b(s) be the first derivative of s**5/10 - s**3 + 2*s**2 - 2*s + 3. Let z(i) be the first derivative of b(i). Factor z(w).
2*(w - 1)**2*(w + 2)
Let s(d) be the second derivative of d**5/10 - d**4/2 + 2*d**3/3 + 15*d. Find x such that s(x) = 0.
0, 1, 2
Let m = 25 + -10. Suppose 5*h + 0*h - m = 0. Let 6/7*s**h + 4/7 + 2*s + 16/7*s**2 = 0. Calculate s.
-1, -2/3
Let -4/13*g**5 + 4/13*g**3 + 0*g + 2/13 + 6/13*g**4 - 8/13*g**2 = 0. What is g?
-1, -1/2, 1
Let t(k) be the first derivative of -2/3*k**3 - 4*k**2 - 8*k + 9. Factor t(j).
-2*(j + 2)**2
Let g(l) = -l**3 - 3*l**2 + 5*l. Let y(c) = c**2 - 7*c + 5. Let v be y(6). Let j(p) = -p**3 + p**2 - p. Let u(i) = v*g(i) - 5*j(i). Find q such that u(q) = 0.
0, 1/3
Let v(x) be the second derivative of -x**5/50 + x**4/15 + x**3/15 - 2*x**2/5 - 6*x. Factor v(p).
-2*(p - 2)*(p - 1)*(p + 1)/5
Let q(z) = -z**3 + 35*z**2 - 18*z - 8. Let g(i) = i**3 - 23*i**2 + 12*i + 5. Let l(m) = 8*g(m) + 5*q(m). Factor l(o).
3*o*(o - 2)*(o - 1)
Let a be (3 + 3 - 2) + 1. Suppose a*x + 1 + 4 = 4*g, -4*x - 4 = -3*g. Solve 0 + 2/5*o**4 + 0*o - 2/5*o**3 + g*o**2 = 0.
0, 1
Let a(i) be the third derivative of -i**5/45 - i**4/3 + 5*i**2 + 8*i. Factor a(t).
-4*t*(t + 6)/3
Factor -40*a + 5*a**2 - 17*a + 245 - 13*a.
5*(a - 7)**2
Let c(d) be the first derivative of 2/21*d**3 - 1/42*d**4 - d - 1/7*d**2 + 2. Let r(i) be the first derivative of c(i). Factor r(j).
-2*(j - 1)**2/7
Let a(u) be the second derivative of -u**10/30240 - u**9/15120 - u**4/4 - 2*u. Let v(x) be the third derivative of a(x). Factor v(n).
-n**4*(n + 1)
Let j(o) be the first derivative of -5*o**6/6 + 2*o**5 - 10*o**3/3 + 5*o**2/2 - 14. Suppose j(w) = 0. Calculate w.
-1, 0, 1
Let j(i) be the third derivative of i**5/210 - i**4/7 + 12*i**3/7 + 22*i**2. Find l such that j(l) = 0.
6
Let w(p) be the first derivative of p**5/35 + 3*p**4/14 + 13*p**3/21 + 6*p**2/7 + 4*p/7 - 8. Factor w(r).
(r + 1)**2*(r + 2)**2/7
Let l(j) be the first derivative of -j**6/360 - j**5/180 - 2*j**2 + 5. Let u(y) be the second derivative of l(y). Factor u(t).
-t**2*(t + 1)/3
Let k(z) be the third derivative of z**9/1512 + z**8/840 - z**7/420 - z**6/180 + z**3/3 - 3*z**2. Let r(g) be the first derivative of k(g). Solve r(y) = 0.
-1, 0, 1
Let o = 11 - 6. Suppose 11 + 4 = o*i. Suppose j**2 + 0*j + 0*j**i - 1/2 - 1/2*j**4 = 0. What is j?
-1, 1
Let z(q) be the second derivative of 1/6*q**4 - 5*q + 0*q**2 + 0 + q**3. Factor z(i).
2*i*(i + 3)
Let s = 11323/4720 + 1/944. Solve -8/5*a + 16/5*a**3 + s*a**2 - 4/5 - 16/5*a**4 = 0 for a.
-1/2, 1
Let x(p) = p**2 - 7*p - 2. Let n be x(7). Let k = n + 4. Factor 2*o + 5*o**2 + o**2 - 4*o**3 - 6*o**4 + k*o.
-2*o*(o - 1)*(o + 1)*(3*o + 2)
Suppose 0 = 3*o - 3*o + 5*o. Let i(x) be the third derivative of 0 + x**2 + 1/240*x**5 + 1/32*x**4 + o*x + 1/12*x**3. Solve i(c) = 0.
-2, -1
Suppose -4*o + p + 12 = 0, -6*o + 11*o - 14 = p. Factor -1/3 + 2/3*s - 1/3*s**o.
-(s - 1)**2/3
Suppose 10 = 14*i - 12*i. Let d(c) be the first derivative of 0*c - 2/35*c**i + 2/21*c**3 - 1/14*c**4 + 0*c**2 + 1/21*c**6 + 1. Factor d(u).
2*u**2*(u - 1)**2*(u + 1)/7
Let w(u) = -6*u**4 + 12*u**3 - 21*u**2 + 9*u. Let i(v) = 5*v**4 - 12*v**3 + 20*v**2 - 10*v + 1. Let z(o) = -3*i(o) - 2*w(o). Factor z(l).
-3*(l - 1)**4
Let c(v) be the second derivative of -8/11*v**2 - v - 1/11*v**4 - 9/110*v**5 + 0 + 20/33*v**3. Factor c(y).
-2*(y + 2)*(3*y - 2)**2/11
Let a be (-4*21/(-28))/2. Factor -21/4*r + 9/4*r**2 + a.
3*(r - 2)*(3*r - 1)/4
Suppose 9*l = -3*l. Let d(i) be the second derivative of 0 + 0*i**2 + l*i**3 + 1/30*i**6 - 1/6*i**4 + 1/20*i**5 + 3*i. Find u, given that d(u) = 0.
-2, 0, 1
Factor 9/5*y**2 - 2/5 + 7/5*y.
(y + 1)*(9*y - 2)/5
Let t(k) be the first derivative of k**4/4 - k**3/3 - k**2/2 + k - 8. Suppose t(z) = 0. Calculate z.
-1, 1
Let o(j) be the second derivative of -11/24*j**3 - 17/80*j**5 + 7/16*j**4 + 1/24*j**6 - 2*j + 1/4*j**2 + 0. Factor o(f).
(f - 1)**3*(5*f - 2)/4
Let o(m) = -3*m + 3*m - 5 - 7*m**2 + 7*m**4. Let k(v) = -7*v**4 + v**3 + 8*v**2 + 6. Let x(f) = 5*k(f) + 6*o(f). Solve x(g) = 0.
-1, 0, 2/7
Let d = -127/4 + 389/12. Determine g so that d*g**2 + 1/3*g**3 - 1/3*g - 2/3 = 0.
-2, -1, 1
Let t be (8 - 3) + -2 + 0. Factor 0*a**3 + 6*a**3 + t*a**2 - 6*a**2 + 3*a**4 - 6*a.
3*a*(a - 1)*(a + 1)*(a + 2)
Find s, given that 9/4 - 3*s**5 + 27/4*s**4 + 21/2*s**3 - 15/2*s - 9*s**2 = 0.
-1, 1/4, 1, 3
Let h(b) be the second derivative of -b**7/5040 - b**6/720 - b**5/360 - 5*b**3/6 - 7*b. Let g(l) be the second derivative of h(l). Find n, given that g(n) = 0.
-2, -1, 0
Factor -4/13 - 2/13*r + 4/13*r**2 + 2/13*r**3.
2*(r - 1)*(r + 1)*(r + 2)/13
Factor 0*j**3 - j**2 + 590*j - 3*j**3 + 7*j**2 - 593*j.
-3*j*(j - 1)**2
Find p, given that 3/8 + 7/8*p**3 - 11/8*p**2 + 1/8*p = 0.
-3/7, 1
Let o(h) = h**3 + h**2 + h. Let p(x) = -5*x**4 + 22*x**3 - 23*x**2 + 12*x. Let t(q) = -2*o(q) + p(q). Find z