Solve -q - 1/5*q**i - 4/5*q**2 - 2/5 = 0.
-2, -1
Let m(w) be the first derivative of 2*w**5/45 - w**4/9 + 2*w**2/9 - 2*w/9 + 14. Let m(i) = 0. Calculate i.
-1, 1
Let y be (2 - 0) + (4 - 4). Let j(p) be the second derivative of 1/7*p**y + 1/105*p**6 + 0 - 2*p - 1/21*p**4 - 1/21*p**3 - 1/147*p**7 + 1/35*p**5. Factor j(a).
-2*(a - 1)**3*(a + 1)**2/7
Let n(i) = -i**2 + 11*i + 3. Let t be n(11). Suppose -2*d - 2*f + 10 = 0, 5*d - 4*f = 1 - t. Factor -2/5*m - 2/5*m**d + 4/5.
-2*(m - 1)*(m + 2)/5
Let s(d) be the first derivative of d**3/3 - 4*d**2 + 2*d - 1. Let v be s(8). Factor -6*i**v + 3*i + 7*i - 4 + i - i.
-2*(i - 1)*(3*i - 2)
Suppose -1 - 3 = 4*t. Let w = 3 - t. What is n in -2*n**5 - 6*n**3 + 8*n**w - n**2 - 2*n**4 + 3*n**2 = 0?
0, 1
Let t be ((-4)/(-6))/(2/39). Let y = t - 25/2. Factor 0 + 1/2*w**4 - y*w**3 + 0*w**2 + 0*w.
w**3*(w - 1)/2
Factor -3*n**5 - 2*n**5 - 17*n**3 + 8*n - 10 + 13*n**4 + 3*n**2 + 2*n**5 + 6.
-(n - 2)*(n - 1)**3*(3*n + 2)
Factor 1/7*j**4 + 0 - j**3 - 5/7*j + 11/7*j**2.
j*(j - 5)*(j - 1)**2/7
Let b(r) be the first derivative of -r**4/16 + r**2/8 - 3. Suppose b(t) = 0. Calculate t.
-1, 0, 1
Suppose 18 = -v - 2*v. Let y be v/27 - (-34)/72. Factor 1/4 + 0*p - y*p**2.
-(p - 1)*(p + 1)/4
Let d(j) = -12*j**4 + 8*j**3. Let n(f) = 8*f**4 - 5*f**3. Let s(h) = 5*d(h) + 8*n(h). Factor s(a).
4*a**4
Let y = 92 - 50. Let o be y/12*2/5. Suppose -1/5*r**5 + r**4 - 9/5*r**3 - 2/5*r + 0 + o*r**2 = 0. What is r?
0, 1, 2
Let d = -4827 + 168909/35. Let h = 10/7 + d. Factor -2/5*v**2 - h*v + 0.
-2*v*(v + 1)/5
Suppose 17*o + 20*o - 15*o + 12 + 6*o**2 = 0. What is o?
-3, -2/3
Let k(l) be the first derivative of -3 - 2/9*l**3 + 0*l - 1/12*l**4 - 1/6*l**2. Determine h so that k(h) = 0.
-1, 0
Let m be -3 + (5 - 0/(-3)). Let s(u) be the first derivative of 1/9*u**3 + 1/24*u**4 + 1/12*u**m + 0*u + 3. Determine f so that s(f) = 0.
-1, 0
Let y be ((-2)/8)/((-10)/24). Let h be 0/1 - (-2 - 0). Factor -1/5*k**h - y*k - 2/5.
-(k + 1)*(k + 2)/5
Let x(d) be the third derivative of d**7/140 + d**6/240 - d**5/40 - d**4/48 - 25*d**2. Solve x(g) = 0 for g.
-1, -1/3, 0, 1
Let v(z) be the first derivative of z**4/38 - z**2/19 + 3. Factor v(b).
2*b*(b - 1)*(b + 1)/19
Determine z, given that 0 - 3/2*z**2 + 3/2*z = 0.
0, 1
Let y(q) be the first derivative of q**7/70 - q**5/20 + 3*q**2/2 + 1. Let n(g) be the second derivative of y(g). Factor n(m).
3*m**2*(m - 1)*(m + 1)
Suppose -2*l = -l - 2. Suppose p**2 + 1 + p**4 - 1 + 0 + l*p**3 = 0. What is p?
-1, 0
Let o be (0/3)/((-8)/4 - -1). Let a(r) be the second derivative of 1/3*r**4 + o + 0*r**2 + 3*r + 1/10*r**5 + 1/3*r**3. Suppose a(j) = 0. What is j?
-1, 0
Suppose -9 + 23 = -h + 3*y, -5*y + 20 = -5*h. Let m be h/(-4) - (-95)/28. Find k such that 8/7*k**3 - 4*k**2 - 4/7 + 2*k**5 - m*k + 32/7*k**4 = 0.
-1, -2/7, 1
Suppose 9 = 6*x - 15. Factor 0*f + 0*f**2 - 2/3*f**3 - 2*f**x + 0.
-2*f**3*(3*f + 1)/3
Let p = -49 + 52. Let h(w) be the second derivative of 0 + 1/20*w**5 - 1/6*w**p - 1/2*w**2 + 1/12*w**4 + 3*w. Let h(n) = 0. What is n?
-1, 1
Let x be 5/(-15) - (-7)/3. Factor 2*q**3 + 2*q**2 + q**x + q**2.
2*q**2*(q + 2)
Let t(b) be the first derivative of -3*b**5/5 - 3*b**4/2 - b**3 + 4. Factor t(u).
-3*u**2*(u + 1)**2
Let j be -2*(2 + -5 - -1). Suppose -4*z = j*b, 2*b + b = 2*z - 15. Factor -1/4*a**2 + 0*a + 3/4*a**z + 0 + a**4.
a**2*(a + 1)*(4*a - 1)/4
Factor 2*y**3 - 63*y + 2*y**4 - 4*y**5 + 63*y + 2*y**5 - 2*y**2.
-2*y**2*(y - 1)**2*(y + 1)
Let f(g) = -g**2 - 8*g + 5. Let i be f(-9). Let c(b) = -b**3 - 4*b**2 - 2*b - 5. Let z be c(i). Find p, given that 3 + 3*p**2 - 5*p**2 - 4 + z*p**2 = 0.
-1, 1
Let l(w) be the second derivative of -w**6/6 - w**5/2 - 5*w**4/12 - 17*w. Factor l(n).
-5*n**2*(n + 1)**2
Let m(p) be the third derivative of p**5/30 - p**4/12 - p**2. Factor m(d).
2*d*(d - 1)
Let g(d) be the second derivative of -1/2*d**4 + 2*d - 1/30*d**6 - 2/3*d**3 - 1/5*d**5 - 1/2*d**2 + 0. Solve g(v) = 0.
-1
Let o(a) be the first derivative of a**7/30 + 2*a**6/15 + 11*a**5/60 + a**4/12 - 3*a**2 + 3. Let d(u) be the second derivative of o(u). Solve d(j) = 0 for j.
-1, -2/7, 0
Factor r**3 + 0*r**3 + 5*r**4 - 6*r**4.
-r**3*(r - 1)
Let n(a) be the first derivative of -7*a**4/4 - 2*a**3/3 - a**2 - a - 1. Let w be n(-1). Factor -2*g**3 + 3*g**2 - 3 + 3*g**2 - w*g + 5.
-2*(g - 1)**3
Let c(q) = -q**3 - 2*q**2 - q + 1. Let g be c(-2). Let r be (5/(-30))/(3/(-12)). Find t, given that -r*t**g + 0 + 2/3*t**2 - 2/3*t**4 + 2/3*t = 0.
-1, 0, 1
Let r(z) = z**3 - 4*z**2 + 2. Let w(j) = j**3 - 3*j**2 + 1. Let l(b) = -3*r(b) + 4*w(b). Let x(y) be the first derivative of l(y). Find a such that x(a) = 0.
0
Factor -12*m**2 + 19*m**3 + 2*m**3 + 6*m**3 + 6*m**2.
3*m**2*(9*m - 2)
Suppose -5*v + 23 = 2*m, 29 = 5*v - 6*m + 2*m. Let j = v - 3. Factor 4*y - 2*y + 2*y**j - 2*y**3 - 2*y**4 + 0*y**4.
-2*y*(y - 1)*(y + 1)**2
Let q = -27/4 + 41/6. Let d(t) be the first derivative of -1/16*t**4 + 0*t**2 + 1 + 0*t + q*t**3. Factor d(f).
-f**2*(f - 1)/4
Let y(t) = -10*t**3 + 5*t**2 - 22*t - 1. Let g(a) = -3*a**3 + 2*a**2 - 7*a. Let u be 72/15 - (-4)/(-5). Let o(q) = u*y(q) - 14*g(q). What is n in o(n) = 0?
1, 2
Let k(m) be the first derivative of m**6/2 + 9*m**5/5 + 3*m**4/2 - 2*m**3 - 9*m**2/2 - 3*m - 3. Determine w so that k(w) = 0.
-1, 1
Let q(w) = -w**3 + w. Let b(c) = c**3 + 3*c**2 - 1. Let d be b(-1). Let v be q(d). Let 1/2*l**2 + 1/2*l + v = 0. What is l?
-1, 0
What is r in 0 - 2/9*r + 2/9*r**2 = 0?
0, 1
Let s = -7 + 12. Factor -m**4 - 4*m**s + m**5 + 4*m**5.
m**4*(m - 1)
Find r such that -5 - r - 5*r**3 + 16*r - 1 - 4 = 0.
-2, 1
Let u(w) be the second derivative of w**6/105 - w**5/35 + w**4/42 - 3*w. Find i, given that u(i) = 0.
0, 1
Let l(h) = 2*h - 10. Let g(b) = -b**3 - b**2 + b + 7. Let k be g(0). Let o be l(k). Find m such that -3*m - 4*m**2 + o*m + 3*m**2 = 0.
0, 1
Let g(l) = -l**2 + 3*l. Let c be g(6). Let f = 30 + c. Find j such that -5*j**5 - 8*j**2 - f*j**3 - 8*j**4 - 2*j + 0*j + 3*j**5 = 0.
-1, 0
Let x(o) be the second derivative of -8/3*o**2 + 0 + 10*o - 4/9*o**3 - 1/36*o**4. Let x(h) = 0. Calculate h.
-4
Suppose -12 = 4*f + 8. Let b = 0 - f. Find t, given that 6*t**2 + 3*t**3 - 5*t**3 - 7*t**2 - 2*t + b*t**2 = 0.
0, 1
Let l = 3 + 0. Let z be 6*(l - 0)/63. Factor -z*u**4 - 2/7*u**3 + 0 + 2/7*u**2 + 2/7*u.
-2*u*(u - 1)*(u + 1)**2/7
Factor 0*g - 4/3*g**3 + 4*g**2 - 16/3.
-4*(g - 2)**2*(g + 1)/3
Let r = 2 + 4. Factor r*z**3 - 8*z + 15*z**2 - 7*z**4 - 8*z**4 + 2*z.
-3*z*(z - 1)*(z + 1)*(5*z - 2)
Let v be (-1 + 336/9)/(-1). Let a = -36 - v. Factor 0*q**2 + 0 + 0*q**4 - 2/3*q**3 + a*q**5 + 1/3*q.
q*(q - 1)**2*(q + 1)**2/3
Let x(v) be the first derivative of 2*v**5/5 - v**4/2 - 10*v**3/3 - 3*v**2 - 6. Factor x(c).
2*c*(c - 3)*(c + 1)**2
Let s(j) = 3*j + 4. Let p be s(4). Let v = p - 63/4. Factor 1/4*q**2 - v + 0*q.
(q - 1)*(q + 1)/4
Let d(k) be the third derivative of 2*k**7/35 + k**6/30 - k**5/5 - k**4/6 + 8*k**2. Factor d(g).
4*g*(g - 1)*(g + 1)*(3*g + 1)
Let j(x) = 3*x**4 - 3*x**3 + x**2 - x. Let k(z) = -z**4 + z**3. Let u(v) = -j(v) - 4*k(v). Factor u(a).
a*(a - 1)**2*(a + 1)
Suppose -2 + 7 = h, c - 19 = 2*h. Factor -3*n**4 + 26*n - 9*n**2 - c*n - n**3 - 8*n**3.
-3*n*(n + 1)**3
Let h = -3 + 5. Let -u + 5*u + 4 + 2*u + 2*u**h = 0. What is u?
-2, -1
Factor 2/7*m + 4/7 + 2/7*m**4 - 6/7*m**2 - 2/7*m**3.
2*(m - 2)*(m - 1)*(m + 1)**2/7
Let w(o) = -3*o**2 + 4*o + 7. Let f(u) = -3*u**2 + 5*u + 6. Let n(d) = 4*f(d) - 3*w(d). Find r such that n(r) = 0.
-1/3, 3
Let d(f) = -5*f**5 + 4*f**4 + 14*f**3 - 5*f - 4. Let i(n) = 5*n**5 - 3*n**4 - 13*n**3 + 5*n + 3. Let x(u) = 3*d(u) + 4*i(u). Factor x(t).
5*t*(t - 1)**2*(t + 1)**2
Let m be (1/(-5))/((-329)/470). Factor -4/7*f + 2/7 + m*f**2.
2*(f - 1)**2/7
Let z(r) be the third derivative of r**6/300 + r**5/50 - 4*r**3/15 + 46*r**2. Factor z(j).
2*(j - 1)*(j + 2)**2/5
Let t(i) be the third derivative of -i**6/360 + i**4/24 + i**3/6 - 4*i**2. Let d(g) be the first derivative of t(g). Suppose d(j) = 0. Calculate j.
-1, 1
Let g(y) = -y**3 - y**2 - y. Let l(t) = -7*t**3 - 13*t**2 - 7*t. Let i(q) = 18*g(q) - 2*l(q). Solve i(o) = 0.
0, 1
Let x(u) = 2*u + 4 + 3 - 3*u. Let q be x(5). Let j(z) = 4*z**3 - 2*z**2 - 4*z - 2. Let o(p) = -p**4 - p**2. Let s(g) = q*o(g) - j(g). Find b such that s(b) = 0.
-1, 1
Let d(v) = 