e j(c) = 0. Calculate c.
-1, 0
Let p(d) be the second derivative of -d**7/735 + d**5/210 - 2*d**2 + 4*d. Let y(c) be the first derivative of p(c). Factor y(i).
-2*i**2*(i - 1)*(i + 1)/7
Suppose 2*b - c = 1, b - 5*c = -0*b - 13. Factor 3/4*m + 1/4*m**b + 1/2.
(m + 1)*(m + 2)/4
Let j(q) be the third derivative of -1/120*q**6 + 0*q + 0 + 0*q**4 - 1/168*q**8 - 1/30*q**5 + 1/42*q**7 + 0*q**3 - 7*q**2. Find y such that j(y) = 0.
-1/2, 0, 1, 2
Find q, given that 1/5*q**2 + 0*q - 1/5 = 0.
-1, 1
Let l be (9/(36/10))/(15/9). Let d = -31/3 + 133/12. Find q, given that -d*q - 3/4*q**4 - 3/4*q**5 + 3/2*q**2 + l*q**3 - 3/4 = 0.
-1, 1
Suppose 65 = w - 5*s, 0 = -3*s - 3 - 9. Let h be (30/w)/(1*3). Factor -2/9*a - 2/9*a**2 + 0 + h*a**4 + 2/9*a**3.
2*a*(a - 1)*(a + 1)**2/9
Let u = -4 - -11. Suppose 3 = -r + 2*b, 5*r + 2*b = u*b - 5. Factor -5/4*i**3 - 7/4*i**2 + 2*i + r.
-(i - 1)*(i + 2)*(5*i + 2)/4
Let s(b) be the first derivative of 2/3*b - 1 - 4/3*b**2 + 2/3*b**3. Factor s(x).
2*(x - 1)*(3*x - 1)/3
Let r(q) = q**5 + 25*q**4 - 41*q**3 + 23*q**2 - 8*q + 5. Let f(t) = -2*t**5 - 38*t**4 + 62*t**3 - 34*t**2 + 12*t - 8. Let h(w) = 5*f(w) + 8*r(w). Factor h(m).
-2*m*(m - 2)*(m - 1)**3
Let x(y) be the third derivative of -y**5/90 - 2*y**4/9 - y**2. Factor x(d).
-2*d*(d + 8)/3
Let a(b) be the second derivative of 0*b**3 + b - 1/20*b**5 + 1/12*b**4 + 0 + 0*b**2. Factor a(m).
-m**2*(m - 1)
Let f(d) be the first derivative of d**5/16 + d**4/24 + 3*d - 7. Let h(s) be the first derivative of f(s). Suppose h(i) = 0. What is i?
-2/5, 0
Let r(o) = -o**2 - 3*o + 2. Let w be r(1). Let k be w/(-5)*(-15)/(-21). Factor -4/7*x**2 - k*x**3 + 4/7 + 2/7*x.
-2*(x - 1)*(x + 1)*(x + 2)/7
Let s(d) = -3*d**5 - 6*d**4 - 15*d**3 + 12*d**2 + 6*d + 6. Let v(o) = -o**4 + o**3 + o - 1. Let c(j) = -s(j) - 6*v(j). Factor c(g).
3*g*(g - 1)*(g + 1)*(g + 2)**2
Let v(q) be the third derivative of 1/40*q**6 + 2*q**2 + 0 - 1/84*q**8 + 1/42*q**7 + 0*q**3 + 1/24*q**4 + 0*q - 1/12*q**5. Determine k so that v(k) = 0.
-1, 0, 1/4, 1
Let z(y) be the third derivative of y**10/45360 - y**9/9720 + y**8/6048 - y**7/11340 + y**4/3 - y**2. Let m(r) be the second derivative of z(r). Factor m(n).
2*n**2*(n - 1)**2*(3*n - 1)/9
Suppose 0 = -3*v - 2*q + 16, 4*v - 5*q - 1 + 18 = 0. Determine k so that -v*k**3 + 2*k**5 - 7*k + 4*k + 3*k = 0.
-1, 0, 1
Let c be ((-22)/(-8))/((-3)/12). Let b be (c - -6)*(-8)/10. Let p**5 - 2*p**3 - 2/3*p**2 + 1/3*p**b + p + 1/3 = 0. What is p?
-1, -1/3, 1
Let s be ((-4)/(-6))/((-3)/(45/(-40))). Solve -s*t**5 - 1/4*t + 0*t**2 + 0 + 1/2*t**3 + 0*t**4 = 0 for t.
-1, 0, 1
Suppose -28*j + 51 = -5. Factor 3/4*i**3 + 3/4*i**4 + 0 + 0*i + 1/4*i**5 + 1/4*i**j.
i**2*(i + 1)**3/4
Let x(l) be the third derivative of l**5/270 + l**4/18 + l**3/3 + 4*l**2. Let x(s) = 0. Calculate s.
-3
Suppose 20 = 5*m, 2*d - m - 4*m = -12. Factor -6*r - d - 3*r**2 - 1/2*r**3.
-(r + 2)**3/2
Let h(u) = 3*u**2 + u + 10. Let d(v) = v**2 + 3. Let x(g) = 7*d(g) - 2*h(g). Factor x(j).
(j - 1)**2
Let u(w) be the second derivative of w**6/1440 + w**5/160 + w**4/48 - 5*w**3/6 + 6*w. Let s(z) be the second derivative of u(z). Let s(i) = 0. What is i?
-2, -1
Let v be (-7)/(-3)*(-2)/(-21). Factor 2/9*d**3 - v*d - 4/9 + 4/9*d**2.
2*(d - 1)*(d + 1)*(d + 2)/9
Let s(c) = -c**3 + 9*c**2 - 8*c - 5. Let x be s(8). Let k be 32/12*x/(-20). Factor 2/3*u - k*u**2 + 2/3*u**4 - 2/3*u**3 + 0.
2*u*(u - 1)**2*(u + 1)/3
Let n be 4*(39/(-12) + 2). Let h be (8/n)/((-14)/35). Factor 1/3*v**5 + 0*v**2 + 0*v + 0 - 1/3*v**3 + 0*v**h.
v**3*(v - 1)*(v + 1)/3
Determine l so that -3/4*l**4 + 3/4*l**2 + 1/4*l**5 + 1/4*l**3 + 0 - 1/2*l = 0.
-1, 0, 1, 2
Find m such that -1/4*m**2 - 1/8*m**3 - 1/8*m + 0 = 0.
-1, 0
Let o(r) = -2*r - 8. Let u be o(-6). Let d = 4 + -2. Solve p**4 + p**u - p**4 - p - 5*p**2 + 4*p**d + p**3 = 0.
-1, 0, 1
Let q(w) = -w - 6. Let n be q(-9). Factor -3/5*p**3 + n*p + 6/5 + 9/5*p**2 - 3/5*p**4.
-3*(p - 2)*(p + 1)**3/5
Solve 2/11 + 4/11*h + 2/11*h**2 = 0 for h.
-1
Let q = -47 + 143/3. Let w be 1/(1*(-3)/(-2)). Suppose q*c**3 - 2/3*c - 2/3*c**2 + w*c**4 + 0 = 0. Calculate c.
-1, 0, 1
Let b be 7/3 - 8/(-12). Let 0*g + 0 + 6*g**b + 4/3*g**2 + 14/3*g**4 = 0. Calculate g.
-1, -2/7, 0
Factor 91*h**3 + 89*h**3 - 324*h**4 + 22*h**2 - 43*h**2 + 16*h + 149*h**2.
-4*h*(h - 1)*(9*h + 2)**2
Let b(q) = 2*q - 9. Let z(g) = -g + 3. Let p be z(-3). Let s be b(p). Find x, given that x**3 + 2*x + 0*x**3 - s*x**2 + 0*x**3 = 0.
0, 1, 2
Factor -1 - 4*f - 3*f**2 + f**2 + 6*f + 13.
-2*(f - 3)*(f + 2)
Let s(a) = -12*a**4 + a**3 + 7*a**2 - 7. Let q(k) = 6*k**4 - 3*k**2 + 3. Let x(w) = 7*q(w) + 3*s(w). Let x(j) = 0. What is j?
-1/2, 0
Let i(v) be the third derivative of v**5/60 + v**4/24 - v**3/3 + 7*v**2. Factor i(h).
(h - 1)*(h + 2)
Let x(t) = 3*t + 6. Let n be x(-4). Let i = n - -9. Solve -i*g**2 - 3/2*g**4 + 0 + g + 1/4*g**5 + 13/4*g**3 = 0 for g.
0, 1, 2
Let r(f) be the third derivative of 0*f - 4*f**2 + 1/75*f**5 + 1/10*f**3 + 13/120*f**4 + 0. Factor r(g).
(g + 3)*(4*g + 1)/5
Let d be -6*(-1 + 2/4). Suppose -d*c = c. Factor c - 1/2*o**2 - 1/2*o.
-o*(o + 1)/2
Let t(q) be the second derivative of -q**7/49 - q**6/15 + q**5/7 + 5*q**4/21 - q**3/3 - 3*q**2/7 + 33*q. Let t(r) = 0. What is r?
-3, -1, -1/3, 1
Let w = 17 + -8. Suppose k - 5 = -2. Factor -6*l**2 + l + k + 14*l**2 - w*l - 1.
2*(2*l - 1)**2
Factor 128/9 + 32/3*k + 8/3*k**2 + 2/9*k**3.
2*(k + 4)**3/9
Let y(d) = -d**2 + d + 2. Let i be y(0). Factor 4*h**i - 8*h**2 + 9*h + 7*h**2.
3*h*(h + 3)
Let k(s) be the first derivative of 2/9*s**3 - 2/15*s**5 - 1/3*s**2 + 0*s - 1 + 1/6*s**4. What is a in k(a) = 0?
-1, 0, 1
Determine r so that 1469/5*r - 338/5 + r**5 - 1796/5*r**2 + 542/5*r**3 + 118/5*r**4 = 0.
-13, 2/5, 1
Let w = -47 - -17. Let c be (-7)/6 + w/(-20). Solve -1/3*h**3 + c*h**2 + 0 - 1/3*h**4 + 1/3*h = 0.
-1, 0, 1
Let y(k) = 2*k**2 - k + 1. Let c be (-1)/2 + (-5)/(-2). Let v(z) = -3*z**2 + 0*z**2 + 2*z**2 - z. Let m(q) = c*y(q) + 2*v(q). Factor m(p).
2*(p - 1)**2
Let b(z) be the third derivative of -3*z**2 + 1/60*z**5 + 0 + 2/3*z**3 - 1/6*z**4 + 0*z. Solve b(v) = 0 for v.
2
Factor -2*a**3 + 3*a**2 + 7*a**2 + 6*a**2 + 16*a + 6*a**3.
4*a*(a + 2)**2
Let l(v) be the second derivative of -v**7/3360 - v**6/720 - v**5/480 - 11*v**3/6 - 3*v. Let m(g) be the second derivative of l(g). What is b in m(b) = 0?
-1, 0
Let j = 4 - -4. Let x be (-3 + j)/(10/4). Let 1/4*w**4 + 1/2*w**3 - 1/4*w**x - 1/2*w**5 + 0 + 0*w = 0. Calculate w.
-1, 0, 1/2, 1
Let m = -10 + 23. Determine w, given that 5*w**2 - 39*w**4 - 40*w**3 - m*w**2 + 3*w**4 - 14*w**4 = 0.
-2/5, 0
Let n(b) be the second derivative of -b**5/18 + 2*b**4/27 + b**3/27 - 2*b. Factor n(d).
-2*d*(d - 1)*(5*d + 1)/9
Let u(a) = -a**3 - 9*a**2 + 2. Suppose -3*k - 45 = 2*k. Let n be u(k). Factor -2/9*o**4 - 16/9 + 14/9*o**3 + 40/9*o - 4*o**n.
-2*(o - 2)**3*(o - 1)/9
Let z(v) be the third derivative of -v**7/210 + v**6/15 - 2*v**5/5 + 4*v**4/3 + 5*v**3/6 + 2*v**2. Let o(u) be the first derivative of z(u). Factor o(r).
-4*(r - 2)**3
Let a(l) = -l**2 - 31*l - 146. Let x be a(-25). Factor 0*f + 0 + 0*f**2 + 2/5*f**3 - f**x.
-f**3*(5*f - 2)/5
Let a(w) be the first derivative of 2*w**3/9 + 2*w**2/3 + 2*w/3 + 8. What is f in a(f) = 0?
-1
Let m = -1 + 4. Factor -y**5 + 3*y**3 - y**m - y**5.
-2*y**3*(y - 1)*(y + 1)
Let y(p) = 2*p**2 + 30*p + 6. Let d(o) = o. Let j(n) = 44*d(n) - 2*y(n). Factor j(s).
-4*(s + 1)*(s + 3)
Let i(c) = -c**3 + 7*c**2 - 8*c + 7. Let g be i(6). Let z = -5 - g. Factor -2/7*d**2 + 0 + z*d.
-2*d**2/7
Let m = -31 + 33. Solve 2*z**3 + 2*z**m + 0 + 2/3*z + 2/3*z**4 = 0.
-1, 0
Let j(z) be the second derivative of 1/120*z**5 + 1/12*z**3 + 1/12*z**2 + 3*z + 0 + 1/24*z**4. Let j(g) = 0. What is g?
-1
Let f = 383/570 - 1/190. What is l in 0 + f*l**3 - 2*l**2 + 4/3*l = 0?
0, 1, 2
Let i = -77 - -141. Let a be i/(-56)*7/(-3). Factor -8*t + a + 6*t**2.
2*(3*t - 2)**2/3
Factor -3*j**3 + 4*j - 4*j**5 - 8*j**4 + 4*j**4 + 4*j**2 + 3*j**5 + 0*j**5.
-j*(j - 1)*(j + 1)*(j + 2)**2
Let z(i) be the first derivative of -5*i**4/48 - i**3/2 - i**2/2 + 5*i - 3. Let y(l) be the first derivative of z(l). Factor y(r).
-(r + 2)*(5*r + 2)/4
Factor -3/2*g**2 + 3/4*g**3 - 15*g - 18.
3*(g - 6)*(g + 2)**2/4
Let f be ((-1 - 0)/(-1))/2. Factor 0*z + 1/2*z**2 - f*z**3 + 0.
-z**2*(z - 1)/2
Let v(l