et u be 3 - 2 - (-113)/218. Let r = -2/109 + u. Factor 1/4*c**5 + 0 - c**2 + 1/4*c - c**4 + r*c**3.
c*(c - 1)**4/4
Let v(d) be the second derivative of 1/15*d**3 - 1/105*d**7 + 0*d**5 - d - 2/75*d**6 + 0*d**2 + 0 + 1/15*d**4. Factor v(w).
-2*w*(w - 1)*(w + 1)**3/5
Let v(u) be the second derivative of 1/18*u**4 + 0*u**2 - 3*u + 0 - 1/9*u**3. Solve v(c) = 0.
0, 1
Factor 416*x**4 - 4*x**5 - 16 + 13*x - 392*x**4 - 32*x**3 - 8*x**2 + 23*x.
-4*(x - 4)*(x - 1)**3*(x + 1)
Let f(s) = 5 - 3*s + s**2 + 0*s**2 - 3*s. Let v be f(6). Find w, given that w + 4*w**3 - 4*w - 3*w + 4*w - 2*w**v = 0.
-1, 0, 1
Let u(a) be the third derivative of 2*a**7/735 - a**6/105 - a**5/105 + a**4/21 - 9*a**2. Factor u(k).
4*k*(k - 2)*(k - 1)*(k + 1)/7
Let k(q) = 3*q**2 + 3*q. Let n(f) = f + 14*f + 16*f**2 + 5 - 6. Let s(w) = 33*k(w) - 6*n(w). Suppose s(y) = 0. Calculate y.
-2, -1
Suppose 2*r + 2*r + 3*u - 14 = 0, 5*r = 5*u. Let a(i) be the first derivative of -i**r + 5/6*i**6 - 7/5*i**5 + 0*i - 1 + 7/3*i**3 - 3/4*i**4. Factor a(j).
j*(j - 1)**2*(j + 1)*(5*j - 2)
Let u(d) be the second derivative of 0 + 0*d**4 + 0*d**2 + 1/6*d**5 - 5*d + 0*d**3 + 5/18*d**6. Factor u(x).
5*x**3*(5*x + 2)/3
Let b(w) be the third derivative of 4*w**7/945 - 7*w**6/540 - w**5/135 + 16*w**2. Factor b(l).
2*l**2*(l - 2)*(4*l + 1)/9
Let s(w) be the second derivative of w**6/50 + 3*w**5/20 + w**4/5 - 30*w. Suppose s(r) = 0. What is r?
-4, -1, 0
Let z(f) be the first derivative of f**3/3 + f**2 + 11. Solve z(m) = 0.
-2, 0
Let h(d) be the third derivative of d**6/24 - d**5/4 + 5*d**4/12 + 24*d**2. Find n, given that h(n) = 0.
0, 1, 2
Suppose 2*n + 10 = -4*t, t - 5*n = 5 + 20. Let b(z) be the third derivative of 1/60*z**5 + z**2 + 0 + t*z**4 - 1/6*z**3 + 0*z. Factor b(p).
(p - 1)*(p + 1)
Let b be 3/(-1) - -2*(-78)/(-36). Let -14/3*u - b*u**3 - 4/3 + 4/3*u**4 - 16/3*u**2 + 2/3*u**5 = 0. Calculate u.
-1, 2
Let h(w) be the first derivative of -w**3/7 + 3*w/7 + 12. Find a such that h(a) = 0.
-1, 1
Let n = -24 + 20. Let u be n/6 - (-22)/24. Suppose -u*m**5 - m**2 + 0 - 3/2*m**3 - m**4 - 1/4*m = 0. What is m?
-1, 0
Let s be 5*((-72)/(-15))/(-4). Let a(y) = -4*y**5 - 2*y**4 + 8*y**3. Let u(x) = 9*x**5 + 5*x**4 - 17*x**3. Let w(i) = s*u(i) - 13*a(i). Factor w(g).
-2*g**3*(g + 1)**2
Let x be -3 + (-33)/(-6) + -2. Find w such that 1/2*w**2 + x + w = 0.
-1
Let k = 11 - 7. Suppose 0 = -k*h - 3*s + 14, h + 3*s - 12 = -4. What is o in -2 + 12*o - 8*o**5 - 2*o**3 - 16*o**2 + 18*o**4 - h*o**3 + 0*o**5 = 0?
-1, 1/4, 1
Let l = 22 - 16. Let c(y) = 2 - 1 + 3*y**2 + y**2 + 2*y. Let m(p) = 3*p**2 + 2*p + 1. Let s(r) = l*m(r) - 4*c(r). Factor s(i).
2*(i + 1)**2
Let f be ((-11)/44)/((-1)/36). Factor -4*d + 6*d**2 + 5/2*d**4 + f*d**3 + 0.
d*(d + 2)**2*(5*d - 2)/2
Let h(k) be the third derivative of -7*k**6/120 + k**5/30 + 6*k**2. Factor h(m).
-m**2*(7*m - 2)
Let z = 2 - -1. Let d = 6 - z. Determine f, given that d*f**2 + 4 - 2 - f**4 + 4*f + f - f**3 = 0.
-1, 2
Let u(f) = -f**2 + f. Let v(m) = -3*m**2 + 3*m. Suppose 14 = -3*y + 2*q + 3*q, -2*y = 3*q - 16. Let c(l) = y*v(l) - 9*u(l). Factor c(o).
3*o*(o - 1)
Let b be (2/3)/(7/(-3486)). Let h = 1668/5 + b. Factor 8/5 + h*w + 2/5*w**2.
2*(w + 2)**2/5
Let p(a) be the third derivative of a**5/90 + a**4/9 - 5*a**3/9 + 10*a**2. Factor p(s).
2*(s - 1)*(s + 5)/3
Let b(o) be the second derivative of o**5/70 - o**4/42 - o**3/21 + o**2/7 - 8*o. Factor b(t).
2*(t - 1)**2*(t + 1)/7
Let t be ((-5)/10)/((-2)/8). Suppose 0 = 5*p - 4 - 11. Find n such that -2/7*n + 2/7*n**p + 2/7 - 2/7*n**t = 0.
-1, 1
Suppose n + 3*r - 27 = 0, -5*r = 8 - 3. Suppose -4*q + 2*q = -n. Suppose -8*b + 51*b**2 - 3*b**3 - 39*b**4 - 12 + 0*b**4 - 4*b + q*b**5 = 0. What is b?
-1, -2/5, 1, 2
Factor 40*z + 141*z**2 + 51*z**2 - 45*z**3 - 22*z**2.
-5*z*(z - 4)*(9*z + 2)
Let j be 423/36 + 21/(-12). Suppose -2/3*b + 0 - 6*b**4 - 14/3*b**2 - j*b**3 = 0. What is b?
-1, -1/3, 0
Let j(b) be the first derivative of -b**3/12 - b**2/2 + 28. Determine y so that j(y) = 0.
-4, 0
Let r(x) be the second derivative of x**7/1260 + x**6/360 - x**4/2 + 7*x. Let p(k) be the third derivative of r(k). Factor p(j).
2*j*(j + 1)
Suppose -111 = -4*d - 3. Suppose -4*y = -5*v - d, -5*y + 6*y + v = 0. Determine u, given that -4/7*u**2 - 2/7*u**y + 2/7*u + 4/7 = 0.
-2, -1, 1
Let b be 0 - (-8 - -1 - 1). Let o = -4 + b. Factor 2*y**2 - 3*y**3 - 2*y**2 + o*y**3.
y**3
Suppose 0 = -4*v + 40 - 32. Suppose 0 = -0*l - l. Find p such that l - 2/7*p**5 + 6/7*p**4 + 2/7*p**v - 6/7*p**3 + 0*p = 0.
0, 1
Let h(y) be the second derivative of y**5/5 - 4*y**4/3 + 10*y**3/3 - 4*y**2 - 3*y. Find c such that h(c) = 0.
1, 2
Let c(r) = -3*r**2 + 5*r - 7. Let p(k) = -3 + 0*k + k**2 - 2*k**2 + 2*k. Let i(j) = -2*c(j) + 5*p(j). Factor i(l).
(l - 1)*(l + 1)
Let 30/11*w**2 + 0 + 40/11*w**4 - 4/11*w - 6*w**3 = 0. Calculate w.
0, 1/4, 2/5, 1
Solve -5/2*a + 3/2*a**2 + 1/2*a**4 + 5/2*a**3 - 2 = 0 for a.
-4, -1, 1
Let f(u) be the first derivative of 3*u**5/10 + 3*u**4/8 - 2*u**3 - 3*u**2 + 31. Factor f(s).
3*s*(s - 2)*(s + 1)*(s + 2)/2
Let v = -63 + 65. Suppose 3*f - 30 + 9 = 0. Solve 9*r**2 + 1 - 3 - f*r**v = 0.
-1, 1
Let j = -10 - -13. Let z be 22/30 + (-2)/5. Factor -z - 5/3*k - 7/3*k**2 - k**j.
-(k + 1)**2*(3*k + 1)/3
Let w(u) = -2*u + 2. Let q be w(-2). Suppose q*a - a - 31 = -4*g, 8 = -4*a + 5*g. Solve -i**3 - 2*i + a*i**3 - 1 - 1 + 10*i**2 - 8*i**3 = 0 for i.
-1/3, 1
Let l(q) be the first derivative of 3/5*q + 1 + 1/5*q**3 - 3/5*q**2. Factor l(k).
3*(k - 1)**2/5
Let z(n) = n**3 + 5*n**2 + 2*n - 2. Let c be z(-3). Suppose -f + c = f. What is i in 2/3*i**3 + 2/3*i**f + 0*i**2 + 0*i + 4/3*i**4 + 0 = 0?
-1, 0
Let y(o) be the second derivative of 5*o**7/42 - 2*o**6/3 + 5*o**5/4 - 5*o**4/6 - 15*o. Let y(d) = 0. What is d?
0, 1, 2
Let i(s) be the second derivative of s**5/360 - s**3/36 + s**2/2 - 5*s. Let c(g) be the first derivative of i(g). Find q, given that c(q) = 0.
-1, 1
Suppose i - 2*i**2 + 5*i - 10*i**5 - 1 + 18*i**5 + 3 - 14*i**3 = 0. What is i?
-1, -1/2, 1
Factor -2/3*j**4 + 0*j - 2/3*j**2 + 0 + 4/3*j**3.
-2*j**2*(j - 1)**2/3
Let v be (64/9)/(-4) - -2. Let g(i) be the first derivative of 0*i - 2 + 1/3*i**4 + v*i**3 - 2/15*i**5 - 2/3*i**2. Solve g(r) = 0 for r.
-1, 0, 1, 2
Suppose -9*q - 513 = -540. Find f such that 2/3*f - 2/3*f**2 + 2/3 - 2/3*f**q = 0.
-1, 1
Let c(y) be the first derivative of 2*y**3/33 - 4*y**2/11 + 8*y/11 + 2. Let c(n) = 0. What is n?
2
Suppose -2*r - 2*n = -0*n - 12, 2*r + 5*n = 27. Let a be (14/4)/r + -1. Factor 2*y**2 + a*y**3 + 0 + y**4 + 1/2*y.
y*(y + 1)**2*(2*y + 1)/2
Let i = -1004 + 1007. What is g in 2/5*g**i + 2/5*g**2 + 0*g + 0 = 0?
-1, 0
Let d be ((-2)/(-4))/(8/32). Let o = -104 - -316/3. What is c in o*c - 2/3 - 2/3*c**d = 0?
1
Let p(t) be the third derivative of 1/60*t**4 + 0 + 0*t**3 + 0*t + t**2 + 1/150*t**5. Suppose p(d) = 0. Calculate d.
-1, 0
What is f in -2/5*f**3 - 6/5*f - 2*f**2 + 18/5 = 0?
-3, 1
Let s = -656 + 1970/3. Solve -1/3*q**2 + s*q + 1 = 0.
-1, 3
Let y(w) = -4*w**3 + 12*w - 2. Let m(p) = 3*p**3 + p**2 - 11*p + 2. Let r = -8 - -13. Let c(u) = r*y(u) + 6*m(u). Find v, given that c(v) = 0.
1
Let f(w) be the first derivative of -w**7/840 + w**6/160 - w**5/80 + w**4/96 + 3*w**2 + 5. Let h(y) be the second derivative of f(y). Factor h(z).
-z*(z - 1)**3/4
Let -20/3*z + 20/3*z**3 + 0 - 4/3*z**4 + 4/3*z**2 = 0. What is z?
-1, 0, 1, 5
Let h(i) be the third derivative of 1/6*i**3 + 0*i**5 - i**2 - 1/48*i**4 + 0 + 1/720*i**6 + 0*i. Let q(v) be the first derivative of h(v). Factor q(d).
(d - 1)*(d + 1)/2
Let p(j) be the third derivative of -j**7/210 - j**6/120 + j**5/30 - 13*j**2. Factor p(o).
-o**2*(o - 1)*(o + 2)
Let s(q) be the second derivative of -q**6/1260 + q**5/210 - q**4/84 - q**3/2 + 5*q. Let h(g) be the second derivative of s(g). Factor h(p).
-2*(p - 1)**2/7
Let w(a) = a**4 - 2*a**3 - 3. Suppose -q = -5*y + 16, -3*y = -6*q + 2*q - 13. Let r(x) = -x**4 + 2*x**3 + x + 4. Let n(j) = y*w(j) + 2*r(j). Factor n(f).
(f - 1)**3*(f + 1)
Let c(y) be the third derivative of -y**5/210 + 5*y**4/84 - 2*y**3/7 + 2*y**2. Factor c(l).
-2*(l - 3)*(l - 2)/7
Let y(f) be the third derivative of -f**5/60 + f**4/12 + f**3/2 + 10*f**2. Factor y(j).
-(j - 3)*(j + 1)
Let l = 28/5 + -186/35. Factor -4/7*j + 4/7*j**3 - l*j**4 + 0*j**2 + 2/7.
-2*(j - 1)