- 7/2*a**4 - 6*a**2.
-(a + 1)**4*(3*a + 2)/4
Let g be -1 - (-41)/18 - 174/(-783). Find x such that 1 + 5/2*x + g*x**2 = 0.
-1, -2/3
Let 47*k**5 + 9*k**4 - 42*k**5 + k**4 = 0. Calculate k.
-2, 0
Let m = 1669/12 + -139. Let s(r) be the third derivative of 0*r + 1/480*r**6 + 0 - 1/96*r**4 - m*r**3 - r**2 + 1/120*r**5. Let s(h) = 0. Calculate h.
-2, -1, 1
Suppose 162/17*x**2 + 0 + 0*x + 98/17*x**5 - 154/17*x**4 - 90/17*x**3 = 0. Calculate x.
-1, 0, 9/7
Let v(t) be the second derivative of 4/27*t**3 + 0 - 2/45*t**5 - 4/9*t**2 + 1/135*t**6 - t + 1/18*t**4. Factor v(s).
2*(s - 2)**2*(s - 1)*(s + 1)/9
Let b be 8/(-14) - (5980/(-273) + 12). Factor -116/3*p + 40*p**2 + 8 - b*p**3.
-4*(p - 3)*(p - 1)*(7*p - 2)/3
Let p be ((-4)/30)/(1*(-3)/15). Find w, given that 2/9 + 2/9*w**4 - 2/3*w**5 + 4/3*w**3 - p*w - 4/9*w**2 = 0.
-1, 1/3, 1
Suppose -2*y - 10 = -0. Let l be (-11)/(-5) - (-10)/y. Factor l*g**3 + 0*g**2 + 2/5 - 3/5*g.
(g - 1)**2*(g + 2)/5
Let g(t) be the first derivative of t**4 + 16*t**3 + 72*t**2 - 21. Factor g(s).
4*s*(s + 6)**2
Let a(i) be the third derivative of i**6/240 - i**5/40 + i**4/24 - 21*i**2. Find v such that a(v) = 0.
0, 1, 2
Let l(p) be the second derivative of -p**5/10 - p**4 - 4*p**3 - 8*p**2 + 22*p. Factor l(f).
-2*(f + 2)**3
Factor -2 - 2/3*r - 2/9*r**3 + 10/9*r**2.
-2*(r - 3)**2*(r + 1)/9
Let c be (-42)/(-9) + (-4)/(-12). Let y(r) be the first derivative of -1/5*r**c + 1 + 0*r**3 + 1/12*r**6 + 1/8*r**4 + 0*r + 0*r**2. Find k, given that y(k) = 0.
0, 1
Let p(m) = m**3 - 4*m**2 + 2*m + 4. Let a be p(2). Let -1/2*s**5 - 7/4*s**4 - 1/4*s - 5/4*s**2 + a - 9/4*s**3 = 0. What is s?
-1, -1/2, 0
Let f(c) be the first derivative of -c**5/5 + c**4/2 - c**3/3 + 8. Factor f(l).
-l**2*(l - 1)**2
Let m(g) be the third derivative of g**7/1260 + g**6/90 + g**5/15 - 5*g**4/12 - 2*g**2. Let q(l) be the second derivative of m(l). Factor q(r).
2*(r + 2)**2
Let l(t) be the second derivative of -t**4/24 - 7*t**3/6 + 15*t**2/4 + 16*t. Factor l(a).
-(a - 1)*(a + 15)/2
Let p be (-20)/(-6) + (-6)/(-9). Suppose -4*k = -2*k - p. Factor -2*i**4 + 7*i**2 + i - i**5 - 5*i**k + 0*i**4.
-i*(i - 1)*(i + 1)**3
Let t(q) be the first derivative of -2 + 4*q - 2/3*q**2 + 2/9*q**3 - 1/36*q**4. Let v(r) be the first derivative of t(r). Determine d, given that v(d) = 0.
2
Let u(c) be the first derivative of 0*c**2 - 2 - 1/6*c**3 + 1/2*c. Find s, given that u(s) = 0.
-1, 1
Determine o, given that -4/3*o - 2 + 2/3*o**2 = 0.
-1, 3
Determine a so that -2/15*a**2 + 4/15*a + 0 = 0.
0, 2
Suppose 3*p - 8*p = z - 23, z = -2*p + 11. Find g such that 2/3*g**3 + 0 - 2/3*g - 7/3*g**2 + 7/3*g**p = 0.
-1, -2/7, 0, 1
Let u(w) be the second derivative of -w**7/126 + w**6/45 + w**5/15 - w**4/18 - w**3/6 - 28*w. Let u(m) = 0. What is m?
-1, 0, 1, 3
Let p be ((-12)/8)/((-3)/4). Find h, given that -5*h**p - 4*h**2 - 2*h**3 - h**3 + 6*h**2 = 0.
-1, 0
Let i(x) be the third derivative of -x**4/24 - 5*x**3/6 + 2*x**2. Let g be i(-5). Factor 2/5*h**2 + g*h + 0.
2*h**2/5
Let k be (-3)/63*61 - -3. Let g = 5/21 + k. Find b, given that -1/3*b + 1/3*b**4 + g*b**3 - 1/3*b**2 + 0 = 0.
-1, 0, 1
Let u(o) be the first derivative of o**3 - 12*o**2 - 27*o + 35. Solve u(l) = 0.
-1, 9
Let f be 0 + 0 + 1 + 0. Let x(d) = -2*d - 3 - 3*d**2 + 2*d**2 + 4 + d. Let u(k) = 15*k**2 + 18*k. Let l(t) = f*u(t) + 3*x(t). Factor l(y).
3*(y + 1)*(4*y + 1)
Let w(t) = t**2 + 11*t + 32. Let g be w(-7). Solve -2/9*r + 4/9*r**3 + 0*r**g + 0*r**2 + 0 - 2/9*r**5 = 0 for r.
-1, 0, 1
Let n(k) be the third derivative of k**9/15120 - k**8/3360 + k**7/2520 - k**4/8 + 3*k**2. Let x(p) be the second derivative of n(p). Solve x(d) = 0 for d.
0, 1
Let w(i) be the first derivative of -5*i**4/4 + 35*i**2/2 - 30*i + 30. Determine d, given that w(d) = 0.
-3, 1, 2
Let a = -18/23 - -113/115. Let a*u**2 + 0*u + 0 + 1/5*u**5 + 3/5*u**3 + 3/5*u**4 = 0. Calculate u.
-1, 0
Suppose 2*h + 4*f = h + 22, 0 = -3*f + 15. Factor h*n**5 + 12*n**3 - 10*n**4 - 54 + 8*n**2 - 16*n + 54.
2*n*(n - 2)**3*(n + 1)
Let q(m) be the second derivative of -m**5/40 - m**4/8 - m**3/4 - m**2/4 - 6*m. Solve q(d) = 0 for d.
-1
Let c = -6 + 16. Suppose -6 = -2*r + r - 3*v, 2*r - c = -4*v. Factor 3*g**r + 0*g + 3*g**2 + 0 + 3 - 3*g - 6.
3*(g - 1)*(g + 1)**2
Let l(f) = 5*f**5 - 5*f**4 - 3*f**3 + 3*f**2. Let n(r) = -35*r**5 + 35*r**4 + 20*r**3 - 20*r**2. Let b(c) = 20*l(c) + 3*n(c). Factor b(y).
-5*y**4*(y - 1)
Let j(h) = -h**3 + 8*h**2 + 8*h + 11. Let s be j(9). Suppose 4*p - p**3 + 2*p**3 - 2*p**s - 3*p**3 = 0. What is p?
-2, 0, 1
Let u(j) be the third derivative of j**5/90 + 3*j**2. Factor u(i).
2*i**2/3
Find k such that 12*k**4 + 15*k**4 - 4*k + 37*k**4 - 28*k**2 - 32*k**3 = 0.
-1/4, 0, 1
Let s(j) be the first derivative of -j**4/20 - 13*j**3/15 - 7*j**2/2 + 49*j/5 - 24. Solve s(o) = 0 for o.
-7, 1
Let z(a) be the first derivative of -a**4/2 + 4*a**3/3 + a**2 - 4*a - 7. Find r such that z(r) = 0.
-1, 1, 2
Let c(m) be the second derivative of 3/2*m**2 + 0 + 23/12*m**3 + 7/24*m**4 - 2*m. Factor c(w).
(w + 3)*(7*w + 2)/2
Let o = 36 - 57. Let g be 17 + o/(-6) + -2. Suppose 2*z + g*z**3 + 0 + 9/2*z**5 + 10*z**2 + 15*z**4 = 0. Calculate z.
-1, -2/3, 0
Factor 4/5*r**2 - 2/5*r**3 + 0 - 2/5*r.
-2*r*(r - 1)**2/5
Let k(d) = 9*d**5 - 3*d**4 + 25*d**3 - 14*d**2 + 11*d. Let l(o) = -o**5 - o**4 - o**3 - o. Let t(y) = -2*k(y) - 14*l(y). Let t(f) = 0. What is f?
0, 1, 2
Let m = 23 + -10. Suppose -5*u + 2 = -x + m, 0 = u - 1. Factor 0 - 32/5*d**5 + 4*d**2 + x*d**4 - 66/5*d**3 - 2/5*d.
-2*d*(d - 1)**2*(4*d - 1)**2/5
Suppose -4*z + 0*z - 12 = 0. Let i(w) = 0 - 3*w**3 + 3 - 1 - 3*w. Let f(h) = 4*h**3 - h**2 + 4*h - 3. Let a(k) = z*i(k) - 2*f(k). Factor a(y).
y*(y + 1)**2
Let k(l) = -11*l**2 - 2*l**3 - 1 + 2 + l**3 + 18*l. Let b be (-16 + 1)*6/18. Let a(f) = f**3 + 7*f**2 - 12*f - 1. Let g(z) = b*k(z) - 7*a(z). Factor g(n).
-2*(n - 1)**3
Factor 3/5*v**2 + 12/5 + 12/5*v.
3*(v + 2)**2/5
Let w(n) be the first derivative of 8*n**6 - 72*n**5/5 + 27*n**4/4 - n**3 - 32. Let w(b) = 0. What is b?
0, 1/4, 1
Let t be -3 - ((-339)/84 - (-6)/8). Factor -t*d**2 + 2/7*d + 4/7.
-2*(d - 2)*(d + 1)/7
Let t(j) = -j**2. Let x be t(0). Let g(u) be the first derivative of -1 - 1/15*u**6 - 1/5*u**2 + 1/5*u**4 + x*u**3 + 0*u + 0*u**5. Determine w so that g(w) = 0.
-1, 0, 1
Let y(u) be the first derivative of 1 + 0*u**2 + 1/80*u**5 - 1/12*u**3 + 3*u - 1/48*u**4. Let q(j) be the first derivative of y(j). Let q(x) = 0. Calculate x.
-1, 0, 2
Let j be (-124)/(-12) + 1/(-3). Suppose -5*g = -j - 0. Factor 4/3*t + 14/3*t**4 - 8*t**3 + 2*t**g + 0.
2*t*(t - 1)**2*(7*t + 2)/3
Let p be (63/7)/(9/6). Let f be (-8)/p*(-14 + 11). Let -4/9*t**3 - 8/9*t**2 + 4/9*t**f + 2/9*t**5 + 4/9 + 2/9*t = 0. What is t?
-2, -1, 1
Determine h so that -5/8*h**3 - h**2 - 1/8*h + 1/4 = 0.
-1, 2/5
Let v be (9/6)/3 - 42/(-12). Suppose -2*k + 31 = 5*o, -3*k = o - 13 - 1. Suppose 2/5*z**2 - 2/5*z**v + 2/5*z**k - 2/5*z**5 + 0 + 0*z = 0. Calculate z.
-1, 0, 1
Let m(p) = -p - 11. Let s be m(-13). Suppose 3/4*h**s - 1/4*h - 1/2 = 0. Calculate h.
-2/3, 1
Let i = 8 + -4. Let f be (-3)/i + 4 + -3. Factor -1/2*g - f*g**2 - 1/4.
-(g + 1)**2/4
Let h = 59887/30 - 1996. Let n(o) be the third derivative of -h*o**5 - 2/3*o**4 - 4/9*o**3 + 0 - 3*o**2 + 0*o + 49/180*o**6. Find s, given that n(s) = 0.
-2/7, 1
Let c(n) = n**2 - 3*n + 7. Let s be c(2). Let v(j) be the first derivative of -1/7*j**4 + 2/35*j**s - 2 + 1/21*j**6 - 4/21*j**3 + 2/7*j + 1/7*j**2. Factor v(q).
2*(q - 1)**2*(q + 1)**3/7
Let v(c) be the second derivative of -c**7/42 - c**6/15 + c**5/10 + 2*c**4/3 + 7*c**3/6 + c**2 - 5*c. Factor v(h).
-(h - 2)*(h + 1)**4
Let k(j) be the first derivative of -j**8/560 + j**7/70 - j**6/24 + j**5/20 + 3*j**3 + 9. Let t(i) be the third derivative of k(i). Suppose t(g) = 0. What is g?
0, 1, 2
Let l(u) be the second derivative of -u**5/10 + 2*u**4/9 - 4*u**3/27 + u. Determine x so that l(x) = 0.
0, 2/3
Let t(b) be the first derivative of -5*b**3/3 + 30*b**2 - 180*b - 27. Suppose t(h) = 0. What is h?
6
Let f(t) be the third derivative of t**6/180 - t**5/90 - t**4/36 + t**3/9 + 3*t**2. Let f(q) = 0. Calculate q.
-1, 1
Let p(m) be the third derivative of 4*m**6/3 + 68*m**5/15 + 53*m**4/12 + 2*m**3 + 11*m**2. Find x such that p(x) = 0.
-6/5, -1/4
Suppose 5*p + 5 = 3*l, 0 = -l - 5