v**4 - 4/7*v**2 + 2/7*v + 2/7 + 2/7*v**5 - 4/7*v**3 = 0.
-1, 1
Let n(l) = 6*l**4 - l**3 - 5*l**2 + 17. Let x(j) = -2*j**4 + 2*j**2 - 6. Let a(c) = -6*n(c) - 17*x(c). Determine b so that a(b) = 0.
0, 1, 2
Let m(d) be the first derivative of -1/30*d**5 + 0*d**3 + 1/2*d**2 + 0*d - 1 + 0*d**4. Let w(j) be the second derivative of m(j). Factor w(a).
-2*a**2
Factor -16/7 + 4/7*r**2 + 16/7*r - 4/7*r**3.
-4*(r - 2)*(r - 1)*(r + 2)/7
Let u be (-3)/2*32/(-24). Suppose -22 - 2 = -5*x + f, -u*x = 3*f + 4. Factor -4/3*g - 1/3 - 4/3*g**3 - 2*g**2 - 1/3*g**x.
-(g + 1)**4/3
Suppose 3*m + 2 = 4*m. Let v(t) = t**3 - 2*t**2 + t. Let d be v(m). Factor 1/4*r**3 + 0*r + 1/2*r**d + 0.
r**2*(r + 2)/4
Let g(j) = j + 3. Let c be g(-5). Let w be (c - -1)*4/(-20). Let w*z**2 + 1/5 - 2/5*z = 0. What is z?
1
Suppose 2 - 5 = -3*r, 0 = 4*m - 5*r + 21. Let i = -1 - m. Determine v, given that -v**i - 5*v + v**2 + 5*v = 0.
0, 1
Let g(w) be the third derivative of 2*w**7/525 + w**6/50 - 2*w**4/15 + 10*w**2. Determine m, given that g(m) = 0.
-2, 0, 1
Suppose 0*p = 4*p - 16. Suppose -3*d - 2*o = -6*d - 2, -2*d = -p*o + 4. Find f, given that 4*f**2 + 8*f**3 - 2*f**5 + d + 3*f**5 + 5*f**4 + 0 = 0.
-2, -1, 0
Suppose -4*a = -7 + 3. Let s = -4 - -9/2. Solve -s*h**2 - 3/2*h - a = 0 for h.
-2, -1
Let -3/7*q**2 + 5/7*q - 2/7 = 0. What is q?
2/3, 1
Let r(q) be the second derivative of q**10/120960 + q**9/30240 + q**8/26880 + q**4/2 + 4*q. Let o(i) be the third derivative of r(i). Find z such that o(z) = 0.
-1, 0
Let d(s) be the second derivative of 5*s**4/24 - 5*s**3/6 + 18*s. Solve d(z) = 0.
0, 2
Let q(a) be the first derivative of a**3/9 + a**2/3 + 4. Determine b, given that q(b) = 0.
-2, 0
Let o(b) be the second derivative of b**9/5040 - b**8/1120 + b**6/120 - b**5/40 + b**4/3 - 4*b. Let j(h) be the third derivative of o(h). Factor j(w).
3*(w - 1)**3*(w + 1)
Let u(x) = x**2. Let c(m) = -2*m**4 - 8*m**3 - 5*m**2 - 4*m. Let i(d) = c(d) - 5*u(d). Factor i(y).
-2*y*(y + 1)**2*(y + 2)
Let v(t) be the second derivative of t**5/80 + t**4/24 + t**3/24 + 16*t. Factor v(r).
r*(r + 1)**2/4
Factor 1/3*k + 0*k**2 + 0*k**4 - 2/3*k**3 + 0 + 1/3*k**5.
k*(k - 1)**2*(k + 1)**2/3
Let a(l) be the second derivative of -l**6/120 + 3*l**5/80 - l**4/16 + l**3/24 + 2*l. Determine g so that a(g) = 0.
0, 1
Let j be (-14)/(-3)*(9 + 3). Factor j*q**3 - 11*q**2 + 3*q**2 - 98*q**4 + 0*q**2.
-2*q**2*(7*q - 2)**2
Let c(u) be the first derivative of u**5/40 - 7*u**4/24 + 2*u**3/3 + 4*u**2 - 4*u + 5. Let w(d) be the first derivative of c(d). Factor w(h).
(h - 4)**2*(h + 1)/2
Let f(k) be the third derivative of k**5/570 - 4*k**2. Let f(l) = 0. Calculate l.
0
Let t = -23 - -25. Let l(o) be the second derivative of -t*o - o**2 + 0 - 2/3*o**3 - 1/6*o**4. Factor l(c).
-2*(c + 1)**2
Let c(z) be the third derivative of z**5/140 - 3*z**4/56 + z**3/7 + 70*z**2. Find v such that c(v) = 0.
1, 2
Let s(m) be the third derivative of -m**6/420 + m**5/30 - 2*m**4/21 - 16*m**3/21 + m**2. Solve s(t) = 0 for t.
-1, 4
Factor -41*m**3 + 33*m**3 - 7*m**2 - 11*m**2 - 4*m.
-2*m*(m + 2)*(4*m + 1)
Let z(p) = 4*p**2 - p. Let i be z(1). Suppose 4*g**2 - 2 - 219*g**i - 2*g**4 + 219*g**3 = 0. What is g?
-1, 1
Let d(a) be the first derivative of 3*a**4/4 - 5*a**3 + 9*a**2 + 32. Factor d(t).
3*t*(t - 3)*(t - 2)
Suppose 5*m + 22 - 62 = 0. Solve -m + d**3 + 2 + 8 - 3*d = 0.
-2, 1
Let q(s) be the first derivative of -s**3/12 - 3*s**2/8 - 14. Solve q(t) = 0 for t.
-3, 0
What is m in -5 - 3*m**2 - 3 - 3*m - 3*m + 5 = 0?
-1
Let z(r) be the third derivative of -r**6/24 - r**5/3 - 5*r**4/8 + 2*r**2 - 2. Factor z(n).
-5*n*(n + 1)*(n + 3)
Let b(a) be the second derivative of a**9/2268 + a**8/1260 - a**7/315 + a**3/2 + 5*a. Let g(r) be the second derivative of b(r). Let g(w) = 0. What is w?
-2, 0, 1
Let u be (-6)/480*2/(-3). Let c(y) be the third derivative of 0*y**5 + 0*y + 0*y**7 + 1/48*y**4 + 0 + 0*y**3 + 2*y**2 + 1/672*y**8 - u*y**6. Factor c(m).
m*(m - 1)**2*(m + 1)**2/2
Factor -1/2*i + 0 - 8*i**3 + 4*i**2.
-i*(4*i - 1)**2/2
Factor -1/3*s**3 - s**2 + 0 + 0*s.
-s**2*(s + 3)/3
Let l be 2200/(-210)*474/4. Let a = 1244 + l. Find r such that -4*r**2 + a*r**3 - 4/7*r**4 + 18/7*r - 4/7 = 0.
1/2, 1, 2
Let g = 95/69 + -1/23. Let a(p) be the first derivative of 0*p**4 - 4/5*p**5 - 1/3*p**6 + 0*p + g*p**3 + p**2 - 1. Factor a(q).
-2*q*(q - 1)*(q + 1)**3
Let j(o) be the third derivative of 49/9*o**6 + 112/15*o**5 + 44/9*o**4 + 0*o + 49/45*o**7 + 16/9*o**3 + 3*o**2 + 0. Factor j(z).
2*(z + 2)*(7*z + 2)**3/3
Suppose 4*s - 9 = 15. Factor -3*x**3 + 6*x**2 + 6*x**3 - 2*x - s*x**3 - x**3.
-2*x*(x - 1)*(2*x - 1)
Let o(p) be the third derivative of -p**5/12 + 5*p**4/12 - 11*p**2. Let o(r) = 0. What is r?
0, 2
Let l(d) = d**3 + d**2 + 3*d + 7. Let z(q) = 2*q**3 + 2*q**2 + 3*q + 8. Let t(h) = 5*l(h) - 4*z(h). Factor t(k).
-3*(k - 1)*(k + 1)**2
Let g(y) = -y**2 + 6*y - 11. Let f be g(6). Let t = f + 34/3. Suppose -t*v**3 + 1/3*v - 1/3*v**4 + 0 + 1/3*v**2 = 0. What is v?
-1, 0, 1
Let o(p) = -2*p**3 + p**2 - 3*p - 2. Let y be o(-2). Suppose r = 3, 0 = -m + 5*m + 4*r - y. Factor -7*f**2 + 3*f**m - 2*f**3 + 6*f**2 - 2*f**3.
-f**2*(f + 1)
What is j in 1/3*j**2 - j - 2/3 + j**3 + 1/3*j**4 = 0?
-2, -1, 1
Let q = -9 + 17. Suppose -9 = -u + 3*n + q, -4*n = u + 18. Factor -w**2 + u*w**2 - 2*w**2 - w**3 + w**4 + w**5.
w**2*(w - 1)*(w + 1)**2
Determine t, given that 5/4*t**4 - 9/4*t**3 + 7/4*t**5 + 0 + 1/2*t - 5/4*t**2 = 0.
-1, 0, 2/7, 1
Factor -m**3 + 1/3*m**2 + 0 + 2/3*m + 1/3*m**5 - 1/3*m**4.
m*(m - 2)*(m - 1)*(m + 1)**2/3
Let z(l) be the first derivative of 1/6*l**4 + 0*l**3 + 7/60*l**6 - 2*l**2 - 2 + 0*l - 3/10*l**5. Let p(k) be the second derivative of z(k). Factor p(b).
2*b*(b - 1)*(7*b - 2)
Let w = 19/106 + -2/159. Let b be (-1 - 1)*(-1)/12. Factor 1/3*d - b*d**2 - w.
-(d - 1)**2/6
Suppose 0*k = -k + 6. Let f = k - 4. Factor 4/9 + 22/9*n + 2*n**f.
2*(n + 1)*(9*n + 2)/9
Let l = -4 - -5. Let f = l - 1. Solve 0 - 1/4*c**2 + f*c = 0 for c.
0
Let f(r) = -3*r - 41. Let q be f(-15). Let t(z) be the first derivative of 0*z - z**3 + 3*z**2 - 9/4*z**q - 2. Factor t(j).
-3*j*(j + 1)*(3*j - 2)
Let m(p) = -p**2 + p + 4. Let o be m(-2). Let h = o + 2. Solve 2/9*x**3 + 0 + h*x + 0*x**2 = 0 for x.
0
Let b(f) be the second derivative of 1/90*f**6 + 2/3*f**4 + 8/3*f**2 + 2/15*f**5 + 0 + 16/9*f**3 - 3*f. Factor b(y).
(y + 2)**4/3
Suppose 0 = -5*x + h + 135, -2 = 2*x + 2*h - 68. Factor -30*g**3 - 15*g + 5*g + 6 + x*g**3 - 2 + 8*g**2.
-2*(g - 2)*(g - 1)**2
Let u be 11 + -5 + 4*-1. Let d(w) be the second derivative of 1/135*w**6 - 1/90*w**5 + 0*w**3 + 0*w**u + 1/189*w**7 + 0 - 1/54*w**4 - 2*w. Solve d(m) = 0.
-1, 0, 1
Let m be 2 - -1 - (-21 + 2). Determine d, given that m*d**3 + 12 - 177*d**2 - 181*d**3 + 24*d - 30*d**3 = 0.
-1, -2/9, 2/7
Let f(n) be the first derivative of -3/16*n**4 + 0*n - 3/20*n**5 - 2 + 1/4*n**3 + 3/8*n**2. Solve f(t) = 0 for t.
-1, 0, 1
Factor 1/4*w**3 + 0 + 1/4*w**2 - 1/2*w.
w*(w - 1)*(w + 2)/4
What is l in 3/7*l**5 - 3/7*l**3 + 0*l - 6/7*l**4 + 6/7*l**2 + 0 = 0?
-1, 0, 1, 2
Let c(z) be the second derivative of 0 + 1/24*z**3 - 1/48*z**4 + 0*z**2 + 4*z. Factor c(o).
-o*(o - 1)/4
Let g(v) be the first derivative of 0*v + 1/9*v**3 - 2 - 1/6*v**2. Factor g(q).
q*(q - 1)/3
Let z = 4/37 + 29/74. Determine a, given that a - z - a**3 + 1/2*a**4 + 0*a**2 = 0.
-1, 1
Let v = -40 + 37. Let g be v + 3 + (-36)/(-8). Factor 1/2*c**2 - 3*c + g.
(c - 3)**2/2
Factor -8/3*t**2 + 10/3*t - 4/3 + 2/3*t**3.
2*(t - 2)*(t - 1)**2/3
Let o be (-4)/(-2) + (-6)/(-3). Let u be -1 + 1 - 32/(-16). Determine p, given that -12*p - o*p**u + p**2 - 18 + p**2 = 0.
-3
Let m = 0 + 3. Find o, given that 3*o**4 - 3*o**4 + 2*o**2 + m*o**4 - 4*o**3 - o**4 = 0.
0, 1
Suppose -2*u = 3*a + 9, 0*a - 3*a - 9 = u. Find b such that u*b + 0 + 1/3*b**4 - 1/3*b**2 + 1/3*b**3 - 1/3*b**5 = 0.
-1, 0, 1
Let c(m) be the second derivative of 3*m**5/100 - m**4/4 + 7*m**3/10 - 9*m**2/10 + 4*m. Let c(w) = 0. What is w?
1, 3
Let s(l) be the first derivative of -5*l**8/1344 + l**7/280 + l**6/240 + 2*l**2 + 1. Let x(u) be the second derivative of s(u). Factor x(n).
-n**3*(n - 1)*(5*n + 2)/4
Let p(c) be the third derivative of c**8/5040 - 2*c**7/315 + 4*c**6/45 - 7*c**5/60 + 5*c**2. Let v(h) be the third derivative of p(h). Factor v(q).
4*(q -