j**2 - 3*j - 3. Let u(r) = 4*r**5 - 5*r**4 + r**2 + 2*r + 2. Let p(n) = -3*u(n) - 2*v(n). Let p(f) = 0. What is f?
-1/4, 0, 1
Suppose -4*j = 2*d - 8, -10*d - 6 = -7*d - 3*j. Let a(k) be the third derivative of 0 - 1/12*k**3 - 3*k**2 + d*k + 1/240*k**5 + 1/96*k**4. Factor a(o).
(o - 1)*(o + 2)/4
Factor 8*m**3 - 3 - 1 - 3 + 8*m + 9 + 2*m**4 + 12*m**2.
2*(m + 1)**4
Factor -16/11*k + 2/11*k**2 + 24/11.
2*(k - 6)*(k - 2)/11
Factor 9/4*s**3 + 9/4*s**2 + 0 + 3/4*s**4 + 3/4*s.
3*s*(s + 1)**3/4
Suppose a = 4*a - 6. Determine p so that 1 + 6 - p**3 - 3 - 8*p + 5*p**a = 0.
1, 2
Let w(u) be the first derivative of -3*u**5/80 - u**4/16 + u**3/8 + 3*u**2/8 + 2*u - 3. Let l(y) be the first derivative of w(y). Determine q so that l(q) = 0.
-1, 1
Let t be 78 + 3*(4 + -3). Factor -1 - 355*u**3 + 14*u**2 - t*u**5 + 279*u**4 + 5 + 187*u**2 - 48*u.
-(u - 1)**3*(9*u - 2)**2
Let p(a) be the second derivative of 0 + 0*a**3 + 2/15*a**5 + 2*a + 3/2*a**2 + 1/12*a**4. Let t(o) be the first derivative of p(o). Let t(h) = 0. Calculate h.
-1/4, 0
Let j(w) be the second derivative of w**7/1800 - w**6/225 + w**5/150 + w**4/6 - 3*w. Let p(c) be the third derivative of j(c). Determine v so that p(v) = 0.
2/7, 2
Find g such that 1/2 + g**3 + 1/2*g**5 + g**2 - 3/2*g**4 - 3/2*g = 0.
-1, 1
Suppose 1 + 5 = -3*i. Let n be (0/(-2))/(5 + i). Suppose n - 4/7*k + 18/7*k**2 = 0. What is k?
0, 2/9
Let y(p) be the first derivative of p**4 + 16*p**3/3 + 10*p**2 + 8*p - 11. Factor y(c).
4*(c + 1)**2*(c + 2)
Let w = -7/16 - -113/240. Let d(p) be the second derivative of 1/9*p**3 + 0 + 0*p**2 + 5/36*p**4 - w*p**5 + 3*p - 1/18*p**6. Factor d(m).
-m*(m - 1)*(m + 1)*(5*m + 2)/3
Suppose 0 = 2*s + 3 - 17. Let t be (-2 + s)/((-10)/(-4)). Find c, given that 0 - 2/7*c**3 - 4/7*c**t - 2/7*c = 0.
-1, 0
Suppose -4*z = 3*w + 5, -2*w - z + 8 = 3. Let -4/7*x**3 + 4/7*x**4 + 2/7*x + 4/7 - 8/7*x**2 + 2/7*x**w = 0. What is x?
-2, -1, 1
Suppose 22/7*k**2 - 13/7*k - 18/7*k**3 - 1/7*k**5 + 3/7 + k**4 = 0. Calculate k.
1, 3
Let i(x) = x**4 + x**3 - 4*x**2 - 7*x - 3. Let n(z) = -z**4 - 2*z**3 + 3*z**2 + 8*z + 4. Let h(q) = -4*i(q) - 3*n(q). Solve h(c) = 0.
-1, 0, 4
Suppose 4*x = 20, -3*g - 3*x + 23 = g. Find p, given that 4 + g*p - 4*p + p**2 - 2*p = 0.
2
Let s(d) be the second derivative of 9*d + 1/30*d**6 + 3/20*d**5 + 0 + 0*d**2 + 1/6*d**4 + 0*d**3. Determine x, given that s(x) = 0.
-2, -1, 0
Let b(l) be the second derivative of 4*l + 0 - 1/3*l**3 + 1/6*l**4 + 0*l**2. Solve b(c) = 0 for c.
0, 1
Let u(p) be the second derivative of -p**8/13440 + p**4/12 + 2*p. Let q(g) be the third derivative of u(g). Determine v, given that q(v) = 0.
0
Let f(b) = -b - 3. Let p(w) = -2*w**2 + 5*w - 2. Let k be p(3). Let n be f(k). Let -g**n + 1 + 0 + 2 - 2*g**2 = 0. What is g?
-1, 1
Let p(c) be the first derivative of -4*c**5/35 + 9*c**4/7 + 44*c**3/7 + 10*c**2 + 48*c/7 - 25. Factor p(g).
-4*(g - 12)*(g + 1)**3/7
Solve 2/3*y**2 - 16/3 - 4/3*y = 0 for y.
-2, 4
Let r = 27 - 24. Suppose -r*t = -3*p - 0*p, 4*p = 2*t. Factor 2/7*w**2 - 4/7*w + t.
2*w*(w - 2)/7
Let m be (7 - 3)/(2 - (-1 - -2)). Let z(f) be the second derivative of -f**2 - 1/24*f**m + 1/3*f**3 - 3*f + 0. Factor z(v).
-(v - 2)**2/2
Let m(p) be the third derivative of -p**7/105 + p**6/60 + p**5/10 - p**4/12 - 2*p**3/3 - 2*p**2. Find t such that m(t) = 0.
-1, 1, 2
Let i(o) = o**2 + 5*o - 6. Let v be i(-6). Let w be ((-5 - -7)*-3)/(-3). Find p, given that -3/5*p**3 + 0 + 0*p**w + v*p - 3/5*p**4 = 0.
-1, 0
Let p(l) be the third derivative of l**8/112 + 2*l**7/35 + l**6/10 - l**5/10 - 5*l**4/8 - l**3 + 4*l**2. Find w such that p(w) = 0.
-2, -1, 1
Suppose 0*y - 4 = 4*y + 3*o, -2*o - 18 = -5*y. Suppose 5*m - 4 = 1, m + 11 = 4*z. Determine a so that -a**2 - 2*a**3 + 4*a**z + 3*a**y = 0.
-1, 0
Let h(n) be the second derivative of n**6/40 - n**5/20 + n**4/24 + n**3/3 + 4*n. Let w(g) be the second derivative of h(g). Determine v so that w(v) = 0.
1/3
Let b(s) be the first derivative of -s**6/1080 - s**5/180 + s**3 - 1. Let w(j) be the third derivative of b(j). What is f in w(f) = 0?
-2, 0
Suppose 25 = -5*m + 5*u, -2*u - 3*u = m - 25. Suppose 27 = 2*n + j, m = -4*n - j - 3*j + 48. Factor -v**2 - n + 15 + v**3.
v**2*(v - 1)
Suppose -2*r + 3 = -r + 4*j, 3*r + j = 9. Determine l, given that 0*l**r + 7*l**4 - 2*l**3 - 3*l**4 - 2*l**5 = 0.
0, 1
Let l be 6/4*-2 - -6. Factor 14*x**2 - 4 - 11 - 6*x**l + 7.
-2*(x - 2)*(x - 1)*(3*x + 2)
Let m(r) be the first derivative of -r**6/6 + 6*r**5/5 + r**4/4 - r**3/3 - 5*r**2/2 + 1. Let s(q) = q**4 - q. Let l(w) = -m(w) + 5*s(w). Factor l(y).
y**2*(y - 1)**2*(y + 1)
Let -1/3*o**4 - o**2 - o**3 + 0 - 1/3*o = 0. Calculate o.
-1, 0
Solve -1/2*m**2 - 3/2 + 2*m = 0.
1, 3
Suppose -u + 3 = -5*i - 3, 4*i + 24 = -4*u. Let n be (-32)/(-12) - u/3. Let -14*q**3 - 8/3*q - 40/3*q**n + 50/3*q**5 + 40/3*q**2 + 0 = 0. What is q?
-1, 0, 2/5, 1
Let o(x) be the second derivative of x**6/30 + x**5/20 - 7*x. Factor o(n).
n**3*(n + 1)
Determine l, given that -2/3*l**4 + 0 + 2/3*l**2 + 1/3*l + l**5 - 4/3*l**3 = 0.
-1, -1/3, 0, 1
Let q(j) = j**2 - 2*j - 19. Let u be q(6). Factor 4/9*c**3 - 2/3*c - 2/3*c**4 + 4/9*c**2 + 2/9 + 2/9*c**u.
2*(c - 1)**4*(c + 1)/9
Let q = -6 - -2. Let w be -1*(-7)/((-14)/q). Determine i, given that -i**w - 1/2*i + 0*i**3 + 1/2*i**5 + i**4 + 0 = 0.
-1, 0, 1
Suppose -13*p + 5*p + 48 = 0. Let q(x) be the third derivative of 0*x + 1/1050*x**7 - 1/100*x**5 + 0 - 1/300*x**p + 2/15*x**3 + 3*x**2 + 1/30*x**4. Factor q(d).
(d - 2)**2*(d + 1)**2/5
Let i(c) be the first derivative of -c**4/12 - 11*c**3/9 - 19*c**2/6 - 3*c + 36. Factor i(p).
-(p + 1)**2*(p + 9)/3
Let k(n) be the second derivative of -n**5/4 - n**4/4 + n**3/3 - 3*n. Let p(r) = 51*r**3 + 30*r**2 - 21*r. Let a(c) = -21*k(c) - 2*p(c). Solve a(w) = 0.
-1, 0
Let p(j) = 8*j**2 + 3*j. Let c(h) = -h + 6. Let d be c(7). Let g(y) = y**2. Let m(b) = d*p(b) + 5*g(b). Suppose m(u) = 0. Calculate u.
-1, 0
Let z = 60 + -58. Factor -a**z + 2/3*a**3 + 1/3 + 0*a.
(a - 1)**2*(2*a + 1)/3
Let p(d) be the first derivative of -1/8*d + 0*d**2 + 1/24*d**3 + 1. Factor p(c).
(c - 1)*(c + 1)/8
Let b(j) be the second derivative of -j**5/120 - j**4/16 - j**3/6 + j**2/2 + 3*j. Let g(a) be the first derivative of b(a). Solve g(c) = 0.
-2, -1
Let w(q) = 10*q**5 + 5*q**4 - 15*q**3 + 5*q. Let m(k) = -5*k**5 - 3*k**4 + 8*k**3 - 3*k. Let o(c) = -5*m(c) - 3*w(c). Solve o(u) = 0 for u.
-1, 0, 1
Let t be 18/8 - (-3)/(-12). Let l be 1/t*(-8)/(-2). Suppose 18*p**2 + 70*p**5 - 6*p + 46*p**3 + 6*p**l - 2*p - 132*p**4 = 0. What is p?
-2/5, 0, 2/7, 1
Suppose -m - h = 1, 3*m + 1 + 8 = -5*h. Suppose -8 - 4 = -m*p. Factor -4*o + p*o**2 + o**2 - 2*o**3 - o**2.
-2*o*(o - 2)*(o - 1)
Let d(n) = n**3 + n + 1. Let u(l) = 5*l**3 - 3*l**2 + 15*l + 7. Let v(c) = 6*d(c) - u(c). Let t(o) be the first derivative of v(o). Factor t(s).
3*(s - 1)*(s + 3)
Suppose -2 = -11*o + 20. Factor -4/7 + 4/7*j**4 + o*j + 4/7*j**3 - 2/7*j**5 - 16/7*j**2.
-2*(j - 1)**4*(j + 2)/7
Let y(j) be the second derivative of j**5/18 - j**4/18 - 2*j**3/27 + j. Factor y(h).
2*h*(h - 1)*(5*h + 2)/9
Suppose -14/13*t - 20/13 - 2/13*t**2 = 0. What is t?
-5, -2
Let c be 34*(-2)/(-4)*1. Let a = 55/3 - c. Let 4*s - a - 3*s**2 = 0. Calculate s.
2/3
Let h(t) be the third derivative of 3*t**2 - 1/36*t**4 - 2/27*t**3 + 0*t + 0 + 1/540*t**6 + 0*t**5. Factor h(x).
2*(x - 2)*(x + 1)**2/9
Suppose -7*d = -3*d - 12. Let j(p) be the third derivative of 0 + 2*p**2 + 0*p - 1/48*p**4 + 1/120*p**5 + 0*p**d. Suppose j(v) = 0. What is v?
0, 1
Let s(q) = -5*q**4 + 7*q**3 + 8*q**2. Let a(m) = 6*m**4 - 6*m**3 - 8*m**2 + m. Let l(y) = 3*y. Let c be l(1). Let j(d) = c*s(d) + 4*a(d). Factor j(k).
k*(k + 1)*(3*k - 2)**2
Let m = 47/30 + 44/15. Solve 0 - m*p**2 + 3*p**3 + 3/2*p = 0 for p.
0, 1/2, 1
Factor -g**3 + 2*g**3 - 9*g**2 + 3*g**3 - g**3.
3*g**2*(g - 3)
Let m = -47 - -47. Let g = 2 + m. Factor -y**3 - y**g - 1/3*y - 1/3*y**4 + 0.
-y*(y + 1)**3/3
Let i(g) be the second derivative of -4*g**2 + 1/2*g**4 + 1/10*g**5 + 5*g + 0*g**3 + 0. Factor i(t).
2*(t - 1)*(t + 2)**2
Let u(i) be the second derivative of 0 - 4*i + 1/8*i**2 - 1/48*i**4 + 0*i**3. Factor u(k).
-(k - 1)*(k + 1)/4
Suppose 0 + 0*o + 2/13*o**2 = 0. Calculate o.
0
Let v = 23/50 + 1/25. Let f = -21 + 24. Factor -v*s**5 - 3/2*s**f - 1/2*s**2 - 3/2*s**