 + 1)**2*(2*z + 1)
Let x(j) = -j**4 - j**2 - j - 1. Let h(n) = -42*n**4 - 26*n**3 - 6*n**2 - 2*n - 2. Let c be (-7)/(42/4)*3. Let f(v) = c*x(v) + h(v). What is y in f(y) = 0?
-2/5, -1/4, 0
Suppose -2*p - 10 = 3*p. Let l be p + 1/(3/6). Determine g, given that l + 2*g + 1 + g**4 - 2 - 2*g**3 = 0.
-1, 1
Let l(k) be the first derivative of k**5/60 - k**4/6 + 2*k**3/3 - 3*k**2/2 - 3. Let m(t) be the second derivative of l(t). Find g, given that m(g) = 0.
2
Let y(c) be the first derivative of -2*c**3/9 + c**2 - 18. What is d in y(d) = 0?
0, 3
Suppose -4*b + 15 = b - 4*c, 0 = -b + 2*c + 3. Factor -5*u**2 - 2*u**3 + 4*u**3 - 8*u - 4 - b*u**3.
-(u + 1)*(u + 2)**2
Factor -6*n + 490*n**5 - 5*n**4 - 4*n + 13*n**2 - 491*n**5 + 3*n**3.
-n*(n - 1)**2*(n + 2)*(n + 5)
Let l = 10 - 6. Suppose -n + 3*x - l = -13, -4*n + x + 25 = 0. Find c such that 2*c**4 - n*c + 6*c - 2*c**3 = 0.
0, 1
Let v be 10/5*(-1 - -2). Factor -4 + 1 - 4*d + 4*d**v + 2 - 7.
4*(d - 2)*(d + 1)
Let h = -2/503 + 16102/1509. Factor -2/3*u**2 - h + 16/3*u.
-2*(u - 4)**2/3
Let z = 18 - 16. Solve 7/3*v**z + v**4 + 0 - 8/3*v**3 - 2/3*v = 0.
0, 2/3, 1
Let d be (-24 - 4) + 4 - -4. Let h = d - -20. Find l, given that -2/3*l**3 + 0*l + h + 0*l**2 = 0.
0
Let k(h) be the third derivative of h**8/1344 - h**7/105 + h**6/40 + h**5/120 - 13*h**4/96 + h**3/4 - 9*h**2. Factor k(n).
(n - 6)*(n - 1)**3*(n + 1)/4
Let a = -127 - -129. Factor -3/2*p + 1/2 + p**a.
(p - 1)*(2*p - 1)/2
Let g(y) be the second derivative of 0 - 1/4*y**2 - y - 1/8*y**3 + 1/80*y**5 + 0*y**4. Factor g(h).
(h - 2)*(h + 1)**2/4
Suppose 5*m - 20 = 0, -3*d - 2*m = -5*d - 4. Factor 2*l**3 - 27 + 27 + d*l**5 - 4*l**4.
2*l**3*(l - 1)**2
Let j(v) be the third derivative of -v**8/3360 + v**7/420 - v**6/120 + v**5/60 - v**4/12 + v**2. Let n(b) be the second derivative of j(b). Factor n(x).
-2*(x - 1)**3
Determine l, given that -6/7 - 2/7*l**2 - 8/7*l = 0.
-3, -1
Factor 4/7*x + 0 - 6/7*x**2 + 2/7*x**3.
2*x*(x - 2)*(x - 1)/7
Factor 42*h**3 - 40*h**3 + 2 + 32*h**3 + 94*h**3 + 96*h**2 + 24*h.
2*(4*h + 1)**3
Let n(b) be the second derivative of b**7/10080 - b**6/2880 - b**5/240 + b**4/6 + 3*b. Let p(q) be the third derivative of n(q). Factor p(g).
(g - 2)*(g + 1)/4
Let y(r) = -r + 3. Let o be y(-8). Suppose 0 = -b - 0*f + f + 5, -3*f = -2*b + o. Solve -p**3 - p**5 + 0*p**3 + p**4 + p**b = 0 for p.
0, 1
Let 0*i**2 + 0*i**4 - 4/5*i**3 + 0 + 2/5*i**5 + 2/5*i = 0. What is i?
-1, 0, 1
Let o(k) be the first derivative of k**4/18 + 6. Let o(n) = 0. Calculate n.
0
Let k(h) be the second derivative of h**6/10 - h**5/20 - 5*h**4/12 + h**3/6 + h**2 - 4*h. Factor k(g).
(g - 1)**2*(g + 1)*(3*g + 2)
Let h(i) be the second derivative of i**6/420 + i**5/210 - i**3/3 + 4*i. Let a(p) be the second derivative of h(p). Factor a(j).
2*j*(3*j + 2)/7
Suppose -3*h = -0*h - 5*u - 7, 3*u = 3. Solve 0*v**2 + 3*v**2 - 2*v**h + 0*v**2 - v**2 = 0.
-1, 0, 1
Let a = -13 + 13. Let t(l) be the first derivative of 0*l + 1/10*l**4 + 0*l**3 - 1/15*l**6 + 0*l**5 + a*l**2 + 2. Solve t(s) = 0 for s.
-1, 0, 1
Let m(l) be the first derivative of -l**6/27 - 2*l**5/45 + l**4/6 + 10*l**3/27 + 2*l**2/9 + 27. Factor m(d).
-2*d*(d - 2)*(d + 1)**3/9
Suppose -22/5*j + 4/5 - 14/5*j**3 + 32/5*j**2 = 0. What is j?
2/7, 1
Let g(k) be the second derivative of 0 + 3*k + 3/10*k**5 - 3/2*k**3 + 1/14*k**7 + 1/2*k**4 + 3/2*k**2 - 3/10*k**6. Factor g(f).
3*(f - 1)**4*(f + 1)
Suppose 17 = 5*a - 0*a - g, -5*g - 19 = -3*a. Let c be ((-2)/(-2))/(5/a). Factor -c*o**2 + 6/5 + 3/5*o.
-3*(o - 2)*(o + 1)/5
Let l(m) be the first derivative of -m**5/5 - m**4 - 5*m**3/3 - m**2 - 1. What is q in l(q) = 0?
-2, -1, 0
Let d(s) be the first derivative of s**4/2 - 2*s**3/3 - 2. Find a such that d(a) = 0.
0, 1
Let b be (-7)/((-21)/6) + 0. Let s(j) be the first derivative of 4*j + 1 - 2*j**b + 1/3*j**3. Suppose s(p) = 0. Calculate p.
2
Let z be 1 - -41*(2 - -2). Let a = z - 491/3. Suppose -a*u**4 - 7/3*u**3 - 2/3*u**2 + 1/3*u + 0 = 0. What is u?
-1, 0, 1/4
Let p(m) be the third derivative of m**6/480 - m**4/32 + m**3/3 - 3*m**2. Let d(r) be the first derivative of p(r). Factor d(t).
3*(t - 1)*(t + 1)/4
Let l(k) be the first derivative of -k**6/15 + 4*k**5/25 + 8. Solve l(b) = 0 for b.
0, 2
Find y such that 140*y + 33*y**2 + 13*y**3 + 27*y**3 + 82*y**2 + 5*y**4 + 19 + 41 = 0.
-3, -2, -1
Let c = 7514/2169 - -22/241. Let k = c + -26/9. Factor -4*o + k*o**2 + 6.
2*(o - 3)**2/3
Suppose -12/7*c**3 - 3/7*c**5 + 48/7 + 96/7*c - 15/7*c**4 + 48/7*c**2 = 0. What is c?
-2, -1, 2
Suppose -186*g = -189*g + 6. Let 0*r + 0 - 1/4*r**g + 1/4*r**4 + 0*r**3 = 0. Calculate r.
-1, 0, 1
Let t = -130 + 132. Find x such that 5*x**t + 0 - x - 25/4*x**3 = 0.
0, 2/5
Let a(q) be the second derivative of q**4/12 + q**3/3 - 7*q. Factor a(d).
d*(d + 2)
Let z(n) be the first derivative of 2*n**5/5 - 3*n**4 + 8*n**3 - 10*n**2 + 6*n + 29. Factor z(f).
2*(f - 3)*(f - 1)**3
Let -2*t**4 + 2*t**2 + 10733 - 10733 = 0. What is t?
-1, 0, 1
Let m(x) be the second derivative of 7/78*x**4 - 3/13*x**3 + 0 + 2/13*x**2 + x. Determine p so that m(p) = 0.
2/7, 1
Suppose 0 = 10*i - 4*i - 24. Determine m so that -2/7*m**i + 4/7*m - 4/7*m**3 + 2/7 + 0*m**2 = 0.
-1, 1
Find c such that 1/3*c**3 - 1/3*c**4 + 0*c + 0 + 0*c**2 = 0.
0, 1
Let d(z) = z + 6. Let v be d(-6). Let i = -7 - -26. Let -i*g**3 + 2*g**4 - 2*g**2 + 21*g**3 + v*g - 2*g = 0. Calculate g.
-1, 0, 1
Factor -56/11*d - 18/11*d**3 - 16/11 - 60/11*d**2.
-2*(d + 2)*(3*d + 2)**2/11
Let k be (-2)/3 - 8/6. Let r be (-1)/(k + 1) - 1. Determine m so that -2/3*m**3 + 0*m + r*m**2 + 2/3*m**5 + 0 + 0*m**4 = 0.
-1, 0, 1
Let m(o) be the first derivative of 2/21*o**3 - 2/7*o**2 - 4 + 0*o - 2/35*o**5 + 1/7*o**4. Factor m(h).
-2*h*(h - 2)*(h - 1)*(h + 1)/7
Let i(h) be the third derivative of -h**5/60 - h**4/24 + 2*h**2. Factor i(n).
-n*(n + 1)
Let l be (-3)/2 - 801/(-486). Let n(g) be the first derivative of 2 + l*g**3 + 4/9*g - 5/9*g**2. Factor n(x).
2*(x - 2)*(2*x - 1)/9
Suppose 5*j - 5 = 10. Suppose 12 - j = 3*q. Let -2*w**4 + 2*w**2 - 2*w**q + 0*w**2 + 0*w**4 + 2*w**5 = 0. Calculate w.
-1, 0, 1
Let k(o) be the second derivative of -1/15*o**5 + 0 + 0*o**6 + 3*o + 1/63*o**7 + 0*o**4 + 0*o**2 + 1/9*o**3. Factor k(n).
2*n*(n - 1)**2*(n + 1)**2/3
Let c(y) be the first derivative of 2*y**5/3 - 19*y**4/6 + 32*y**3/9 + 4*y**2/3 + 7. Suppose c(f) = 0. What is f?
-1/5, 0, 2
Let s(d) be the first derivative of d**4/10 + 14*d**3/45 - 2*d**2/5 - 34. Factor s(p).
2*p*(p + 3)*(3*p - 2)/15
Suppose -4 = 2*l + 2*k + 2, -k - 9 = -2*l. Let -2*g + l + 1/2*g**2 = 0. Calculate g.
2
Let q(y) be the third derivative of -y**6/540 - y**5/135 - y**4/108 + 5*y**2. Factor q(n).
-2*n*(n + 1)**2/9
Let f(p) be the first derivative of 3*p**6 - 12*p**5/5 - 11*p**4/2 + 8*p**3/3 + 4*p**2 - 16. Factor f(x).
2*x*(x - 1)**2*(3*x + 2)**2
Let j be (0/(-2))/(37 + -35). Find a such that 9/4*a**2 + j - 3/4*a = 0.
0, 1/3
Solve -1 - 7/2*k + 5/2*k**4 - 3/2*k**2 + 7/2*k**3 = 0.
-1, -2/5, 1
Let t(x) = x**2 + x - 4. Let p be t(-3). Factor -8 + 8 - c**2 - p*c**2.
-3*c**2
Let j(v) be the second derivative of -v**7/2100 - v**6/300 - v**5/100 - v**4/60 + 5*v**3/6 - 4*v. Let n(o) be the second derivative of j(o). Factor n(x).
-2*(x + 1)**3/5
Let i(d) be the first derivative of d**4/4 - 10*d**3/3 + 4*d**2 + 11*d + 2. Let h be i(9). Solve 4*y**3 + 2*y**4 + 2 + h*y - 4*y**4 - 6*y = 0 for y.
-1, 1
Let c(u) be the third derivative of u**6/180 - 5*u**2. What is p in c(p) = 0?
0
Factor -1/6*r - 1/12*r**2 - 1/12.
-(r + 1)**2/12
Let l(d) = -29*d**3 - 51*d**2 + 9*d + 80. Let x(k) = -7*k**3 - 13*k**2 + 2*k + 20. Let y(j) = 2*l(j) - 9*x(j). What is g in y(g) = 0?
-2, 1
Let v = 11 - 13. Let c be v/3*2/(-4). Factor -1/3*n + 0 + c*n**2.
n*(n - 1)/3
Factor -3*d**5 - 2 + 2 + 6*d**4 + 0*d**5.
-3*d**4*(d - 2)
Suppose 4*p = -3*o, 0 = -2*p - 2*o - 3*o. Find q, given that p + 1/2*q - q**2 = 0.
0, 1/2
Let v(b) be the second derivative of b**4/6 - 5*b**3/3 + 6*b**2 + 20*b. Factor v(k).
2*(k - 3)*(k - 2)
Determine d so that 18*d**4 + 59*d**3 + 6*d - 10*d**4 + 35*d**2 + 19*d**4 + 7*d**5 + 10*d**4 = 0.
-3, -1, -2/7, 0
Suppose -2*n - 2 = -8. Let g = -11/4 + n. Factor 0*f - 1/4 + g*f**2.
(f - 1)*(f + 1)/4
Let h be 174/29 + (-19)/4. Find q such that -1/2 + h*q - q**2 + 1/4*q**3 = 0.
1, 2
Let j be 2/(-4)*(-12)/3. Let