33*p**4 + 38*p**4 = 0. What is p?
-2, -1, 0
Let z be (-108)/5*((-60)/(-9))/2. Let y = 72 + z. Factor 0 + 6/5*g**3 + 0*g**2 + y*g + 3*g**5 - 21/5*g**4.
3*g**3*(g - 1)*(5*g - 2)/5
Let n be 1 + (-16)/(560/25). Suppose 0 + n*v**2 + 4/7*v = 0. What is v?
-2, 0
Suppose 158*n + 2*b + 8 = 162*n, 4*n - 4 = 3*b. Let p(r) be the second derivative of -7/5*r**5 - 4/3*r**3 + 0*r**2 + 0 - n*r - 3*r**4. Factor p(h).
-4*h*(h + 1)*(7*h + 2)
Let l be 3*4/(-12) - -13. Factor 20*g - 5*g**2 - 8*g**2 + 30*g**2 - l*g**2 + 15.
5*(g + 1)*(g + 3)
Suppose 63 + 37 = 50*o. Let j = 53 - 97/2. Factor 3*x - 21/2*x**4 - 18*x**3 + 0 - j*x**o.
-3*x*(x + 1)**2*(7*x - 2)/2
Let s(q) be the second derivative of -q**4/60 + q**3/6 - 2*q**2/5 - 13*q. Factor s(r).
-(r - 4)*(r - 1)/5
Let w(r) = -r**2 + 3*r - 2. Let n(b) = 4*b**2 - 10*b + 7. Suppose 3*q = 3*k - 12, 2*q + 11 = -0*q + k. Let a(i) = q*w(i) - 2*n(i). Factor a(v).
-v*(v + 1)
Find l such that 2/9*l**3 + 8/9*l**2 + 0 + 0*l = 0.
-4, 0
Let z(k) = -12*k - 5. Let x be z(-11). Let a = -379/3 + x. Suppose a - 3*f**3 - 19/3*f**2 + 17/3*f**4 - f + 4*f**5 = 0. What is f?
-1, -2/3, 1/4, 1
Factor 3362/9 + 2/9*p**2 - 164/9*p.
2*(p - 41)**2/9
Let x(l) be the second derivative of l**4/12 - 2*l**3/3 - 3*l**2/2 - 5*l. Let j be x(5). Suppose 4*v**3 + j*v + 0 - 1 - 2 + 2 + 7*v**2 = 0. Calculate v.
-1, 1/4
Let i(g) be the first derivative of -g**4/12 + 290*g**3/3 - 42050*g**2 + 24389000*g/3 - 422. Factor i(j).
-(j - 290)**3/3
Factor 15/2*a**4 + 0*a**2 + 9*a**3 + 0 + 0*a + 3/2*a**5.
3*a**3*(a + 2)*(a + 3)/2
What is f in 138*f - 5268 - 1004 - 5*f**2 + 86*f + 3*f**2 = 0?
56
Let w(p) be the second derivative of 2/3*p**3 + 0*p**2 + p + 0 - 2/5*p**5 + 0*p**6 + 2/21*p**7 + 0*p**4. Factor w(j).
4*j*(j - 1)**2*(j + 1)**2
Let g be (4 + 130/(-4))*2/(-3). Suppose 0 = 8*q - g - 21. Solve 1/4*i**4 - 1/2*i**3 + 1/4*i**q + 1/4*i - 1/2*i**2 + 1/4 = 0 for i.
-1, 1
Let c(l) = l**3 - l**2 + l. Let g(m) = 15*m**3 - 3*m**2 - 279*m - 297. Let t(j) = -12*c(j) + g(j). Suppose t(s) = 0. What is s?
-11, -1, 9
Let b(v) = 3*v**2 - 7. Let j(h) be the second derivative of 0 + 1/3*h**4 - h - 4*h**2 + 1/6*h**3. Let m(w) = -5*b(w) + 4*j(w). Factor m(y).
(y + 1)*(y + 3)
Let s be -6 + -5 + 488/40. Factor -4/5*u + s*u**2 - 2/5.
2*(u - 1)*(3*u + 1)/5
Let b(f) be the second derivative of -f**5/5 + f**4 + 6*f**3 - 54*f**2 - 2*f - 1. Determine i, given that b(i) = 0.
-3, 3
Let b(w) = w**2. Let u(m) be the first derivative of -7*m**3/3 + 5*m**2 + 15*m + 22. Let c(n) = -2*b(n) - u(n). Factor c(i).
5*(i - 3)*(i + 1)
Let o be 69/(-28)*432/(-9). Let t = o - 118. Factor 2/7*k**2 - t + 0*k.
2*(k - 1)*(k + 1)/7
Let y = 28 + -20. Let x be (-12)/8*y/(-6). Suppose 2/7*v**x + 2/7 + 4/7*v = 0. Calculate v.
-1
Let n = 136 - 92. Let g = -40 + n. Factor -4*a + 4 + 1 - g*a**2 + 3.
-4*(a - 1)*(a + 2)
Let m(i) be the third derivative of -i**4/12 - 7*i**3/3 - 55*i**2 - 2. Let h be m(-8). Determine p so that -1/2*p + 1/4*p**h + 1/4 = 0.
1
Let f(n) be the third derivative of 0*n**4 + n**2 + 0 + 0*n**3 + 1/2352*n**8 + 1/420*n**5 - 1/1470*n**7 - 1/840*n**6 + 0*n. Determine c so that f(c) = 0.
-1, 0, 1
Let k be (-4)/(32/(-442)) - (-2)/(-8). Let s = -377/7 + k. Let -6/7*c**2 + 8/7 - s*c = 0. Calculate c.
-2, 2/3
Let o be (3/3)/((-14)/21678) + -2. Let z = o - -1553. Factor -z*w**2 - 4/7*w - 2*w**3 + 0.
-2*w*(w + 1)*(7*w + 2)/7
Let h(g) be the first derivative of 0*g**2 - 12/25*g**5 + 0*g - 8/15*g**3 + 9/10*g**4 + 1/15*g**6 - 37. Factor h(d).
2*d**2*(d - 4)*(d - 1)**2/5
Let h be 3 + (-1612)/(-143)*2/(-8). Let z be 5 - 6 - 30/(-22). Factor 0 + z*p + h*p**2.
2*p*(p + 2)/11
Let y(k) be the first derivative of -4*k**3/15 - 6*k**2/5 + 8*k + 15. Factor y(i).
-4*(i - 2)*(i + 5)/5
Suppose 4*n = g + 15, -3*n = -0 - 6. Let c be ((-2)/(-3))/(-3*g/9). Let 0 - c*s + 2/7*s**2 = 0. What is s?
0, 1
Factor 0 - 24/11*y**2 + 2/11*y**3 + 0*y.
2*y**2*(y - 12)/11
Let a = -416 - -1225/3. Let u = a + 173/21. Determine p so that 2*p**2 - u - 10/7*p = 0.
-2/7, 1
Let f = 37/12 + -29/12. Let a(k) be the first derivative of 2/25*k**5 + f*k**3 - 3 + 2/5*k**4 + 2/5*k**2 + 0*k. Find r, given that a(r) = 0.
-2, -1, 0
Let s = -2147 - -10749/5. Let 4/5*p**2 + 16/5*p**4 - s*p**3 - 6/5*p**5 + 0*p + 0 = 0. What is p?
0, 2/3, 1
Let w(p) = 9*p**3 - 9*p**2 + 151*p - 343. Let t(b) = -b**3 + b**2 - 19*b + 43. Let m(i) = -51*t(i) - 6*w(i). Let m(k) = 0. Calculate k.
-5, 3
Let h(k) be the first derivative of -k**4/4 + 3*k**3 + k**2/2 - 9*k - 173. Find u, given that h(u) = 0.
-1, 1, 9
Factor -39 + 65*y - 24*y - 3*y**2 - 22*y + 12 - 37*y.
-3*(y + 3)**2
Let k(o) be the second derivative of o**4/96 + 3*o**3/8 + 2*o**2 - o + 55. Factor k(w).
(w + 2)*(w + 16)/8
Let s(w) = -w**4 + 2*w**3 + 2*w - 1. Let x(l) = -2*l**5 + 7*l**4 + 38*l**3 - 136*l**2 + 183. Let r(n) = 3*s(n) + x(n). What is i in r(i) = 0?
-5, -1, 2, 3
Let g(k) be the third derivative of 0*k + 0 + 3*k**2 - 5*k**4 - 2/15*k**6 - 6*k**3 + 23/15*k**5. Factor g(z).
-4*(z - 3)**2*(4*z + 1)
Let x(f) = 11*f**4 - 33*f**3 - 12*f**2 - 2*f - 2. Let j(l) = -14*l**4 + 33*l**3 + 11*l**2 + 3*l + 3. Let c(m) = 2*j(m) + 3*x(m). Find a such that c(a) = 0.
-2/5, 0, 7
Let i = 1/8 - 1/12. Let y(v) be the second derivative of -i*v**4 + 3*v + 1/12*v**3 + 0 + 0*v**2. Find a such that y(a) = 0.
0, 1
Let m = 143 - 137. Suppose 2*p = -4*a + 22, -m*p + 3*p = a - 13. Factor 0*s - 1/5*s**a - 1/5*s**2 + 0 - 2/5*s**3.
-s**2*(s + 1)**2/5
Let r be 8 - ((-3 - 0) + 2). Suppose -3*z = d - 7, 5*z + d = -2*d + r. Factor -4*x**2 + 4*x**4 + 2*x - 2*x**5 + 0*x**4 - 2*x**z + 2*x**3.
-2*x*(x - 1)**3*(x + 1)
Suppose -15*w + 7*w + 16 = 0. Let u(d) be the first derivative of 0*d - 1/4*d**3 - 1/16*d**4 - 5 + 0*d**w. Factor u(r).
-r**2*(r + 3)/4
Let z be 6*4/14 + (2 - 2). Let v = 50/21 - z. Determine f, given that -1/3*f**2 + 1/3*f**4 + 0 - 2/3*f**3 + v*f = 0.
-1, 0, 1, 2
Let u(p) be the first derivative of p**6/27 + 2*p**5/9 - 7*p**4/6 + 46*p**3/27 - 8*p**2/9 + 277. Factor u(y).
2*y*(y - 1)**3*(y + 8)/9
Let b = 6981/28 + -1698/7. Factor -33/4*a**2 - 3/4*a**3 - 57/4*a - b.
-3*(a + 1)**2*(a + 9)/4
Let a(h) = h - 1. Let z(t) = 7*t - 13. Let l(n) = -3*a(n) + z(n). Let d be l(3). Determine p so that 0 - 1/4*p**4 + 1/4*p**3 + 1/2*p**d + 0*p = 0.
-1, 0, 2
Let s be (-2)/(-4)*(-6 + (7 - -5)). Factor 19*z**3 - s*z + 7*z + 5*z**2 - 18*z**3.
z*(z + 1)*(z + 4)
Let b(u) be the second derivative of -u**5/160 + 41*u**4/48 - 161*u**3/48 + 5*u**2 + 64*u - 2. What is c in b(c) = 0?
1, 80
Let r(m) be the first derivative of 5/3*m**3 + 17 + 25/2*m**2 + 1/12*m**4 + 125/3*m. Let r(g) = 0. Calculate g.
-5
Let a(r) be the second derivative of r**7/294 - r**6/90 + r**5/105 + 3*r**3/2 - 5*r. Let v(k) be the second derivative of a(k). Factor v(u).
4*u*(u - 1)*(5*u - 2)/7
Suppose 2*p + 0 = 2*k - 14, 4*k = -5*p + 10. Let o be ((p - 1) + 0)/(-1). Solve -12*g**3 - 4*g**4 - o + 2 + 16*g + 1 = 0 for g.
-2, 0, 1
What is o in 4/19*o**3 - 34/19 - 34/19*o**4 + 68/19*o**2 - 2/19*o - 2/19*o**5 = 0?
-17, -1, 1
Let l(t) = -3*t**3 + 4*t**2 - 3*t + 2. Let o(b) be the second derivative of -b**4/12 + b**2/2 + 8*b. Let z(v) = -l(v) + 2*o(v). Factor z(n).
3*n*(n - 1)**2
Let w(c) = -c**3 - c**2 - 2*c - 2. Suppose 0 = k - 4*y + 2, 3*k + 3*y + 6 = -0*y. Let b(z) = 3*z**3 + 4*z**2 + 9*z + 9. Let m(x) = k*b(x) - 9*w(x). Factor m(s).
s**2*(3*s + 1)
Let l(o) = 4*o**2 + 13 + 7 - 22 + 8*o. Let y(s) = 5*s**2 + 9*s - 2. Let t(k) = -6*l(k) + 5*y(k). Factor t(x).
(x - 2)*(x - 1)
Let s be (-148)/12*(-5 - (0 - 2)). Let o = s + -32. Factor 4/3*u**o - 8/3*u**2 + 16/3*u**4 + 16/3*u**3 - 8/3 - 20/3*u.
4*(u - 1)*(u + 1)**3*(u + 2)/3
Suppose -4*l + 5*c = -3*l + 21, -3*l - 3 = -3*c. Factor 4*g - 4*g**2 - 6*g**2 + 2*g**2 + l*g**3.
4*g*(g - 1)**2
Let u = -9282/5 - -1858. What is y in 14/5*y**3 + 4/5*y**4 - 8/5*y + u*y**2 + 0 = 0?
-2, 0, 1/2
Let v(j) = j**3 - 7*j**2 + 8*j - 8. Let r be v(6). Let f = 73 + -44. Factor -29 + f - r*p + 2*p**2.
2*p*(p - 2)
Factor 5400*b**2 - 216000*b + 1/4*b**4 + 3240000 - 60*b**3.
(b - 60)**4/4
Suppose -3 = w, -18 = 3*k + 3*w - 6*w. Let p be (k/(-6))/(6/8). Let -4*f**2 + 4*f**p + f**2 = 0. Calculate f.
0
Let w(h) be the third derivative of -h**5/510 - 4*h**4/17 - 192*h**3/17 - 12*h**2. Factor w(g).
-2*(g + 24)**2/17
Let b = -14951 - -74758/5. Factor 21/5*a**2 + b*a**3 + 3 + 33/5*a.
3*(a + 