4/2*(-7 - -6). Let f = 124 + z. Suppose 27*m**2 - m**3 + f*m + 4*m + 31 + 4*m**3 + 50 = 0. What is m?
-3
Find s, given that -150/7 - 2/7*s**2 + 152/7*s = 0.
1, 75
Let s(m) = -m**3 + 26*m**2 - 11*m - 7. Let x(d) = -3*d**2 + d + 1. Let y(n) = -5*s(n) - 35*x(n). Factor y(l).
5*l*(l - 4)*(l - 1)
Suppose o - 28 = 5*j, -j - 11 = -4*o + 6. Factor -6*u**3 - 11*u - 6*u**o + 4*u**2 + 4*u**5 + 19*u - 2*u**4 - 2*u**4.
4*u*(u - 2)*(u - 1)*(u + 1)**2
Let k be 708/(-80)*(-4)/(-12). Let g = 16/5 + k. Suppose 1/4*r**4 + 0 + 0*r**3 + 0*r - g*r**5 + 0*r**2 = 0. What is r?
0, 1
Suppose -v - 18 = -20. Factor j**4 - 5*j**3 - 21*j + 3*j**v - 14*j + 44*j.
j*(j - 3)**2*(j + 1)
Let o(k) be the first derivative of k**5/5 - 4*k**4/3 - 2*k**3/3 + 8*k**2 + 10*k + 13. Let q(p) be the first derivative of o(p). Factor q(y).
4*(y - 4)*(y - 1)*(y + 1)
Let c be (0 + -1)*(3 + -65 + 1). Let d = -58 + c. Let 1/3*z - 1/3*z**2 - 1/3*z**d + 1/3 = 0. Calculate z.
-1, 1
Let w(a) = 19*a**4 + 9*a**3 - 41*a**2 + 49. Let f(t) = 9*t**4 + 4*t**3 - 21*t**2 + 24. Let n(r) = 9*f(r) - 4*w(r). Let n(d) = 0. What is d?
-2, -1, 1, 2
Let j(f) = -f**5 - 7*f**4 - 10*f**3 + 17*f**2 + 27*f - 27. Let h(k) = -k**2. Let l(y) = -5*h(y) + 5*j(y). Find a such that l(a) = 0.
-3, 1
Let n = -32 + 36. Let z(i) = -12*i**3 - 4*i**2 + 52*i + 32. Let g(t) = t**4 + 11*t**3 + 3*t**2 - 53*t - 31. Let y(c) = n*g(c) + 5*z(c). Factor y(p).
4*(p - 3)**2*(p + 1)**2
Let z = 58720/11 + -5338. Factor 10/11*o - 8/11 - z*o**2.
-2*(o - 4)*(o - 1)/11
Let t(c) be the second derivative of c**5/20 + 31*c**4/3 - 251*c**3/6 + 63*c**2 - 36*c + 7. Find u such that t(u) = 0.
-126, 1
Let q be (64/1536)/((-3)/(-8)). Let y(w) be the second derivative of 3*w + 1/6*w**2 - q*w**4 + 0 + 1/6*w**3. Determine o so that y(o) = 0.
-1/4, 1
Let f be 52/104 - 5/(-70). Factor f + 2/7*w**4 - 10/7*w**3 + 18/7*w**2 - 2*w.
2*(w - 2)*(w - 1)**3/7
Let h(d) = -d**2 + d - 1. Let i(y) = 3*y**2 - 38*y + 326. Let v(p) = -6*h(p) - 3*i(p). Find z, given that v(z) = 0.
18
Suppose -40*o = -116 - 4. Factor -3/2*w**4 + 9/2*w**o - 3*w**2 + 0*w + 0.
-3*w**2*(w - 2)*(w - 1)/2
Solve -3 + 8*c - 10*c + 8*c + c**2 - 4*c = 0.
-3, 1
Let l = -353 + 353. Let p(v) be the second derivative of 0*v**2 + 1/12*v**3 + l - 8*v - 1/24*v**4. Factor p(i).
-i*(i - 1)/2
Let o(g) be the third derivative of -g**8/221760 + g**7/6930 - g**6/495 - 3*g**5/20 + 7*g**2. Let h(r) be the third derivative of o(r). Let h(l) = 0. What is l?
4
Let i(m) be the second derivative of m**8/896 - 13*m**7/1680 - m**6/80 + 2*m**4 + 31*m. Let s(g) be the third derivative of i(g). Determine y so that s(y) = 0.
-2/5, 0, 3
Let v(w) be the third derivative of 49*w**6/1200 - 161*w**5/600 + 43*w**4/240 - w**3/20 - 241*w**2. Factor v(h).
(h - 3)*(7*h - 1)**2/10
Let t be 2*1 + 15 + -4. Suppose 0 = t*w - 9*w - 292. Determine o, given that w - 64 + 3*o + 2*o**3 - o**3 - 5*o**2 = 0.
-1, 3
Let a(n) be the second derivative of n**5/120 - n**3/36 - 67*n. Find w such that a(w) = 0.
-1, 0, 1
Let z(m) be the second derivative of -m**10/10080 + m**8/2240 - 11*m**4/12 - 38*m. Let i(s) be the third derivative of z(s). Solve i(p) = 0.
-1, 0, 1
Let i be (-4)/5*(-105)/6. Suppose -6*k**2 - 9*k**3 - 3*k**4 + 0*k**2 + i*k - 14*k = 0. What is k?
-2, -1, 0
Let z = 6469/12 + -539. Let n(x) be the third derivative of -3*x**2 - 1/90*x**5 + 0 - 2/9*x**3 + z*x**4 + 0*x. Factor n(f).
-2*(f - 2)*(f - 1)/3
Let h(t) be the second derivative of -t**5/180 - t**4/36 + t**3/6 - 5*t**2/18 + 3*t. Factor h(g).
-(g - 1)**2*(g + 5)/9
Let b(f) = -4*f - 14. Let p be b(-5). Suppose 3*n**2 - n**3 + n + p - 5 - 4*n**2 = 0. What is n?
-1, 1
Let y(a) = a**2 - 4*a - 3. Let r be y(5). Factor -14*c**3 + 4*c**2 + 13*c**3 - 2*c - c**r.
-c*(c - 2)*(c - 1)
Let l(f) be the second derivative of -f**6/60 - f**5/12 - f**4/24 - 2*f + 251. Find s such that l(s) = 0.
-3, -1/3, 0
Let i = 411 + -411. Let n(l) be the second derivative of 0 + 7*l + i*l**3 + 6*l**2 - 1/4*l**4. Find b, given that n(b) = 0.
-2, 2
Let k(v) be the first derivative of -v**3 - 1/15*v**5 + 0*v**2 + 0*v - 11 - 1/2*v**4. Factor k(w).
-w**2*(w + 3)**2/3
Let w(g) be the first derivative of -10*g**4 + 5*g**3/3 + 55*g**2 - 75*g + 363. Factor w(c).
-5*(c - 1)**2*(8*c + 15)
Suppose -82 = -38*c + 108. Let z(y) be the second derivative of -c*y + 0 - 2/21*y**3 + 3/7*y**2 - 1/42*y**4. Find f such that z(f) = 0.
-3, 1
Let a be 1/3 - 16/(-6). Factor -a + 0*m**2 - 4*m**2 + 2*m**3 - 6*m**3 + 4*m + 7.
-4*(m - 1)*(m + 1)**2
Let i(b) be the second derivative of b**5/110 - 13*b**4/66 - 4*b**3/33 + 52*b**2/11 + 852*b. Let i(p) = 0. What is p?
-2, 2, 13
Let a(z) = -z**3 + 3*z**2 - 3*z - 1. Let b be a(4). Let c = b + 41. What is h in 4*h**5 + c*h**2 + 9*h - 4*h**2 - 8*h**4 + 3*h - 16*h**3 = 0?
-1, 0, 1, 3
Let c be (-93)/(-62) - (-7)/(-6). Let z(b) be the third derivative of -1/24*b**4 + 0*b + 0 + c*b**3 - 1/60*b**5 + b**2. Factor z(h).
-(h - 1)*(h + 2)
Let p = 7/549 + 6/61. Let d(x) be the second derivative of 5*x + 2/3*x**2 - p*x**4 + 1/5*x**5 - 2/3*x**3 + 0. Factor d(m).
4*(m - 1)*(m + 1)*(3*m - 1)/3
What is g in 170*g**3 - 172/3*g + 551/3*g**2 - 75*g**4 + 4 = 0?
-1, 2/15, 3
Let y be 3/6*(-3 + -19). Let k(r) = 17*r**3 - 5*r**2 - 11. Let w(a) = 6*a**3 - 2*a**2 - 4. Let z(n) = y*w(n) + 4*k(n). Let z(v) = 0. Calculate v.
-1, 0
Let d be 11 - (-30)/25*-5. Let u(s) be the first derivative of -1/2*s**4 - 6*s**3 - 27*s**2 - 54*s + d. Factor u(y).
-2*(y + 3)**3
Let n(b) be the third derivative of -1/4*b**4 - 1/70*b**7 + 0*b**5 + 0*b + 3 + 1/2*b**3 - 15*b**2 + 1/20*b**6. Determine i, given that n(i) = 0.
-1, 1
Let l be -2 + 12/(-189)*-35. Solve -14/9*u - 16/9 + l*u**2 = 0.
-1, 8
Let p be (20/40)/((-1)/(-8)). Factor 28 - 12*f**2 - p*f**2 - 4*f**3 + 7*f - 12*f**2 - 3*f.
-4*(f - 1)*(f + 1)*(f + 7)
Factor -121*l**4 - 5*l**3 + 5*l**2 - 4*l**3 + 125*l**4.
l**2*(l - 1)*(4*l - 5)
Suppose -q + 9 = 6. Solve q*x**2 - 15*x**3 + 2*x**4 + x**4 + 5*x**2 + x**2 + 27*x = 0 for x.
-1, 0, 3
Factor 21*w - 24*w - 20 + w**2 + 2.
(w - 6)*(w + 3)
Let d be ((-16)/(-20))/((-2)/(-10)). Suppose t = -0*r - d*r + 5, 3*r = t + 9. Factor -4 + 4*u**r - 5*u**2 + 2*u + 2*u.
-(u - 2)**2
Let r(z) be the second derivative of 109/8*z**4 - 13*z**3 + 0 + 45/4*z**6 + 3*z**2 - 23*z + 117/4*z**5. Factor r(p).
3*(p + 1)**2*(15*p - 2)**2/2
Let j(w) = -4*w**2 - 7*w + 5*w**2 - 4*w + 14. Let x be j(10). Factor -5 + 5 - 3*m + 3*m**3 + 3*m**2 + 0 - 3*m**x.
-3*m*(m - 1)**2*(m + 1)
Factor -17*a + 4*a**4 - 32 + 19*a**2 + 55*a**2 + 30*a**2 + 46*a**3 + 2*a**4 + 73*a.
2*(a + 2)**2*(a + 4)*(3*a - 1)
Factor -4*g**2 - 6*g**2 - 7*g**2 + 23*g**2 - 219*g - 3*g**2.
3*g*(g - 73)
Let o(p) be the second derivative of 1/42*p**4 + 0 + 0*p**3 + 4*p + 0*p**2. Let o(i) = 0. Calculate i.
0
Suppose 4*s - 4*c = -5*c + 1, 2 = s + 2*c. Suppose -4*i + 2*o + 3 + 5 = s, 0 = 4*i + o - 8. Factor 0*u - 8/7*u**3 + 4/7*u**i + 0 + 5/7*u**4 - 1/7*u**5.
-u**2*(u - 2)**2*(u - 1)/7
Let d(v) = -v**2 + v + 12. Let f be (-8)/12*6*-1. Let l be d(f). Factor -2/5*k**2 + l*k + 2/5.
-2*(k - 1)*(k + 1)/5
Let n(i) be the second derivative of -i**7/1260 - i**6/120 - i**5/30 + i**4/2 + 16*i. Let v(s) be the third derivative of n(s). Factor v(c).
-2*(c + 1)*(c + 2)
Let j = -18304/35 - -523. Let f(d) be the second derivative of -d + 0 - 1/84*d**4 - j*d**5 + 0*d**3 + 0*d**2. Factor f(x).
-x**2*(4*x + 1)/7
Let l(o) = -o**3 - o**2 + 1. Let m(i) = 2*i**4 - i**4 - 6*i**3 + 2*i + 9 + 67*i**2 - 3*i**3 - 79*i**2. Let n(k) = 36*l(k) - 4*m(k). Factor n(s).
-4*s*(s - 1)**2*(s + 2)
Let n(i) = -i**4 - i**3 + i - 1. Let o(w) = 28*w**4 + 63*w**3 + 30*w**2 - 23*w - 12. Let s(m) = -3*n(m) - o(m). Suppose s(t) = 0. Calculate t.
-1, 3/5
Let q(j) be the first derivative of j**4/8 + j**3/2 + j**2/2 - 38. Let q(c) = 0. Calculate c.
-2, -1, 0
Let k(i) be the third derivative of -i**5/15 - 17*i**4/6 + 12*i**3 - 245*i**2. Factor k(h).
-4*(h - 1)*(h + 18)
Let j be 1*1/(-4)*(-1 - -1). Let d(x) be the third derivative of j*x + 0 + 0*x**4 + x**2 + x**3 - 1/40*x**5. Find g such that d(g) = 0.
-2, 2
Suppose 4*q = -4*s - 20, 5*s - 39 = 115*q - 112*q. Let w be 358/6 + 3 - -2. Factor 176/3*p**s - 6 - 44*p - w*p**2 - 32/3*p**4.
-2*(p - 3)**2*(4*p + 1)**2/3
Let o = 31/2 + -15. Suppose -32*l = 13*l. Find w, given that l*w + 1/2 - o*w**2 = 0.
-1, 1
Let u = 27 + -11. Factor 4*d*