-4, -3
Suppose 21*y = 14*y + 175. Factor 36 + 10*d - 15*d - 9*d**2 - y*d - 18*d.
-3*(d + 6)*(3*d - 2)
Suppose 0 = 33*n - 32*n - 4. Let z be ((-576)/(-560))/(-6) - (-32)/56. Suppose -4/15*c - 16/15*c**3 + z*c**n + 0 + 14/15*c**2 = 0. Calculate c.
0, 2/3, 1
Let z(a) be the first derivative of a**7/70 - a**6/40 - a**5/5 + a**4/2 + a**2/2 + 4*a + 41. Let o(t) be the second derivative of z(t). Factor o(q).
3*q*(q - 2)*(q - 1)*(q + 2)
Factor 26*o + 18*o**2 + 15*o**2 + 5*o - 32 - 36*o**2 + 4*o**2.
(o - 1)*(o + 32)
Factor -304/11*r**2 - 2/11*r**3 - 1022*r + 2156.
-2*(r - 2)*(r + 77)**2/11
Let b(f) = 3*f**3 + 77*f**2 + 11*f. Let s(w) = 2*w**3 + 44*w**2 + 6*w. Let h(a) = -4*b(a) + 7*s(a). Factor h(v).
2*v*(v - 1)*(v + 1)
Factor 3258*p**4 - 356218 - 222*p**3 - 190*p**3 - 3256*p**4 - 300800 + 28152*p**2 - 628452*p.
2*(p - 69)**3*(p + 1)
Let t(q) be the first derivative of q**4/7 + 52*q**3/7 + 144*q**2 + 1232*q - 5028. Factor t(z).
4*(z + 11)*(z + 14)**2/7
Let w(a) = 40595*a - 608923. Let n be w(15). Suppose -784/3 - 1/3*x**n + 56/3*x = 0. What is x?
28
Let k be (-3)/((-207)/6) - (-2454)/1932. Let g(q) be the second derivative of 11/28*q**4 - 3/140*q**5 - k*q**3 + 27/14*q**2 + 0 + 10*q. Factor g(n).
-3*(n - 9)*(n - 1)**2/7
Suppose 83*m = 81*m + 6. Factor -1125 + 251*s**2 + 751*s + 5*s**m - 106*s**2 + 263*s - 39*s.
5*(s - 1)*(s + 15)**2
Let i(m) be the first derivative of 16*m**3/3 + 43*m**2/2 - 44*m - 151. Let d(f) = 22*f**2 + 65*f - 66. Let y(s) = -5*d(s) + 7*i(s). Factor y(r).
2*(r - 11)*(r - 1)
Let j(z) = -2*z**2 - 45*z - 230. Let b be j(-8). Let g(u) be the third derivative of 0*u**3 + 1/64*u**4 + 3*u**b + 1/20*u**5 + 1/20*u**6 + 0 + 0*u. Factor g(h).
3*h*(4*h + 1)**2/8
Let 17 + 89*s + 96 + 40 + 45*s - 21 + 2*s**2 = 0. Calculate s.
-66, -1
Let u(g) = g**2 - 22*g - 132. Let h(o) = o**2 + 23*o + 129. Let t be h(-6). Let j be u(t). Factor -3/7*c**4 + 0 - 9/7*c**j - 15/7*c + 27/7*c**2.
-3*c*(c - 1)**2*(c + 5)/7
Let x(v) be the second derivative of -v**5/150 - 2*v**4/5 - 48*v**3/5 - 91*v**2/2 + 6*v + 2. Let z(u) be the first derivative of x(u). What is d in z(d) = 0?
-12
Let a = -18 - -14. Let s = 9 + a. Factor -4*m**3 - s*m**3 - 6*m**2 + 6*m**3.
-3*m**2*(m + 2)
Let q(y) be the third derivative of y**5/10 - 137*y**4/3 - 61*y**3 + 888*y**2. Solve q(x) = 0 for x.
-1/3, 183
Let f(s) = 5*s - 5. Let n be f(4). Suppose 5 = 5*x - n. Factor 4*p + 0*p**4 - 13*p - x + 13*p + 7*p**2 - 10*p**3 + 3*p**4.
(p - 2)*(p - 1)**2*(3*p + 2)
Let z = -1243280 + 1243283. Suppose 86/21*k**z + 16/7*k**2 + 20/7*k**4 + 8/21*k + 0 + 2/3*k**5 = 0. What is k?
-2, -1, -2/7, 0
Suppose 70*x = -10945 + 11295. Let n(h) be the third derivative of -1/2*h**3 + 0*h + 0 - 1/70*h**7 + 1/10*h**x + 0*h**6 + h**2 + 0*h**4. Factor n(o).
-3*(o - 1)**2*(o + 1)**2
Let z(i) = -3*i - 27. Let m(q) = q**2 + 2*q - 2. Let h(y) = -y**2 - 2*y + 32. Let g(v) = -h(v) - 2*m(v). Let f(j) = 3*g(j) - 4*z(j). Factor f(r).
-3*(r - 4)*(r + 2)
Let s be (-3 + (-90)/(-14))*112/(-360)*-3. Factor 2/5*c**3 - s - 8/5*c + 4/5*c**2.
2*(c - 2)*(c + 2)**2/5
Let x(z) be the first derivative of 10*z**6/3 - 892*z**5/5 + 550*z**4 - 656*z**3/3 - 336*z**2 - 744. Determine t, given that x(t) = 0.
-2/5, 0, 1, 2, 42
Let w be (-1 + -727)/(3*(-4)/(-48)). Let d be (-23)/78 - 1344/w. Factor 1/6*s + 1/3 - 1/2*s**2 + d*s**4 - 1/6*s**3.
(s - 2)*(s - 1)*(s + 1)**2/6
Let x(a) = -8*a**2 - 3967*a - 1314727. Let p(g) = 15*g**2 + 7935*g + 2629455. Let i(c) = -5*p(c) - 9*x(c). What is n in i(n) = 0?
-662
Let v = 771 - 768. Let x(z) be the second derivative of 0 - 17*z - 1/6*z**4 + 0*z**v + z**2. Suppose x(y) = 0. What is y?
-1, 1
Suppose -11*q - 27*q = -836. Suppose 21*b + q - 64 = 0. Find r, given that -24/7*r + 24/7*r**b - 6/7*r**3 + 0 = 0.
0, 2
Determine w so that -9/2 + 1/2*w**2 - 4*w = 0.
-1, 9
Let c(x) be the third derivative of 1/6*x**5 + 1/42*x**7 + 2 + 0*x - 5/24*x**4 - 1/12*x**6 + 1/6*x**3 - 5*x**2 - 1/336*x**8. Determine q, given that c(q) = 0.
1
Let g(q) = -q**2 - q. Let o(b) be the first derivative of 165*b**2/2 - 51. Let t(f) = 5*g(f) - o(f). Find s such that t(s) = 0.
-34, 0
Let b(j) = -82*j**3 + 76*j**3 - 5*j - 4*j**2 + 27*j + 4. Let m(h) = 13*h**3 + 9*h**2 - 45*h - 9. Let c(d) = 9*b(d) + 4*m(d). Factor c(u).
-2*u*(u - 3)*(u + 3)
Suppose 58 = 5*y + 4*o, -y - o = 815 - 829. Factor 2/3*x**3 - y*x**2 + 4/3*x + 0.
2*x*(x - 2)*(x - 1)/3
Let r = 2115494/317325 + 2/105775. Let s(v) be the second derivative of -2*v - 1/4*v**5 + r*v**3 - 5/6*v**4 - 28 + 0*v**2. What is o in s(o) = 0?
-4, 0, 2
Let g be (((-1809)/(-2412))/(18/32))/((-4)/(-6)). Determine r so that -27/2*r**g + 0 - 12*r - 3/2*r**3 = 0.
-8, -1, 0
Suppose 11*c + 42 = 17*c. Let n(t) be the third derivative of 5/12*t**4 + 6*t**2 + 5/42*t**c + 0*t + 1/2*t**6 + 0*t**3 + 0 + 3/4*t**5. Factor n(q).
5*q*(q + 1)**2*(5*q + 2)
Let a(n) be the second derivative of -9*n**5/20 - 35*n**4/2 - 149*n**3/2 - 63*n**2 - 1328*n. Factor a(h).
-3*(h + 2)*(h + 21)*(3*h + 1)
Let s(r) be the first derivative of 75*r**4/4 - 1160*r**3 + 1383*r**2/2 - 138*r - 5072. What is c in s(c) = 0?
1/5, 46
Let j(h) = -h**3 + h**2 + 2. Let c(r) = -10*r**3 - 22*r**2 + 18. Let s(k) = -c(k) + 9*j(k). Suppose s(y) = 0. What is y?
-31, 0
Let p(r) be the first derivative of -27/10*r**2 - 1/5*r**3 + 34 + 0*r. Find a such that p(a) = 0.
-9, 0
Suppose h + d + 48 = -0*d, 110 = -2*h + 5*d. Let v = h - -52. Find m, given that 1/4 + m - 5/4*m**v = 0.
-1/5, 1
What is s in 618*s**3 + 3543*s - 607*s**3 + 136*s**2 - 3374*s + 44 = 0?
-11, -1, -4/11
Let x(w) be the third derivative of -w**5/300 + 91*w**4/30 - 16562*w**3/15 + 852*w**2. Factor x(t).
-(t - 182)**2/5
Let i be 210/(-15) - (53 + -69). Suppose 12*n + 7/8*n**i - 7/2 = 0. Calculate n.
-14, 2/7
Let a(f) = 137*f + 22333. Let c be a(-163). Suppose -4*d + 12/5 + 4/5*d**3 + 4/5*d**c = 0. What is d?
-3, 1
Let v(n) be the third derivative of -n**6/300 - 2*n**5/5 - 113*n**4/60 + 58*n**3/5 + 21*n**2 - 43. Factor v(t).
-2*(t - 1)*(t + 3)*(t + 58)/5
Find c, given that -145*c**2 + 47 + 5*c**4 + 93 + 121*c - 60*c**3 - 61*c = 0.
-2, -1, 1, 14
Suppose -9 = 22*w - 25*w - 2*v, 3 = w - 3*v. Let c be (-20)/w*(-3)/(30/4). Factor -20/9*i + 2/9*i**4 - 4/3*i**3 + c*i**2 + 2/3.
2*(i - 3)*(i - 1)**3/9
Let h(l) = -7*l**3 + 36*l**2 - 15*l - 62. Let u(a) = -6*a**3 + 33*a**2 - 15*a - 57. Let b(w) = 3*h(w) - 4*u(w). Factor b(f).
3*(f - 7)*(f - 2)*(f + 1)
Suppose x + 1290 = -5*t, 2*t + 3*x = -0*t - 516. Let a = t - -1809/7. Solve -a*g**2 + 16/7*g - 13/7*g**3 - 4/7*g**4 + 4/7 = 0.
-2, -1/4, 1
Let v(f) be the first derivative of 5/21*f**3 + 13 - 1/42*f**4 - 35*f + 0*f**2. Let a(t) be the first derivative of v(t). Factor a(i).
-2*i*(i - 5)/7
Let b be 22/(-12)*(-606)/2222. Let a be (3 - 0) + 3/(-2). Factor 1/2*m**3 - a*m**2 - b*m + 1 + 1/2*m**4.
(m - 1)**2*(m + 1)*(m + 2)/2
Let h(s) be the second derivative of s**6/15 - 7*s**5/5 - 67*s**4/6 - 88*s**3/3 - 36*s**2 + 253*s - 14. Determine j, given that h(j) = 0.
-2, -1, 18
Let -2*s**2 + 4*s**4 + 0 - 10*s + 15/2*s**3 + 1/2*s**5 = 0. What is s?
-5, -2, 0, 1
What is k in 29/3*k**4 + 17/9*k**5 - 76/3*k**3 - 28/9*k**2 + 0 + 0*k = 0?
-7, -2/17, 0, 2
Let g(a) be the second derivative of a**6/20 - 141*a**5/10 + 4691*a**4/4 - 12831*a**3 + 223587*a**2/4 + 9967*a. Factor g(s).
3*(s - 91)**2*(s - 3)**2/2
Let t(h) = 2*h**3 + 45*h**2 + 121*h + 113. Let n(f) = -f**3 - 24*f**2 - 60*f - 58. Let j(d) = -5*n(d) - 3*t(d). Suppose j(p) = 0. Calculate p.
-7, -1
Let i = -608 - -956. Factor 348*j**2 - 2*j**3 + 14*j - 12 - i*j**2.
-2*(j - 2)*(j - 1)*(j + 3)
Let z(i) = -i**2 + 3*i - 1. Let j = -213 + 212. Let l(x) = 8*x**2 - 28*x + 14. Let t(r) = j*l(r) - 6*z(r). Let t(d) = 0. Calculate d.
1, 4
Factor -8 - 16/3*v**3 - 53/3*v**2 - 62/3*v - 1/3*v**4.
-(v + 1)**2*(v + 2)*(v + 12)/3
Let z(v) be the third derivative of v**5/20 - 279*v**4/4 + 77841*v**3/2 - 513*v**2. Factor z(d).
3*(d - 279)**2
Let p(a) be the second derivative of a**6/105 - 3*a**5/14 - a**4/14 + 43*a**3/21 + 30*a**2/7 - 82*a + 1. What is d in p(d) = 0?
-1, 2, 15
Find x, given that -159*x**2 - 160*x**2 - 161*x**2 - 159*x**2 + 2050624 - 2864*x + 640*x**2 = 0.
1432
Let f(v) = -6*v**2 + 659*v + 631. Let c(b) = -b**2 + 110*b + 105. Let o(p) = -34*c(p) + 6*f(p). Suppose o(g) = 0. Calculate g.
-1, 108
Let r(h) = -61*h**2 - 147*h + 194. Let m