- 6 + 2*d**3 + 6*d**3 - q*d**3 + 15*d.
3*(d - 2)*(d - 1)**2
Let o be (20/(-50))/((-2)/90). Let z be ((-6)/(-18))/(1/o - 0). Determine n, given that 11/4*n + 17/2*n**2 + 1/4 + z*n**3 = 0.
-1, -1/4, -1/6
Suppose -63 = -16*x + 65. Let g be ((-15)/(-70))/((-28)/x + 4). Let -g*r**2 - 15/7*r - 12/7 = 0. Calculate r.
-4, -1
Let h(x) = -4*x**2 - 32*x - 4. Let l(v) = -24 + 5 + 9 + 11. Let z(d) = -h(d) - 4*l(d). Factor z(k).
4*k*(k + 8)
Let u(k) be the second derivative of k**4/3 - 2*k**3/3 + 11*k - 2. Suppose u(i) = 0. What is i?
0, 1
Suppose 2*u = -u + 54. Let y = u - 14. Factor -17*x - 4*x - y*x**2 - 3*x - 36.
-4*(x + 3)**2
Suppose 2*l = -0*l + 6. Suppose 3*c - 15 = -l*y, 3*c - 5 = y + 2*c. Factor n**2 - 3*n + 2 + y*n**2 + 0.
(n - 2)*(n - 1)
Let x(z) be the first derivative of 12*z**4 - 216*z**3 - 333*z**2/2 - 42*z + 95. What is u in x(u) = 0?
-1/4, 14
Let m(a) = 2*a**2 + 10*a + 8. Let x(f) = 19*f - 10*f - 8*f. Let k(p) = -m(p) + 2*x(p). Suppose k(v) = 0. Calculate v.
-2
Let q = -82 + 148. Let -32 + 2*y - 8*y + 212 + q*y + 5*y**2 = 0. Calculate y.
-6
Find z such that -1/4*z**2 + 0 - 9/4*z = 0.
-9, 0
Let n be (18/(-12))/(3/(1*6)). Let v be (4 + n - (-8)/6) + -1. Factor v + 12*q + 27*q**2.
(9*q + 2)**2/3
Suppose -78*k**3 + 18*k**2 - k**4 + 4*k**4 - 11*k**2 + 78*k - 10*k**2 = 0. What is k?
-1, 0, 1, 26
Let r(t) be the second derivative of -t**9/22680 + t**8/1260 - 4*t**7/945 + 19*t**4/12 - 8*t. Let j(h) be the third derivative of r(h). Factor j(c).
-2*c**2*(c - 4)**2/3
Let v be 8/16*22 + -8. Factor 0 - 2/9*m**4 + 4/9*m + 2/9*m**2 - 4/9*m**v.
-2*m*(m - 1)*(m + 1)*(m + 2)/9
Let g(p) = -p**2 + 14*p + 36. Let y be g(14). Factor 4/3*i**4 + 48*i**2 - 72*i - 40/3*i**3 + y.
4*(i - 3)**3*(i - 1)/3
What is d in -5/2 + 1/6*d**2 + 1/3*d = 0?
-5, 3
Determine k, given that -58 + 98 - k**2 - 3*k + 0*k = 0.
-8, 5
Find n such that 10 - 16 - 2 - 30*n - 7*n**2 = 0.
-4, -2/7
Factor -18*o**2 + 6627*o**3 + 72 + 6*o + 6*o - 6630*o**3.
-3*(o - 2)*(o + 2)*(o + 6)
Let p(b) = 2*b**2 - 50*b + 304. Let s be p(15). Factor -1/4*g**s - 3/2*g**3 - 3/2*g + 0 - 11/4*g**2.
-g*(g + 1)*(g + 2)*(g + 3)/4
Suppose 61*x = 56*x + 10. Let n(f) be the second derivative of -3*f + 1/10*f**5 + 0 - 8/5*f**x - 4/15*f**3 + 1/5*f**4 + 1/75*f**6. Factor n(l).
2*(l - 1)*(l + 2)**3/5
Let p(j) be the third derivative of 0*j - 3/10*j**5 + 1/105*j**7 - 32*j**2 + 0*j**3 + 0*j**4 + 0 + 0*j**6. Factor p(t).
2*t**2*(t - 3)*(t + 3)
Let o(f) be the second derivative of 4*f**3/3 - f**2 + 5*f. Let z be o(2). Find n such that 24*n**2 - 4*n - 8*n**3 - z*n**2 + 4*n**4 - 2*n**4 = 0.
0, 1, 2
Suppose 0 = -18*s + 15*s - y + 7, -s + 4 = 2*y. Factor 0*w + 3/7*w**3 + 0 + 3/7*w**s.
3*w**2*(w + 1)/7
Let w = -1831/44 + 173/4. Let 48/11*t + 2/11*t**3 - w*t**2 - 32/11 = 0. Calculate t.
1, 4
Let z(q) = 2*q**3 - 4*q**2 - 2*q + 10. Let s(r) = -r**3 + r - 1. Let b(u) = -6*s(u) - z(u). Factor b(w).
4*(w - 1)*(w + 1)**2
Let c(g) be the first derivative of 9*g**5/5 - 85*g**4/4 + 84*g**3 - 120*g**2 + 64*g + 245. Factor c(k).
(k - 4)**2*(k - 1)*(9*k - 4)
Suppose 14*z - 16*z = 28*z. Factor z + 0*l - l**3 - 1/4*l**2.
-l**2*(4*l + 1)/4
Let t(z) = -3*z**3 - 5*z**2 - 70*z - 81. Let i(a) = a**3 + a**2 + 23*a + 27. Let s(b) = -11*i(b) - 4*t(b). Factor s(w).
(w + 3)**3
Let c(v) = -4*v**2 - 42*v + 91. Let p(t) = -14*t**2 - 124*t + 274. Let b(w) = -10*c(w) + 3*p(w). Let b(g) = 0. Calculate g.
2, 22
Let k(g) be the first derivative of g**7/273 + g**6/195 - 3*g**5/130 - g**4/78 + 2*g**3/39 + 18*g - 1. Let l(h) be the first derivative of k(h). Solve l(f) = 0.
-2, -1, 0, 1
Let -13 - 19 - 2*f + 40 + 2*f**2 + 0*f**2 - 3*f**2 = 0. What is f?
-4, 2
Let q(f) be the second derivative of f**4/42 - 5*f**3/7 - 16*f**2/7 - f - 15. Factor q(z).
2*(z - 16)*(z + 1)/7
Let l = 53535068072/1005 + -53268719. Let n = l - 10/201. Factor 0*u + n*u**4 + 0 + 6/5*u**5 + 36/5*u**3 + 12/5*u**2.
3*u**2*(u + 2)**2*(2*u + 1)/5
Let b(w) = -14*w**3 + 309*w**2 + 7800*w - 8129. Let q(n) = -5*n**3 + 103*n**2 + 2600*n - 2710. Let t(o) = 6*b(o) - 17*q(o). Factor t(h).
(h - 1)*(h + 52)**2
Suppose 5 + 15 = 4*n. Determine d, given that -20 - 7*d**3 + n*d**4 + 15*d**2 - 13*d - 7*d + 27*d**3 = 0.
-2, -1, 1
Factor 11 + 14*f**2 + 16 + 61 - 144*f - 168*f.
2*(f - 22)*(7*f - 2)
Let l be (-105)/(-49) + ((-34)/85 - 176/(-140)). Suppose -7/4*r**2 + r + 0 + 7/4*r**4 - 5/8*r**l - 3/8*r**5 = 0. What is r?
-1, 0, 2/3, 1, 4
Let l(d) = -9*d**2 + 111*d + 6. Let k(i) = -11*i**2 + 108*i + 7. Let q(s) = -6*k(s) + 7*l(s). Let q(v) = 0. What is v?
-43, 0
Let u = 95 - 91. Let 10*y + u*y**2 + 18*y - 32*y = 0. Calculate y.
0, 1
Let x = -53 + 63. Suppose -x*f + f = 0. Factor f*w**2 + 1/2*w**5 + 0*w + 0 - w**4 + 0*w**3.
w**4*(w - 2)/2
Factor -95119 + 95125 + 2*n**2 + n**2 - 9*n.
3*(n - 2)*(n - 1)
Suppose -53*k - 8 = -55*k. Let g(f) be the third derivative of 2*f**2 + 1/660*f**6 + 2/33*f**3 + 0 + 5/132*f**k + 2/165*f**5 + 0*f. Suppose g(t) = 0. What is t?
-2, -1
Let u(i) = -39*i**2 - 136*i + 82. Let q be u(-4). Determine l, given that -1/4*l + 1/2 - 1/4*l**q = 0.
-2, 1
Let i(k) be the first derivative of -k**5 + 35*k**4/4 - 65*k**3/3 - 15*k**2/2 + 90*k - 19. Let i(w) = 0. Calculate w.
-1, 2, 3
Let f(s) be the second derivative of -2*s**7/63 + 2*s**6/45 + s**5/5 - 5*s**4/9 + 4*s**3/9 + s - 4. Solve f(l) = 0.
-2, 0, 1
Let l = 103 - 1. What is t in -229*t**2 - l*t**3 + 37*t**3 + 209*t**2 - 25*t**4 + 20*t = 0?
-2, -1, 0, 2/5
Factor -27/2*g**2 + 12*g + 26 + 1/2*g**3.
(g - 26)*(g - 2)*(g + 1)/2
Let d(x) be the second derivative of 0*x**2 - 1/48*x**4 - 1/12*x**3 + 12*x + 0. Factor d(h).
-h*(h + 2)/4
Suppose 16*f = 23*f. Let o(q) be the first derivative of f*q**3 + 0*q**2 + 2/35*q**5 + 2 + 0*q + 1/7*q**4. Suppose o(a) = 0. What is a?
-2, 0
Let y(p) be the second derivative of -p**6/30 - p**5/4 - 5*p**4/12 + 5*p**3/6 + 3*p**2 + 78*p. What is d in y(d) = 0?
-3, -2, -1, 1
Factor 55*w**2 + 57*w**2 - 4*w - 24*w**3 - 94*w**2 + w.
-3*w*(2*w - 1)*(4*w - 1)
Let z = 177 - 173. Let a(u) be the third derivative of 0*u - 4*u**2 + 0 + 1/10*u**5 + 3/8*u**z + 0*u**7 - u**3 - 1/10*u**6 + 1/112*u**8. Factor a(j).
3*(j - 1)**3*(j + 1)*(j + 2)
Suppose 0 = -5*p + 5 + 485. Let r = p + -95. Find o such that 2/3*o + 2/3*o**r - 4/3*o**2 + 0 = 0.
0, 1
Let l(u) be the third derivative of -u**8/1848 - 4*u**7/1155 + u**6/132 - 118*u**2 + 2*u. Find b, given that l(b) = 0.
-5, 0, 1
Let g = -2845/168 - -137/8. Factor g + 2/21*p**2 + 2/7*p.
2*(p + 1)*(p + 2)/21
Let c be 6 - 12 - (-34)/45*8. Let f(o) be the first derivative of 0*o**2 + 1/9*o**4 + 0*o + 2/27*o**3 + 10 + c*o**5. Find k such that f(k) = 0.
-1, 0
Let s = -30 + 30. Let c be s - 0/(-3*4/6). Find a such that c*a + 0 - 2/7*a**2 = 0.
0
Let g(w) be the second derivative of w**5/80 - w**4/4 + 3*w**3/2 - 3*w - 4. Find y such that g(y) = 0.
0, 6
Let w(f) be the first derivative of 2/57*f**3 - 14 + 72/19*f - 12/19*f**2. Factor w(q).
2*(q - 6)**2/19
Let m(z) be the second derivative of -z**4/8 - 151*z**3/4 + 114*z**2 - 181*z. Factor m(i).
-3*(i - 1)*(i + 152)/2
Suppose 7*x = 45*x. Factor 3/7*w**3 + 3/7*w**4 - 3/7*w - 3/7*w**2 + x.
3*w*(w - 1)*(w + 1)**2/7
Let j(k) be the first derivative of -k**3/15 + k**2/2 + 36*k/5 + 324. Solve j(s) = 0 for s.
-4, 9
Let n(r) be the first derivative of -r**5/25 + r**4/10 + 8*r**3/5 - 465. Find q, given that n(q) = 0.
-4, 0, 6
Let b(y) = -y**3 + 5*y**2 - 5*y + 1. Let q(x) be the first derivative of x**4/4 - 4*x**3/3 + 2*x**2 - x + 12. Let a(u) = 5*b(u) + 6*q(u). Factor a(i).
(i - 1)*(i + 1)**2
Let g be (-1 + 0)*(-40)/110. Let z = 48 + -46. Factor 2/11*t**z - 2/11*t - g.
2*(t - 2)*(t + 1)/11
Find r such that 826*r + 634/3*r**2 + 2/3*r**4 + 588 - 26*r**3 = 0.
-2, -1, 21
Let -36*p - p**3 + 5*p**3 + 1716*p**2 - 1716*p**2 = 0. Calculate p.
-3, 0, 3
Let x(h) be the second derivative of -25*h**5/8 - 325*h**4/24 + 145*h**3/12 - 15*h**2/4 + 7*h + 4. Factor x(p).
-5*(p + 3)*(5*p - 1)**2/2
Suppose -2*a**2 + 0*a**4 + 3*a**2 + 120*a - 121*a - a**4 + a**3 = 0. Calculate a.
-1, 0, 1
Let z(v) be the first derivative of 6*v**5/5 - 63*v**4/4 + 25*v**3 + 27*v**2 + 33. Find y, given that z(y) = 0.
-1/2, 0, 2, 9
Let f = -11 + 11. Suppose f = z - 3. Suppose 0*v**2 - 4*v**z + v**3 + v**2 + 2*v**2 = 0. Calculate v.
0, 1
Let p = 6073/24 + -253. Let h(j) be the first derivative of -5/12*j**2 + 2/