0.
-1, 0, 1
Let o(b) = 4*b**2 + 4*b. Let m(q) = -q**4 - 4*q**2 - 5*q. Let t(r) = 4*m(r) + 5*o(r). Factor t(h).
-4*h**2*(h - 1)*(h + 1)
Suppose 0 = r + 4*r - 65. Suppose 6*t - 17 = r. Factor 0*o**5 - 4*o**3 + 8*o**2 - 8*o**4 + t*o**5 - o**5.
4*o**2*(o - 2)*(o - 1)*(o + 1)
Let w(t) = t**2 - 17*t + 5. Let z be w(17). Suppose 0 = 3*d + z*o - 0 - 16, -14 = -4*d - 3*o. Factor 16/5 - 4*a + 4/5*a**d.
4*(a - 4)*(a - 1)/5
Suppose -2*u = -8*u - 24. Let b(x) = -x**3 - x**2 - x - 3. Let c be b(u). Find o such that 3 - 4*o - c*o**2 + 46*o**2 + o + 3*o**3 = 0.
-1, 1
Let h(r) = -242*r**2 + 104*r - 25. Let i(p) = 121*p**2 - 54*p + 12. Let t(d) = 3*h(d) + 7*i(d). Factor t(j).
(11*j - 3)**2
Let u(m) be the second derivative of -m**7/210 + m**5/30 - m**3/6 + 7*m**2 + 8*m. Let w(a) be the first derivative of u(a). Factor w(y).
-(y - 1)**2*(y + 1)**2
Suppose -4 - 9*p**2 + 7/2*p**3 - 14*p + 5/2*p**4 = 0. What is p?
-2, -1, -2/5, 2
Let p(l) = 2*l**2 - 38*l + 36. Let j(h) = h**2 - h. Let q(f) = -4*j(f) + p(f). Factor q(u).
-2*(u - 1)*(u + 18)
Let g(h) be the third derivative of 0 + 0*h - 5/12*h**4 + 13*h**2 - 5/6*h**3 - 1/12*h**5. Factor g(j).
-5*(j + 1)**2
Let r(l) be the second derivative of -l**6/1440 - 11*l**3/3 - 19*l. Let u(f) be the second derivative of r(f). Let u(o) = 0. What is o?
0
Let t(p) = -11*p**4 - 15*p**3 - 14*p**2 + 24*p - 16. Let o(n) = 7*n**4 + 10*n**3 + 9*n**2 - 16*n + 10. Let d(a) = 8*o(a) + 5*t(a). Factor d(k).
k*(k - 1)*(k + 2)*(k + 4)
Let m(n) be the second derivative of 5*n**4/12 + 55*n**3/6 - 30*n**2 - 456*n. Factor m(u).
5*(u - 1)*(u + 12)
Suppose -2*n = -t - 10, -5*n + t + 4624 - 4608 = 0. Solve 285/2*d**n - 75/2*d**3 - 96*d + 18 = 0 for d.
2/5, 3
Factor -2099*u - 5*u**3 - 4860 - 184*u**2 - 61*u - 72*u**2 + 61*u**2.
-5*(u + 3)*(u + 18)**2
Let v = -49 + 51. Suppose 23*a**2 + 77*a**3 - 29*a**v - 50*a**2 + 8*a + 29*a**3 + 18*a**5 - 76*a**4 = 0. What is a?
0, 2/9, 1, 2
Let r be 44/99*((-9)/(-84))/((-9)/(-18)). Determine b, given that r*b**3 - 4394/21 - 26/7*b**2 + 338/7*b = 0.
13
Solve -1211 + 17*y**2 - 4*y**4 + 40*y**3 - 112*y - 5*y**2 + 1131 = 0 for y.
-1, 2, 10
Suppose -2*z = -2*g - 5*z - 8, -3*z - 10 = g. Find r, given that r**2 - 3*r**5 + 2*r - 3*r**4 - 8*r + g*r**2 - 36*r**3 + 45*r**3 = 0.
-2, -1, 0, 1
Let x = -3023 - -3026. Factor 6/5*w**2 + 0 - 3/5*w**x - 3/5*w.
-3*w*(w - 1)**2/5
Suppose -2*i = -4*g + 18, i + 11 = 4*g - 6. Let x be i*(-5)/(70/2). Determine l, given that -3/7 + 5/7*l - 1/7*l**2 - x*l**3 = 0.
-3, 1
Let v(i) be the second derivative of 0 + 0*i**2 + 1/2*i**4 - 18*i - 3/40*i**5 + i**3 - 1/20*i**6. Solve v(r) = 0.
-2, -1, 0, 2
Let p(f) be the second derivative of f**4/15 - 26*f**3/15 + 24*f**2/5 + 59*f. Factor p(k).
4*(k - 12)*(k - 1)/5
Let n be (11/22)/(1/(-24)*-4). Let z(v) be the third derivative of 0 - 7*v**2 + 0*v**4 - 1/150*v**5 + 0*v + 1/15*v**n. Solve z(w) = 0 for w.
-1, 1
Factor -s - 1/5*s**2 - 4/5.
-(s + 1)*(s + 4)/5
Factor 8/3*g + 1/3*g**4 - 2/3*g**3 - 4/3 - g**2.
(g - 2)*(g - 1)**2*(g + 2)/3
Let a(c) be the third derivative of 7*c**6/20 - 23*c**5/30 + c**4/6 + 589*c**2. Solve a(o) = 0 for o.
0, 2/21, 1
Let i be ((-1)/3)/((885/(-90))/59). Let f(h) be the first derivative of i*h**5 - 5*h - 15/2*h**2 - 2 - 5/3*h**3 + 15/4*h**4. Determine c so that f(c) = 0.
-1, -1/2, 1
Factor -16/5 + 1/5*d**3 + 7/5*d**2 - 2*d.
(d - 2)*(d + 1)*(d + 8)/5
Suppose 0 = -6*l + 44 - 8. Suppose -l*x + 7 = -5. Let 3*f**5 + 1/2*f**x - f + 0 - 19/2*f**4 + 7*f**3 = 0. Calculate f.
-1/3, 0, 1/2, 1, 2
Factor -69/4*y**2 - 1/4*y**3 - 12167/4 - 1587/4*y.
-(y + 23)**3/4
Let m be (24/(-100)*-5)/((-4)/(-30)). Factor -4*v**2 - v + 0*v + 4*v**3 - 8*v**3 + m*v.
-4*v*(v - 1)*(v + 2)
Let w(d) = -3*d + 12. Let n be w(3). Factor 7*h**2 + 2*h**4 - 7*h**2 - 8*h + 4*h**3 + 2*h**n.
2*h*(h - 1)*(h + 2)**2
Suppose 4*c - 3*d = -3, -12*c + 7*c - 4*d = -35. Let p(s) be the first derivative of -3/5*s**5 + 0*s + c*s**2 + 3*s**3 + 0*s**4 - 12. Factor p(y).
-3*y*(y - 2)*(y + 1)**2
Suppose l = 5*a + 27, 4*l - 19 = 2*a + 35. Suppose 11*y = l + 21. Solve 0*g + 0*g**2 + g**y + 1/2*g**5 + 3/2*g**4 + 0 = 0.
-2, -1, 0
Suppose 9*h = 7*h + 6. Suppose -330 + 330 + 3*l**4 - h*l**2 = 0. What is l?
-1, 0, 1
Let i = -13 - -3. Let b be i*2*(-4)/16. Solve d + d**4 - d**4 - d**b - 2*d**2 + 2*d**4 = 0.
-1, 0, 1
Let 0 + 6*d**2 - 3/2*d**4 + 0*d - 35/2*d**3 = 0. Calculate d.
-12, 0, 1/3
Let s be 24/(-4)*4/(-12). Factor -8*x + 8 + 6*x**2 - 8*x**2 + 0*x**s + 2*x**3.
2*(x - 2)*(x - 1)*(x + 2)
Let y(r) be the first derivative of r**3/12 + 8*r**2 + 63*r/4 + 239. What is u in y(u) = 0?
-63, -1
Suppose 5*g + y = 10, -4*y - 32 = -2*g - 2*g. Let v(w) be the second derivative of 0 + 4*w + 1/18*w**4 + 2/9*w**g + 0*w**2. Suppose v(z) = 0. What is z?
-2, 0
Let j be 69/828*(-1)/(-15). Let f(b) be the third derivative of -9*b**2 + 0*b + 0 - 1/9*b**3 - j*b**5 + 1/24*b**4. Factor f(i).
-(i - 2)*(i - 1)/3
Suppose 0 - 1/6*y**2 + 2*y**4 - 11/6*y**3 + 0*y = 0. Calculate y.
-1/12, 0, 1
Let u = 128 + -57. Factor 71*t - t**4 - u*t - t**4 + 2*t**2.
-2*t**2*(t - 1)*(t + 1)
Let s(m) = m**3 + m**2 + m. Let l(k) = -14*k**3 - 53*k**2 - 35*k + 24. Let r = 43 - 44. Let p(q) = r*s(q) + l(q). Factor p(i).
-3*(i + 2)**2*(5*i - 2)
Let a(x) be the third derivative of x**7/56 - 87*x**6/160 + 349*x**5/80 + 279*x**4/32 - 81*x**3/4 - 10*x**2 - 1. Suppose a(b) = 0. What is b?
-1, 2/5, 9
Let c(n) be the second derivative of n**9/15120 - n**8/6720 - n**7/2520 + n**6/720 - 7*n**4/12 - 3*n. Let a(m) be the third derivative of c(m). Factor a(x).
x*(x - 1)**2*(x + 1)
Let n = 3764 - 11288/3. Factor 4/3 + 8/3*x + n*x**2.
4*(x + 1)**2/3
Find d, given that 18*d**3 - 198*d - 3*d**4 + 60*d**2 - 30*d**3 + 135 + 0*d**3 + 18*d**3 = 0.
-5, 1, 3
Let d(i) = -i - 21. Let y be d(12). Let l = y + 167/5. Determine h so that 1/5*h - 3/5*h**2 + l = 0.
-2/3, 1
Let t(l) = 2*l**3 + 3*l**2 - l + 4. Let z be t(-2). Let i(f) be the first derivative of -z - 4/7*f + 2/7*f**3 - 1/7*f**2. Find b such that i(b) = 0.
-2/3, 1
Suppose -4*o + 6*o = 10, r - 11 = -o. Let s(y) be the first derivative of -r + 8/5*y**5 + 8*y - 9*y**4 + 56/3*y**3 - 18*y**2. Solve s(w) = 0.
1/2, 1, 2
Let l(u) be the first derivative of -7*u**5 + 15*u**4 + 100*u**3 + 40*u**2 + 155. Factor l(y).
-5*y*(y - 4)*(y + 2)*(7*y + 2)
Let v = 75 - 65. Factor -8*o**3 + 2*o**4 + 2*o**4 - 2*o + v*o**3 + 4 - 6*o**2 - 2*o**4.
2*(o - 1)**2*(o + 1)*(o + 2)
Let k(j) = 5*j**2 + 4*j - 3. Let g be k(1). Let y(r) be the first derivative of -1/12*r**4 + 2/3*r - 5/6*r**2 - g + 4/9*r**3. Factor y(w).
-(w - 2)*(w - 1)**2/3
Let -8*b - 64/9 - 2/9*b**3 - 8/3*b**2 = 0. Calculate b.
-8, -2
Let t(b) = 37*b**3 - 261*b**2 + 359*b + 89. Suppose -6*a + 10*a = 32. Let y(c) = -12*c**3 + 87*c**2 - 120*c - 30. Let v(i) = a*y(i) + 3*t(i). Factor v(f).
3*(f - 3)**2*(5*f + 1)
Let l(h) be the third derivative of h**7/42 - 31*h**6/60 + 83*h**5/20 - 85*h**4/6 + 50*h**3/3 + h**2 + 70*h. Find o, given that l(o) = 0.
2/5, 2, 5
Suppose -32/3 + 2/3*a**2 + 4*a = 0. Calculate a.
-8, 2
Suppose 8*g - 2*g = 18. Suppose g*x - 14 = -2*o, 4*o = 3*x + x + 8. Factor 2/3 + w + 1/3*w**x.
(w + 1)*(w + 2)/3
Suppose -9*n + 123 - 96 = 0. Let z(m) be the first derivative of 4/3*m**n + 0*m + 2 - 3*m**4 + 4/15*m**5 + 2/3*m**6 + 4/3*m**2. Let z(r) = 0. What is r?
-2, -1/3, 0, 1
Let y(l) = -4*l**3 - 29*l**2 + 5*l - 3. Let w(v) = v**3 - v**2 - v - 1. Suppose 0 = -6*s - 4*s - 10. Let i(r) = s*y(r) + 3*w(r). Let i(g) = 0. What is g?
-4, 0, 2/7
Let j(p) be the third derivative of -p**8/84 - 6*p**7/35 - 4*p**6/5 - 16*p**5/15 + 246*p**2. Factor j(y).
-4*y**2*(y + 1)*(y + 4)**2
Determine j so that 2/7*j**4 + 10/7*j**2 + 12/7*j**3 - 48/7*j - 72/7 = 0.
-3, -2, 2
Let m(f) be the second derivative of f**4/15 - f**3/5 - 9*f**2/5 + 169*f - 1. Solve m(u) = 0.
-3/2, 3
Let o(w) be the first derivative of -w**7/1680 + w**6/320 - w**5/240 + 12*w**2 - 24. Let j(x) be the second derivative of o(x). Let j(v) = 0. Calculate v.
0, 1, 2
Let c(q) be the first derivative of 250/9*q + 34/45*q**5 + 580/27*q**3 - 53/9*q**4 - 325/9*q**2 - 1/27*q**6 - 34. Factor c(m).
-2*(m - 5)**3*(m - 1)**2/9
Let p(c) = c**2 + c - 10. Suppose -21 = 4*g - 49. Let o be p(g). Determine i, given that 5*i + 164*i**3 + 16 - o*i - 20*i**4 - 100*i**5 - 23*i + 4*i**2 = 0.
-1, 2/5, 1
Let n(d) = -8*d**3 - 67*d**2 + 67