0.
1
Suppose -3*b - 27 + 27 = 0. Suppose -4*q + x = -14, -6*q + q + 3*x + 21 = b. Factor 0 - 4/7*c**4 - 4*c**2 + 12/7*c + 20/7*c**q.
-4*c*(c - 3)*(c - 1)**2/7
Let y = -87 - -89. Factor -2*o - 9*o**y - 8 + 5*o**2 - 12*o + 2*o.
-4*(o + 1)*(o + 2)
Let w = 4099 - 4096. Determine c so that -c + 2/5*c**2 + c**w - 2/5 = 0.
-1, -2/5, 1
Let o = 28/15 + -97/60. Let l(k) be the first derivative of -1/2*k**2 + 0*k - o*k**4 + 5 + 2/3*k**3. Factor l(i).
-i*(i - 1)**2
Suppose 0 = 2*i + 3*i - 25. Suppose 4*g - 2*t = t + 57, 3*g + i*t = 21. Factor 0*k**2 - 9*k + 6*k**2 - g*k + 5 + 7 + 3*k**3.
3*(k - 1)**2*(k + 4)
Suppose -3*l = -4*l + 2. Factor 2*n**3 + 3*n**l + 20*n**3 - 18*n + 19*n**3 - 5*n**3.
3*n*(3*n - 2)*(4*n + 3)
Suppose 0 = -7*w + 126 + 14. Solve 5*h**5 + 2*h**2 + w*h**4 - 3*h**2 + 25*h**3 + 11*h**2 = 0.
-2, -1, 0
Determine d, given that -32 - 56*d - 1027*d**3 + 2055*d**3 - 28*d**2 - 1032*d**3 = 0.
-4, -2, -1
Let r(w) be the third derivative of -5*w**8/252 + 23*w**7/315 + 7*w**6/45 - 17*w**5/90 - w**4/3 - 2*w**2 + 598*w. What is m in r(m) = 0?
-1, -1/2, 0, 4/5, 3
Let z(n) be the first derivative of n**3/15 + n**2 - 11*n/5 - 23. Factor z(w).
(w - 1)*(w + 11)/5
Let y(q) = -8*q**3 + 19*q**2 - 17*q + 11. Let n(u) = -3*u**3 + 7*u**2 - 6*u + 4. Let i(a) = -11*n(a) + 4*y(a). Suppose i(s) = 0. What is s?
-1, 0, 2
What is t in -3*t**3 - 15*t**4 - 18*t**2 - 3*t**5 + 7*t + 27*t**4 - 7*t = 0?
-1, 0, 2, 3
Let g(h) be the third derivative of h**7/252 + h**6/12 + 11*h**5/72 - 241*h**2. Factor g(c).
5*c**2*(c + 1)*(c + 11)/6
Let k = 2803 - 2801. Let d(t) be the second derivative of 1/2*t**k + 2/9*t**3 - 12*t + 0 + 1/36*t**4. Factor d(c).
(c + 1)*(c + 3)/3
Let h(p) = -p**5 + 2*p**4 + p**3 + p**2. Let t(n) = -n**5 - 26*n**4 + 4*n**3 - 4*n**2. Let u(r) = -4*h(r) - t(r). Solve u(s) = 0.
-4, 0, 2/5
Suppose 0 = -2*n + 3*a + 306 - 262, -23 = -n + a. Solve n + 10*u - 13/4*u**4 - 1/4*u**5 - 55/4*u**3 - 71/4*u**2 = 0 for u.
-5, -2, 1
Let n(y) be the second derivative of y**4/3 + 2*y**3 - 20*y**2 - 3*y + 4. Solve n(f) = 0.
-5, 2
Factor 0 + 1/2*s**4 - 1/2*s**3 - 2*s**2 + 2*s.
s*(s - 2)*(s - 1)*(s + 2)/2
Let -30/7*w + 3/7*w**3 + 72/7 - 9/7*w**2 = 0. What is w?
-3, 2, 4
Let i(m) be the second derivative of m**6/90 - 7*m**5/12 + 67*m**4/36 - 11*m**3/6 - 135*m + 4. Factor i(f).
f*(f - 33)*(f - 1)**2/3
Let s(p) be the first derivative of 5*p**4/4 - 20*p**3 + 29. Find b such that s(b) = 0.
0, 12
Let w(n) = 2*n**2 - 4*n + 2. Let i(q) = 1 + 6*q**2 - 1 + 7*q - 3 - 10*q**2. Let l be 2/5 + 27/(-5). Let s(u) = l*w(u) - 2*i(u). Factor s(k).
-2*(k - 2)*(k - 1)
Suppose -i - 5*u - 7 = -2*u, 12 = 4*i + 2*u. Suppose q + 73 + 56 = 2*v, -i*v - 2*q = -318. Find o such that 3*o - v + 2*o - 4*o**2 + 17*o + 10*o = 0.
4
Let v(r) = r**3 + 6*r**2 + 5*r - 4. Let j be v(-4). What is m in 6*m**3 - 8*m**4 + j*m**2 - 5*m**5 + 4*m**5 + 3*m**5 - 2*m - 6*m = 0?
-1, 0, 1, 2
Suppose -4*n = 3*b - 43, 2*b + 70 = 5*n + 22. Let v be ((-3)/30)/(1 - n/8). Find j such that -v*j**2 - 8/5*j - 8/5 = 0.
-2
Let u(w) be the second derivative of 6*w - 55/6*w**3 + 35/4*w**4 + 0 - 17/4*w**5 + 5*w**2 + 5/6*w**6. Determine b so that u(b) = 0.
2/5, 1
Let n(v) = -4*v**2 - 64*v - 253. Let h(i) = -12*i**2 - 192*i - 758. Let o be 1 - (7 - 3/1). Let y(f) = o*h(f) + 10*n(f). Factor y(k).
-4*(k + 8)**2
Let i(p) be the first derivative of 0*p**2 + 2/3*p**3 - 8 + 0*p + 1/6*p**6 - 1/4*p**4 - 2/5*p**5. Factor i(a).
a**2*(a - 2)*(a - 1)*(a + 1)
Let r(z) be the second derivative of -z**6/150 - 7*z**5/100 - 4*z**4/15 - 2*z**3/5 + 32*z - 4. Factor r(i).
-i*(i + 2)**2*(i + 3)/5
Let i be 6/(-35) + (-392)/(-686). Factor 0 + 0*u**2 - i*u**3 + 0*u - 1/5*u**4.
-u**3*(u + 2)/5
Let s be (((-1)/7)/((-11)/(-77)) - -3)*1. Factor -1/3*l + 1/12*l**s + 1/3.
(l - 2)**2/12
Let y(k) be the second derivative of -k**7/252 + 2*k**6/45 - 5*k**5/24 + 19*k**4/36 - 7*k**3/9 + 2*k**2/3 + 21*k. Determine q, given that y(q) = 0.
1, 2
Let n be (-1)/2*(-22)/33. Suppose 3*i - 1 + 7 = -4*u, 0 = 2*u + 6. Find w, given that 2/3*w**i - 1/3*w**4 + n*w**3 + 0*w + 0 = 0.
-1, 0, 2
Let p = 1751 - 5248/3. Solve -p*f**2 + 7/3*f - 1 + 1/3*f**3 = 0.
1, 3
Suppose 0 = 2*u - j - 12, -4*j - 8 = 8. Factor -5*m**2 - 2*m**4 + 4*m**2 + 5*m**u - 2*m**2.
3*m**2*(m - 1)*(m + 1)
Let y(u) be the second derivative of u**5/20 + 3*u**4/4 - 8*u**3/3 + 3*u**2 + 8*u. Let b(h) = -h**2 + h - 1. Let o(z) = 6*b(z) + y(z). Factor o(x).
x*(x - 2)*(x + 5)
Let p be (-30)/(-12) + 116/(-72). Factor p*h**3 + 8/9*h**2 + 0*h + 0 + 2/9*h**4.
2*h**2*(h + 2)**2/9
Suppose -3*y - u = -4*u, -6*y = u. Let n(s) be the third derivative of 0*s**4 + 1/735*s**7 + 0*s**3 - 1/140*s**6 + y + 0*s + 1/105*s**5 - 6*s**2. Factor n(d).
2*d**2*(d - 2)*(d - 1)/7
Factor -10*k + 32/3 - 2/3*k**2.
-2*(k - 1)*(k + 16)/3
Let g(v) be the second derivative of 5*v**7/42 - v**6/6 - 7*v**5/4 + 5*v**4/12 + 5*v**3 - 63*v + 1. Determine u so that g(u) = 0.
-2, -1, 0, 1, 3
Suppose -4 - 18 = -11*r. Let g = -431 - -3027/7. Factor 2/7*u**4 - g*u**3 + 12/7*u**r - 16/7 + 8/7*u.
2*(u - 2)**3*(u + 1)/7
Let u(s) = -27*s**2 + 51*s + 16. Let k(h) = 40*h**2 - 76*h - 24. Let l(f) = f - 10. Let z be l(15). Let j(y) = z*k(y) + 8*u(y). Find q such that j(q) = 0.
-1/4, 2
Let z be ((-10)/36)/((-21)/(-12) + -3). What is v in 0 + 0*v - z*v**3 - 2/9*v**2 + 2/9*v**5 + 2/9*v**4 = 0?
-1, 0, 1
Let f(q) = -7*q**3 - 22*q**2 + 14*q - 5. Let u(i) = 3*i**3 + 10*i**2 - 7*i + 2. Let h(r) = -2*f(r) - 5*u(r). Factor h(n).
-n*(n - 1)*(n + 7)
Let r(y) be the second derivative of -2*y**7/21 + 2*y**6/3 - 4*y**5/5 - 16*y**4/3 + 64*y**3/3 - 32*y**2 + 65*y. Solve r(z) = 0.
-2, 1, 2
Let y = -1348 + 1351. Let t(x) be the second derivative of 5/6*x**y + 0 - 4*x + 1/4*x**5 + 0*x**2 + 5/6*x**4. Factor t(h).
5*h*(h + 1)**2
What is y in 151*y**2 + 15*y**4 + 8*y**3 - 7*y**3 - 41*y**3 - y**5 - 2*y**4 - 115*y**2 = 0?
0, 2, 9
Let n(c) = c**2 - 3*c + 4. Let q be n(1). Factor 2*p + 8/7 - 2/7*p**3 + 4/7*p**q.
-2*(p - 4)*(p + 1)**2/7
Let 3*o**4 + 9*o**5 - 2*o**5 - 11*o**5 + 5*o**5 + 2*o**3 = 0. What is o?
-2, -1, 0
Let g(w) be the second derivative of 2*w**6/15 + 14*w**5/5 + 61*w**4/3 + 56*w**3 + 72*w**2 + w - 86. Factor g(n).
4*(n + 1)**2*(n + 6)**2
Let a be (-2)/1 + 18/(90/25). Factor 3/4 + 5/4*j**2 - 7/4*j - 1/4*j**a.
-(j - 3)*(j - 1)**2/4
Let z be (4 - -1) + 4 + -6. Factor 3 + 9 - 3 + z*w + 3*w - 3*w**2.
-3*(w - 3)*(w + 1)
Let q = 7/197 - -964/591. Factor 5*y - q*y**3 + 10/3*y**2 + 0.
-5*y*(y - 3)*(y + 1)/3
Let f(i) be the second derivative of i**7/4200 - i**6/900 - i**5/200 - 17*i**3/6 - i. Let o(r) be the second derivative of f(r). Factor o(v).
v*(v - 3)*(v + 1)/5
Let m(c) be the first derivative of 3*c**5/35 + 27*c**4/28 - 33*c**3/7 + 15*c**2/2 - 36*c/7 - 46. Factor m(d).
3*(d - 1)**3*(d + 12)/7
Factor 40*d + 48 - 23/3*d**2 + 1/3*d**3.
(d - 12)**2*(d + 1)/3
Let m(v) = -180*v**3 - 433*v**2 + 322*v + 49. Let c(u) = 45*u**3 + 108*u**2 - 81*u - 12. Let i(z) = -23*c(z) - 6*m(z). Let i(s) = 0. Calculate s.
-3, -1/5, 2/3
Let k(n) = -4*n - 50. Let o be k(-13). Solve -1 + 20*c**3 + 10*c - 37*c**5 + 22*c**5 + 20*c**o + 10*c**4 + 3 + 17*c**5 = 0 for c.
-1
Let s be (31 + 1)*1 - 2. Let b = -27 + s. Factor -2*y + 4*y + 9*y**b + y + 9*y**2 + 3*y**4.
3*y*(y + 1)**3
Let b(u) = 3*u**3 + 24*u**2 + 81*u + 81. Let q(a) = a**2. Let k(v) = b(v) + 3*q(v). Factor k(w).
3*(w + 3)**3
Let m(f) be the third derivative of 3*f**8/28 - 22*f**7/105 - 5*f**6/6 + f**5 + 8*f**4/3 - 8*f**3/3 - 3*f**2 + 27*f. Solve m(n) = 0 for n.
-1, 2/9, 1, 2
Let h = -389 + 392. Let c(y) be the third derivative of 4*y**2 - 1/15*y**5 + 0*y - 1/3*y**4 + 2*y**h + 0. Let c(l) = 0. What is l?
-3, 1
Determine r so that 64*r**4 - 66*r**3 + 133*r**5 + 29*r**5 - 160*r**5 = 0.
-33, 0, 1
Let v(s) be the first derivative of s**4/32 + s**3/3 + 13*s**2/16 + 3*s/4 + 71. Factor v(a).
(a + 1)**2*(a + 6)/8
Let b = -109 - -113. Let u be ((-5)/b*-5)/((-6)/(-4)). Determine v, given that -u*v**3 + 10/3*v**2 - 2/3*v + 0 = 0.
0, 2/5
Let i = 2/2387 + 7157/4774. Let z(s) be the first derivative of s**3 + i*s**2 - 6*s + 9. Factor z(t).
3*(t - 1)*(t + 2)
Let c(h) be the second derivative of -8*h**7/21 - 14*h**6/5 + 19*h**5/5 + 2*h**4 + 2*h - 10. Find x, given that c(x) = 0.
-6, -1/4, 0, 1
Suppose 7989*w + 24 = 7995*w. Suppose 16/11*k**3 - 8/11*k**2 + 0 - 10/11*k**w + 2/11*k**5 + 0