- 13/12*t**2 + 1/24*t**4 + 5/18*t**3. Factor l(d).
(d - 1)**2*(d + 7)/6
Suppose -t = 3*r + 3*t + 2, -8 = 4*r + 4*t. Let w be (-5)/(-5)*-4*r/8. Determine b, given that 0*b + 0*b**2 + 3/8*b**5 + 0 - 9/8*b**4 + 3/4*b**w = 0.
0, 1, 2
Let g = 19044 - 19041. Factor -3/4*x**4 - 3*x**2 + 15/4*x**g + 0 + 0*x.
-3*x**2*(x - 4)*(x - 1)/4
Let y = -590/2043 + 116/227. Let v(h) = h**2 - 5*h + 6. Let o be v(4). Suppose y*i**3 + 0*i**o - 2/3*i + 4/9 = 0. Calculate i.
-2, 1
Factor -2*m**2 - 741 + 741 + 2*m**4 + m**5 + 0*m**2 - m.
m*(m - 1)*(m + 1)**3
Let c = -67 - -84. Let w be ((-1)/3)/(c/(-102)). Factor -2/11*s**w - 2/11*s + 4/11.
-2*(s - 1)*(s + 2)/11
Let q = -260 - -262. Let d(c) be the first derivative of 3/8*c**q + 1/12*c**3 + 1/2*c - 8. Suppose d(s) = 0. Calculate s.
-2, -1
Let u = -4488/203 + 666/29. Factor 3/7*y + 6/7*y**2 - u - 3/7*y**3.
-3*(y - 2)*(y - 1)*(y + 1)/7
Let 488/5*c**3 - 28/5*c - 1024/5*c**4 + 10*c**2 + 2/5 + 512/5*c**5 = 0. Calculate c.
-1/4, 1/8, 1
Suppose 28*o = 27*o + 2. Let g(x) be the second derivative of 4*x + 0*x**3 + 3/20*x**5 + 0*x**o - 1/4*x**4 + 0. Factor g(l).
3*l**2*(l - 1)
Let x = -54 - -59. Suppose 0 = -4*y - x*y. Factor -3/4*q**3 + 1/2*q**2 + y*q + 0.
-q**2*(3*q - 2)/4
Let y(t) = -7*t**2 + t - 2. Let u(o) = 3*o**2 - o + 1. Let m(b) = -2*u(b) - y(b). Let m(i) = 0. Calculate i.
-1, 0
Let n(h) = -h**2 - 13*h + 68. Let z be n(-17). Let c(j) be the second derivative of z + 1/30*j**4 + 0*j**2 + 7*j - 1/15*j**3. Suppose c(f) = 0. Calculate f.
0, 1
Let 3*g**3 - 3551 + 1093 + 213*g**2 + 3672*g - 1430 = 0. What is g?
-36, 1
Let v(i) = -i**2. Let p(l) = -1209*l**2 - 1372 - 1317*l**2 + 430*l**2 - 500*l**3 - 2940*l. Let b(z) = p(z) + 4*v(z). Factor b(r).
-4*(5*r + 7)**3
Factor 5*k**3 + 8/3*k**2 + 0*k - 2/3*k**4 + 0.
-k**2*(k - 8)*(2*k + 1)/3
Determine s so that 5*s**4 - 46*s**3 + 43 - 3 + 0 - 110*s + 6*s**3 + 105*s**2 = 0.
1, 2, 4
Let h(n) be the first derivative of 5*n**4/4 + 5*n**3 + 57. Let h(r) = 0. What is r?
-3, 0
Let v(p) be the first derivative of -p**4/2 - 4*p**3 - 8*p**2 + 81. Solve v(g) = 0.
-4, -2, 0
Suppose 0 = 5*m + 2*d - 23, 2*m - 56*d + 60*d - 22 = 0. Determine q so that 2/5*q**m - 8/5*q + 28/5*q**2 - 6/5*q**4 - 16/5 = 0.
-2, -2/3, 1, 2
Let z(j) = 6*j**3 - 3*j**2 + 8*j - 3. Let n be z(2). Let w = 51 - n. Factor -1/2*q**3 + 0 + 1/2*q**4 + 1/2*q - 1/2*q**w.
q*(q - 1)**2*(q + 1)/2
Let x(j) = -2*j**3 + 8*j**2 + 27*j + 3. Let p(q) = -q**3 - 3*q**2 - q + 1. Let a(r) = -6*p(r) + 2*x(r). Factor a(i).
2*i*(i + 2)*(i + 15)
Let l = 4377/5 - 875. Factor -4/5*n**2 - n - l - 1/5*n**3.
-(n + 1)**2*(n + 2)/5
Let q(a) be the third derivative of -2*a**7/105 + a**6/5 - 11*a**4/3 - 10*a**3 - 57*a**2. What is d in q(d) = 0?
-1, 3, 5
Suppose -3 + 12 = -3*b, 3*r - 4*b = 60. Let a = 21 - 3. Find k such that 2*k + 0*k - 4 - 10*k**3 - 2*k**4 - r*k - a*k**2 = 0.
-2, -1
Let b(o) = o**3 + 20*o**2 + 19*o + 3. Let j be b(-19). Solve 49 + 23 + 3*m**4 + 18*m**2 + j - 120*m + 24*m**3 = 0.
-5, 1
Find p, given that -3*p**5 + 11/4*p**3 + 0 + 11/4*p**4 - 7/4*p**2 - 3/4*p = 0.
-3/4, -1/3, 0, 1
Let w be 9 + -14 - -14*1/2. Let s(c) be the first derivative of 1/10*c**w + 0*c + 1/15*c**3 - 9. Solve s(g) = 0.
-1, 0
Factor 10/7 + 44/7*g + 6*g**2.
2*(3*g + 1)*(7*g + 5)/7
Let s(n) = 6*n + 23. Let p be s(-3). Let d(t) be the third derivative of 0*t**3 + 0*t**p + 0*t + 0*t**4 + 1/70*t**7 - 3*t**2 - 1/40*t**6 + 0. Factor d(b).
3*b**3*(b - 1)
Suppose -4*r - 5*l + 2 = 0, 0*r - 5*r + 25 = -5*l. Let m be (-37)/(-5) - 3 - 0/r. Find h, given that -26/5*h**2 + 8/5*h**3 - 4/5 + m*h = 0.
1/4, 1, 2
Let d = -51 - -51. Solve -h**5 - 6*h**2 - 9*h**3 + 4*h**5 + d*h**5 = 0.
-1, 0, 2
Suppose 0 = -l - 5*y + 10, 1 = -4*l + 4*y + 17. Suppose 14 = t + l*g, 5*t - 26 = g - 4*g. Factor -1/5*f**2 - 2/5*f**t + 0*f + 3/5*f**3 + 0.
-f**2*(f - 1)*(2*f - 1)/5
Let j be (0 + 0)*(-34)/(-238). Determine r so that 1/3*r - 1/3*r**2 + j = 0.
0, 1
Let v(o) be the first derivative of o**6/24 + o**5/12 - 5*o**4/24 - 5*o**3/6 - 5*o**2/2 - 2. Let g(y) be the second derivative of v(y). Factor g(b).
5*(b - 1)*(b + 1)**2
Let n(q) be the third derivative of -11/72*q**4 + 1/126*q**7 + 7/60*q**5 - 17/360*q**6 + 1/9*q**3 + 0*q + 0 - 12*q**2. Solve n(m) = 0.
2/5, 1
Let g(m) be the second derivative of 23*m + 1/48*m**4 - 1/120*m**6 - 3/80*m**5 + 1/168*m**7 + 1/12*m**3 + 0*m**2 + 0. Find b such that g(b) = 0.
-1, 0, 1, 2
Factor 0 - 2/5*m**3 + 4*m**2 + 0*m.
-2*m**2*(m - 10)/5
Let t be (-30)/(-36) - 90/(-108). Solve -t*q + 2/3 + 1/3*q**3 - 1/3*q**4 + q**2 = 0.
-2, 1
Suppose s + 3*s = 12. Let q = -612/737 + 80/67. Factor 2/11*v + 4/11*v**2 - q - 2/11*v**s.
-2*(v - 2)*(v - 1)*(v + 1)/11
Let a(k) be the first derivative of 1/480*k**6 + 0*k**3 + 0*k + 3/2*k**2 + 7 + 0*k**5 - 1/96*k**4. Let o(m) be the second derivative of a(m). Factor o(x).
x*(x - 1)*(x + 1)/4
Let v(c) be the first derivative of c**5/210 - c**4/21 - 5*c**3/21 + 22*c**2 - 46. Let s(a) be the second derivative of v(a). Solve s(x) = 0.
-1, 5
Let k(u) = u**2 - u + 1. Let v(h) = 7*h**2 + 13*h + 12. Let r(q) = -q**3 + 8*q**2 - 6*q - 8. Let g be r(7). Let f(z) = g*v(z) + 2*k(z). Factor f(d).
-5*(d + 1)*(d + 2)
Let g(i) be the first derivative of 3*i**4/4 - 3*i**3 - 6*i**2 - 7. Suppose g(x) = 0. What is x?
-1, 0, 4
Let a = -6160 + 6163. Determine j, given that 2/5*j**a - 8/5 + 0*j + 6/5*j**2 = 0.
-2, 1
Let b(w) be the second derivative of -10*w - 1/25*w**5 - 2/3*w**3 + 0 + 4/5*w**2 + 4/15*w**4. Suppose b(h) = 0. Calculate h.
1, 2
Let j(h) be the first derivative of h**3 - 36*h**2 + 69*h - 379. Suppose j(s) = 0. What is s?
1, 23
Let m(q) be the third derivative of -q**7/70 - 17*q**6/120 + 13*q**5/90 + 11*q**4/18 - 4*q**3/3 - 122*q**2. What is p in m(p) = 0?
-6, -1, 2/3
Let w(r) be the third derivative of -1/210*r**5 + 0 + 2/21*r**3 - 24*r**2 - r + 1/84*r**4. What is u in w(u) = 0?
-1, 2
Let q(r) = 5*r**3 - 58*r**2 + 42*r. Let a(i) = -16*i**3 + 172*i**2 - 127*i. Let c(t) = 2*a(t) + 7*q(t). Factor c(s).
s*(s - 20)*(3*s - 2)
Solve -6*k**2 - 22*k + 3*k**2 + 2*k**2 - 22 - k = 0.
-22, -1
Let s(h) = -107*h + 2. Let g be s(2). Let a = 215 + g. Factor -2/3*c**2 - 10/9*c**a + 4/9*c + 0.
-2*c*(c + 1)*(5*c - 2)/9
Factor 71 - 15*k - 9*k**4 + 14*k**3 + k**5 + 70 - 134 + 2*k**2.
(k - 7)*(k - 1)**3*(k + 1)
Let k(x) = -3 + 3 - x**2. Let i(d) = 2*d**3 - 18*d**2 + 24*d - 16. Let c(o) = -o - 25. Let h be c(-19). Let p(u) = h*k(u) + i(u). Determine y so that p(y) = 0.
2
Let a(d) = d + 2. Let j be a(2). Suppose 3*n - j*m = -14, -m + 15 = 5*n - 0*m. Factor i**3 + 4*i**2 + n*i**4 - 9*i**2 + 3*i**2 - i**4.
i**2*(i - 1)*(i + 2)
Let x(k) = k + 3*k**2 - 2 + 2*k**2 - 4*k**2. Let w be x(2). Factor 20 + w*r**2 + 154*r - 4 - 170*r.
4*(r - 2)**2
Let m = -10439/40 - -261. Let r(u) be the third derivative of -m*u**5 + 0*u**3 + 0 + 1/8*u**4 + 9*u**2 - 1/80*u**6 + 0*u. Determine d, given that r(d) = 0.
-2, 0, 1
Let n be 9 + (3 - (-4 - -10)). Let m(l) = l**2 - 5*l - 2. Let k(h) = h. Let y(j) = n*k(j) + m(j). Factor y(d).
(d - 1)*(d + 2)
Let k(q) be the third derivative of -q**6/80 + q**5/10 - q**4/16 - 3*q**3/2 - 436*q**2. Factor k(j).
-3*(j - 3)*(j - 2)*(j + 1)/2
Let w = 281 + -276. Let f(v) be the second derivative of -3/14*v**2 - 2*v + 0 - 3/28*v**4 - 3/140*v**w - 3/14*v**3. Factor f(p).
-3*(p + 1)**3/7
Let y = -48 + 48. Suppose 6*o - 10*o = y. What is z in -1/4*z**3 + 0*z + o + 0*z**2 = 0?
0
Let g(x) be the first derivative of 0*x + 1/2*x**5 + 3/4*x**4 - 2/3*x**3 + 1/12*x**6 + 30 - 2*x**2. Find n such that g(n) = 0.
-2, 0, 1
Suppose 5*g - 39 + 16 = u, 2*g - 16 = -3*u. Let y(v) be the first derivative of -g + 21/4*v**4 + 9/2*v**2 + 6*v - 12*v**3. Factor y(i).
3*(i - 1)**2*(7*i + 2)
Let t(d) = 20*d**2 - 11*d + 3. Let a(o) be the first derivative of -7*o**3/3 + 2*o**2 - o - 2. Let k(j) = -17*a(j) - 6*t(j). Let k(g) = 0. Calculate g.
-1
Let c be 42/12 + (-2)/(-4). Suppose 6 = -b + c*b. Factor 4/5 + 2/5*z - 42/5*z**b.
-2*(3*z - 1)*(7*z + 2)/5
Suppose -2 = -5*k + n, 0 = 3*n - 2*n + 2. Factor -143*w**2 + 140*w**2 + k*w - 12*w.
-3*w*(w + 4)
Find j such that 12 - 181*j**2 - 9 - 45*j**3 + 22 - 95*j + 40*j**2 = 0.
-5/3, 1/5
Let v be 6 - 70/154 - 5. Find r such that 0 + 2/11*r**3 + 4/11*r - v*r**2 = 0.
0, 1, 2
Let c(x) be the second derivative of x**6/105 + 2*x**5/35 + x**4/14 + 4*x + 1. Factor c(b).
2*b**2