 5*x. Let j = -21 + 16. Let w be i(j). Factor w + 1/3*k**2 + 1/3*k.
k*(k + 1)/3
Let y be 2*((-12)/20 - -1). Suppose 0 = c - 4, -3*p = -4*p + c - 2. Factor 6/5*d + y + 2/5*d**p.
2*(d + 1)*(d + 2)/5
Factor -x**3 + 2*x - 3/2*x**2 + 2 + 1/2*x**4.
(x - 2)**2*(x + 1)**2/2
Factor 8*s**2 - 7 - 10 + s + 5*s + 15.
2*(s + 1)*(4*s - 1)
Let t(s) be the first derivative of 2*s**3/27 + 4*s**2/9 + 8*s/9 + 13. Find z such that t(z) = 0.
-2
Suppose 5*f - 3*c - 76 = 0, -5*f + 5*c + 11 = -59. Let 3*z**4 - 6*z**2 + 2 + f*z**2 + 13*z**3 + 11*z + 8*z**2 = 0. Calculate z.
-2, -1, -1/3
Suppose 2/3*u**2 + 4/3*u + 2/3 = 0. What is u?
-1
Determine l so that -l**5 - 2*l - l**5 + 11*l**3 - 7*l**3 = 0.
-1, 0, 1
Let l(g) = g**2 - g. Let i = 18 + -19. Let y be l(i). Suppose 3/2*f**4 - 3/4*f**y + 9/4*f**3 - 9/4*f - 3/4 = 0. What is f?
-1, -1/2, 1
Let z = 67 - 62. Let t(x) be the third derivative of 0 + 1/54*x**4 + 3*x**2 + 0*x - 1/270*x**z + 0*x**3. Factor t(f).
-2*f*(f - 2)/9
Let c(i) be the first derivative of 2/3*i**3 - 1 + 0*i + i**2. Factor c(n).
2*n*(n + 1)
Let x = -4820 + 2024401/420. Let s(y) be the third derivative of 0*y**6 + 0*y**5 + 0*y**3 + 0*y**4 + 0 + 0*y + x*y**7 - 3*y**2. Let s(v) = 0. Calculate v.
0
Let t be (-5)/(-45) + -1*(-5)/(-45). Determine p so that t*p + 2/3*p**4 + 0 - 2/3*p**3 + 0*p**2 = 0.
0, 1
Factor 1387*m - 2*m**2 + 2 - 1387*m.
-2*(m - 1)*(m + 1)
What is r in -2/9*r + 0 + 2/9*r**2 = 0?
0, 1
Suppose 0 = 4*u + 7*p - 3*p + 4, -p - 6 = -4*u. Suppose -u - d**3 + 2*d + 1 - d = 0. Calculate d.
-1, 0, 1
Let s(z) be the second derivative of z**6/45 - z**5/6 + z**4/3 + 4*z**3/9 - 8*z**2/3 - 22*z. Let s(j) = 0. Calculate j.
-1, 2
Let f(s) be the second derivative of 5*s**8/168 + 6*s**7/35 + s**6/5 - 4*s**5/15 + s**2/2 - 2*s. Let k(w) be the first derivative of f(w). Factor k(i).
2*i**2*(i + 2)**2*(5*i - 2)
Let o = -1009/3 + 337. Factor 2/3*g**3 - 4/3 - o*g + 4/3*g**2.
2*(g - 1)*(g + 1)*(g + 2)/3
Let h(w) = -32*w**4 - 43*w**3 - 92*w**2 - 47*w + 17. Let a(x) = 11*x**4 + 14*x**3 + 31*x**2 + 16*x - 6. Let f(s) = 17*a(s) + 6*h(s). Factor f(d).
-5*d*(d + 1)**2*(d + 2)
Let b(u) be the first derivative of u**7/315 - u**6/180 - u**5/90 + u**4/36 + 5*u**2/2 - 2. Let j(q) be the second derivative of b(q). Solve j(r) = 0 for r.
-1, 0, 1
Let z(u) = -4 + 10 - 4*u**2 + 5 + 8*u + 3*u**2. Let v(y) = -6*y**2 + 41*y + 56. Let t(l) = 2*v(l) - 11*z(l). Determine n, given that t(n) = 0.
-3
Let f(p) = 120*p**2 + p + 1. Let a be f(-1). Let z be a/16 + 2/4. Factor z*w**2 - 2*w + 3*w + 5*w - 2.
2*(w + 1)*(4*w - 1)
Let n(l) = l**2 - l. Let d(i) = 6*i**2 - 7*i - 3. Let s(z) = d(z) - 5*n(z). Factor s(a).
(a - 3)*(a + 1)
Let f(l) = l**5 + l**4 + l**2 - l - 1. Let t(y) = 4*y**5 + 10*y**4 + 2*y**2 - 4*y - 6. Let h(v) = -6*f(v) + t(v). Factor h(u).
-2*u*(u - 1)**3*(u + 1)
Let j be ((-3)/126)/((-1)/(-16))*-3. Solve -2/7*q**2 - 8/7 - j*q = 0 for q.
-2
Let x be (30/(-90))/((-4)/3). Let p = 249 + -991/4. Determine n, given that 5/2*n**2 - p*n - x*n**5 - 5/2*n**3 + 1/4 + 5/4*n**4 = 0.
1
Let p(f) be the third derivative of -f**8/504 - 13*f**7/945 - 11*f**6/270 - f**5/15 - 7*f**4/108 - f**3/27 - 7*f**2. Factor p(t).
-2*(t + 1)**4*(3*t + 1)/9
Let p(y) be the third derivative of y**6/180 - y**5/90 - y**4/36 + y**3/9 + 3*y**2. Solve p(c) = 0.
-1, 1
Let v(g) be the third derivative of -1/120*g**4 - 1/150*g**5 + 1/15*g**3 + 0 + 0*g + 1/600*g**6 - 3*g**2. Factor v(z).
(z - 2)*(z - 1)*(z + 1)/5
Let d(o) be the second derivative of -4*o**4/3 + 2*o**3 + 2*o**2 + 26*o. Find j such that d(j) = 0.
-1/4, 1
Let j(k) = 3*k**2 + k - 7. Let n(u) be the first derivative of -u**3/3 - u**2/2 + 3*u - 2. Let f = -2 + 9. Let g(b) = f*n(b) + 3*j(b). Factor g(l).
2*l*(l - 2)
Let z = -326 - -329. Factor 0 - 2/5*k**z + 0*k + 0*k**2.
-2*k**3/5
Let b(t) be the first derivative of -t**3/18 + 7*t**2/3 - 98*t/3 + 76. Factor b(a).
-(a - 14)**2/6
Let -10*t**2 + 4*t - 11*t**2 + 2*t = 0. What is t?
0, 2/7
Let k(d) be the third derivative of -d**8/85680 + d**7/14280 - d**6/6120 + d**5/60 + 8*d**2. Let n(c) be the third derivative of k(c). Factor n(m).
-2*(m - 1)*(2*m - 1)/17
Let b(n) = 2*n**2 - 2. Let g be b(2). Suppose -f + a - 9 = -2*f, 0 = -f + 2*a - g. Factor -f*h**3 - 2 + 24*h**2 - 4*h**3 - 32*h + 18 + h**4.
(h - 2)**4
Solve 1/4*d**2 + 0 - 15/4*d**3 + 19/4*d**4 - 7/4*d**5 + 1/2*d = 0.
-2/7, 0, 1
Factor 4/3 - 2/3*f - 2/3*f**2.
-2*(f - 1)*(f + 2)/3
Factor -8/19 - 6/19*f + 2/19*f**2.
2*(f - 4)*(f + 1)/19
Let r(f) be the second derivative of 0*f**2 + 1/18*f**3 + 0 - 2*f - 1/36*f**4. Factor r(j).
-j*(j - 1)/3
Let n(u) = -6*u**5 + 7*u**4 - 2*u**3 + 4*u**2 - 3*u. Let f(a) = 5*a**5 - 7*a**4 + 3*a**3 - 3*a**2 + 2*a. Let s(k) = -3*f(k) - 2*n(k). What is c in s(c) = 0?
0, 1/3, 1
Suppose 0 = q - b - 3, -3*q + 10*b + 23 = 14*b. Factor -30*m**3 + 0 - 9/2*m**q - 12*m**2 + 0*m - 21*m**4.
-3*m**2*(m + 2)**2*(3*m + 2)/2
Let y be 56/(-72) - (-3)/3. What is a in -2/9 + 2/9*a**2 - y*a + 2/9*a**3 = 0?
-1, 1
Let y be (-50)/(-18) - (-2)/9. Suppose -6*m = y*j - 2*m + 4, -3*m = 3*j. Find p, given that p**2 + 2*p**j - 7*p**4 + 4*p**4 - p**3 + p**5 = 0.
-1, 0, 1
Let v(q) be the first derivative of 3*q**5/5 + 21*q**4 + 294*q**3 + 2058*q**2 + 7203*q - 32. Suppose v(h) = 0. What is h?
-7
Factor 6/5*b - 2*b**2 + 8/5 - 6/5*b**3 + 2/5*b**4.
2*(b - 4)*(b - 1)*(b + 1)**2/5
Let m(q) be the first derivative of -q**5/6 - 7*q**4/12 - 2*q**3/3 - 3*q**2/2 - 4. Let t(f) be the second derivative of m(f). Factor t(v).
-2*(v + 1)*(5*v + 2)
Let u(g) = -g**3 - g**2 - 4*g + 2. Let x(q) = 0*q**3 - 3*q**3 + 5 - 9*q + 3*q**2 - 4*q**2 + q**3. Let v(z) = -5*u(z) + 2*x(z). Factor v(s).
s*(s + 1)*(s + 2)
Solve -7/5*o**3 + 1/5*o - 6/5*o**4 + 0 + 0*o**2 = 0.
-1, -1/2, 0, 1/3
Let o be -3 + (0 - -5) + (-4)/2. Factor 1/4*c**2 + o*c - 1/4.
(c - 1)*(c + 1)/4
Suppose 5*b - 29 = 1. Suppose -b*l + 12 = -2*l. Let 2/7 - 2/7*d + 2/7*d**l - 2/7*d**2 = 0. What is d?
-1, 1
Let q(y) be the second derivative of 1/6*y**3 - 1/5*y**2 + 0 + 1/20*y**4 - 3*y. Solve q(i) = 0 for i.
-2, 1/3
Let v(a) be the first derivative of -2*a**3/3 - a**2 + 11. Solve v(o) = 0.
-1, 0
Let d(t) be the first derivative of t**5/20 - t**3/2 + t**2 - t - 3. Let a(q) be the first derivative of d(q). Let a(z) = 0. What is z?
-2, 1
Let q(s) be the first derivative of 0*s + 1 - 1/5*s**5 + 1/3*s**3 + 0*s**2 - 1/6*s**6 + 1/4*s**4. Factor q(i).
-i**2*(i - 1)*(i + 1)**2
Let t = 15 - 9. Suppose -t*l + 5 + 7 = 0. Let 0 + 1/3*f**3 + 0*f**l - 1/3*f = 0. What is f?
-1, 0, 1
Let o be (-5)/(10/6) + -31. Let s = -101/3 - o. Factor s*r - 1/3*r**2 + 2/3.
-(r - 2)*(r + 1)/3
Let q(j) be the third derivative of j**5/60 + j**4/4 - 7*j**3/6 + 20*j**2 - 2. Factor q(k).
(k - 1)*(k + 7)
Let j(i) be the second derivative of -i**7/210 + i**6/30 - 7*i**5/100 - i**4/60 + 4*i**3/15 - 2*i**2/5 - 2*i. Solve j(c) = 0 for c.
-1, 1, 2
Let q(v) = -3*v**3 + 12*v**2 - 7*v - 2. Let s(f) = f**3 - 4*f**2 + 2*f + 1. Let r(z) = 3*q(z) + 8*s(z). Let r(l) = 0. What is l?
1, 2
Suppose 3*h + 3*h = 36. Let s(r) be the third derivative of 0*r**7 + 0 - 1/1008*r**8 - 1/72*r**4 + 0*r + 0*r**5 + 0*r**3 + 1/180*r**h + r**2. Factor s(w).
-w*(w - 1)**2*(w + 1)**2/3
Factor -32/15*l**4 + 0 - 52/5*l**3 - 98/15*l - 224/15*l**2 - 2/15*l**5.
-2*l*(l + 1)**2*(l + 7)**2/15
Let g(f) = -f**3 - 17*f**2 - 24*f - 14. Let n(o) = -o**3 - 35*o**2 - 48*o - 29. Let r(l) = -5*g(l) + 2*n(l). Determine b so that r(b) = 0.
-2, -1
Let c = -308/5 - -62. Let 2/5*m**2 - 4/5*m + c = 0. Calculate m.
1
Let w(v) be the first derivative of 0*v - 3 - 4/3*v**2 - 4/9*v**3. Factor w(z).
-4*z*(z + 2)/3
Solve 2/3*p**2 + 0 + 4/3*p = 0.
-2, 0
Suppose -13*u + 2*u + 22 = 0. Let a(o) be the second derivative of 5/4*o**4 + 3*o**u + 0 + 7/2*o**3 + 3*o. Factor a(l).
3*(l + 1)*(5*l + 2)
Let p(o) be the third derivative of 1/72*o**4 + 0*o - 1/180*o**5 + 0 - 3*o**2 + 0*o**3. Factor p(b).
-b*(b - 1)/3
Determine z so that -14 - 2*z**2 - 28*z + 38 - z + 7*z = 0.
-12, 1
Let h be 3 + 0/3 + -1. Factor -m**2 - 12*m + 2*m**h + m**2 + 12 + m**2.
3*(m - 2)**2
Let n be 15/3 - 1 - (-33)/(-9). Let j(k) be the first derivative of 1/2*k**2 + 1 - n*k - 1/3*k**3 + 1/12*k**4. Factor j(o).
(o - 1)**3/3
Let k = -58 - -64. Let f(x) be the third derivative of -2/27*x**3 + 0*x + x**2 - 5/108*x**4 - 2/135*x**5 - 1/540*x**k + 0. Determine s so that f(