 u(i) be the first derivative of 3 - 4*i + 0*i**2 + 4/3*i**3. Factor u(c).
4*(c - 1)*(c + 1)
Let f(a) = a**3 + 15*a**2 + 16*a + 31. Let q be f(-14). Suppose 3*j = -j + 20. Let -j*z**5 - 3*z**4 + q*z**5 + z**4 = 0. Calculate z.
-1, 0
Let k(d) be the second derivative of d**7/126 - 7*d**6/45 + 23*d**5/20 - 35*d**4/9 + 50*d**3/9 - 22*d + 1. Find i such that k(i) = 0.
0, 2, 5
Let h(g) be the first derivative of -g**4/4 - 3*g**3 - 7*g**2 - 202. Solve h(w) = 0 for w.
-7, -2, 0
Let a(v) = 48*v. Let u(o) = -o**2 - 50*o. Let x(p) = -5*a(p) - 4*u(p). Suppose x(f) = 0. What is f?
0, 10
Let z(j) be the second derivative of -j**4/48 + 5*j**3/24 + 3*j**2/4 - 432*j. Solve z(n) = 0 for n.
-1, 6
Suppose 31*j - 1021 = 12*j - 964. Determine r, given that 15/2*r + 21/2*r**2 - j = 0.
-1, 2/7
Let z = -5 - -2. Let x be (-3 - z)*2/(-6). Factor x*h - 2*h**2 + 2 + h**2 + 2*h**2 - 3*h.
(h - 2)*(h - 1)
Let a(p) be the second derivative of -p**7/630 + p**6/45 - 29*p**4/12 + 19*p. Let i(j) be the third derivative of a(j). Factor i(w).
-4*w*(w - 4)
Let k(u) = -u**2 + 4*u - 4. Let c(t) = 3*t**2 - 7*t + 7. Let s(o) = 3*c(o) + 5*k(o). Let a be s(1). Factor 7*z + z**2 + a*z**4 - 2*z**4 - 3*z**2 - 5*z - 2*z**3.
2*z*(z - 1)**2*(z + 1)
Let g(s) be the first derivative of s**6/120 + s**5/20 + s**4/16 + 3*s - 15. Let p(i) be the first derivative of g(i). Determine j so that p(j) = 0.
-3, -1, 0
Let c(j) be the second derivative of -j**7/42 + 29*j**6/30 - 163*j**5/20 - 673*j**4/12 - 368*j**3/3 - 128*j**2 + j - 5. Factor c(m).
-(m - 16)**2*(m + 1)**3
Let j(v) be the first derivative of -v**6/70 + 3*v**5/140 + v**4/28 - v**3/14 + 60*v - 32. Let b(q) be the first derivative of j(q). Factor b(r).
-3*r*(r - 1)**2*(r + 1)/7
Factor -2/3*r + 1/3*r**2 - 8/3.
(r - 4)*(r + 2)/3
Suppose -8*p + 14*p - 18 = 0. Factor -6/5 - 3/5*s**p - 3*s - 12/5*s**2.
-3*(s + 1)**2*(s + 2)/5
Let w = 121 + -237/2. Factor 0 + v**2 + 0*v - w*v**3.
-v**2*(5*v - 2)/2
Let k be (4/(-7))/(1936/(-616)). Factor 2/11*c**3 - k*c + 0*c**2 + 0.
2*c*(c - 1)*(c + 1)/11
Let f(d) be the third derivative of -d**6/420 + d**5/30 - 5*d**4/28 + 3*d**3/7 - 141*d**2 + d. Factor f(o).
-2*(o - 3)**2*(o - 1)/7
Let c(n) be the third derivative of n**7/105 - 11*n**6/60 + 16*n**5/15 - 7*n**4/3 + 238*n**2. Suppose c(u) = 0. What is u?
0, 2, 7
Let m(w) be the first derivative of w**7/147 - 3*w**5/70 - w**4/21 + 17*w - 12. Let n(f) be the first derivative of m(f). Factor n(s).
2*s**2*(s - 2)*(s + 1)**2/7
Let y(c) be the second derivative of -7*c**4/3 - 6*c**3 + 32*c**2 - 2*c - 128. Factor y(l).
-4*(l - 1)*(7*l + 16)
Let p be 5/(-2) - (-26767)/9230. Let v = -37/40 - -9/8. Factor -r + p + 4/5*r**2 - v*r**3.
-(r - 2)*(r - 1)**2/5
Let x(n) be the third derivative of -n**9/120960 - n**8/40320 + 7*n**5/30 + 11*n**2. Let f(j) be the third derivative of x(j). Determine k, given that f(k) = 0.
-1, 0
Find b such that -10*b**4 - 3 + 16*b**2 - 2*b**3 + 3 - 4*b**3 - 2*b**5 + 2*b**3 = 0.
-4, -2, 0, 1
Find k such that -1/9*k**5 + 119/9*k**2 - 98/9*k + 0 - 11/9*k**4 - k**3 = 0.
-7, 0, 1, 2
Let v be (-500)/(-375) + 5/3. What is t in 11/3*t**2 - 4/3 + 4*t - 10*t**v - 25/3*t**4 = 0?
-1, 2/5
Let f be 1 - (-16)/40 - -3*2/(-6). Factor -6/5*u + f*u**2 + 0.
2*u*(u - 3)/5
Let f(j) be the third derivative of -1/6*j**4 + 49/720*j**6 - 1/9*j**3 + 0 - 7/120*j**5 + 6*j**2 + 0*j. Determine o, given that f(o) = 0.
-2/7, 1
Let c = -72 + 75. Suppose 4 + 2 = c*f. Factor 0*u + 1/5*u**3 + 0 - 2/5*u**f.
u**2*(u - 2)/5
Let r(k) = k**3 - 5*k**2 - 7*k + 9. Let t be 5*(-4)/(-10)*3. Let y be r(t). Factor 4/9*l**y - 2/9*l**4 + 0*l**2 + 0*l + 0.
-2*l**3*(l - 2)/9
Let c(g) = -4*g**2 - 120*g - 5. Let d(s) = -15*s**2 - 420*s - 18. Let x(k) = 18*c(k) - 5*d(k). Determine l, given that x(l) = 0.
0, 20
Let -1081/4*u**2 - 435/4*u**3 - 39/4*u**4 - 81 - 252*u - 1/4*u**5 = 0. Calculate u.
-18, -1
Let i(v) be the second derivative of -v**6/45 - v**5/5 - 2*v**4/9 + 8*v**3/3 + 32*v**2/3 + 179*v. Suppose i(f) = 0. What is f?
-4, -2, 2
Let q(l) be the third derivative of 0 + 1/180*l**5 - 1/9*l**3 + 0*l + 5*l**2 + 1/72*l**4. Determine w, given that q(w) = 0.
-2, 1
Find t such that -69*t**4 - 11*t**3 + 3*t**3 - 7*t**3 + 72*t**4 + 18*t**2 = 0.
0, 2, 3
Let b(z) = -5*z**2 + 9*z - 8. Let d(h) = 16*h**2 - 27*h + 25. Let y be (0/(0 + -1))/3. Suppose y = -3*n - 7 + 13. Let m(p) = n*d(p) + 7*b(p). Factor m(g).
-3*(g - 2)*(g - 1)
Let p(t) be the first derivative of -10*t**3 + 153*t**2/2 - 15*t - 293. Let p(k) = 0. What is k?
1/10, 5
Let m(j) be the second derivative of -j**6/40 - 3*j**5/20 + 11*j**4/16 - 3*j**3/4 + 139*j - 2. Determine i, given that m(i) = 0.
-6, 0, 1
Let t be -4 + 7 + (-104)/35. Let m = 38/105 - t. Factor 0 + 0*w**2 + m*w - 1/3*w**3.
-w*(w - 1)*(w + 1)/3
Let w(h) be the third derivative of h**5/100 - h**4/4 + 5*h**3/2 - 17*h**2 - 4. Factor w(g).
3*(g - 5)**2/5
Let m(r) be the first derivative of r**5/15 + 25*r**4/12 + 47*r**3/3 - 221*r**2/6 - 338*r/3 - 249. Let m(d) = 0. Calculate d.
-13, -1, 2
What is w in 34/9*w - 1/9*w**2 + 35/9 = 0?
-1, 35
Let i be (-5)/90*-3 - 1/(-3). Factor 1/2*a**3 - 1/4 + 0*a**2 - i*a + 1/4*a**4.
(a - 1)*(a + 1)**3/4
Let w(h) be the second derivative of h**7/357 + 5*h**6/51 + 71*h**5/85 - 97*h**4/51 - 143*h**3/51 + 169*h**2/17 - 7*h - 6. Find s such that w(s) = 0.
-13, -1, 1
Let n(g) be the first derivative of g**5/30 - g**3/3 + 2*g**2/3 + 29*g + 25. Let m(w) be the first derivative of n(w). Determine u so that m(u) = 0.
-2, 1
Let d(j) be the third derivative of -j**6/60 + j**5/15 - 4*j**2 + 33. Solve d(k) = 0 for k.
0, 2
Let q be 4/(-2) + ((-56)/12 - -4). Let t = -4/3 - q. Find b, given that 2/3*b**2 - 2 + t*b = 0.
-3, 1
Let s be (-44)/(-12) - 3/(-9). Factor 12*k + 2*k**3 + 4 - s - 12*k**2 + k**3.
3*k*(k - 2)**2
Let b(u) be the first derivative of u**8/112 - u**7/35 - u**6/40 + u**5/10 - 41*u**2/2 + 42. Let m(y) be the second derivative of b(y). Factor m(v).
3*v**2*(v - 2)*(v - 1)*(v + 1)
Let q(d) be the second derivative of -d**8/6720 + d**7/630 - d**6/720 - d**5/20 + 2*d**4 - 38*d. Let z(n) be the third derivative of q(n). Factor z(i).
-(i - 3)*(i - 2)*(i + 1)
Let p be (-170)/(-255) + (-2)/3. Let j be 4/(-1)*2/(-14). Determine s so that p + 2/7*s**3 + 2/7*s - j*s**2 = 0.
0, 1
Determine h so that -60*h**2 - 4*h**3 + 2*h**3 - 66 - h**3 + 69*h + 60*h + 0*h**3 = 0.
-22, 1
Suppose -q + 4*a = 10, 5*q + 5*a - 44 = q. Suppose -5*f - 4*j + 4 + 15 = 0, 4*j - 4 = 0. Factor -5*h**3 + 6*h**3 + 2*h**f - 9*h**5 - q*h**4.
-3*h**3*(h + 1)*(3*h - 1)
Factor -1/3*g**3 + 1/6*g**4 + 0 - 2/3*g - 7/6*g**2.
g*(g - 4)*(g + 1)**2/6
Let m = 22 + -14. Factor 4*y + 12 - 12 - 10*y**2 + m*y**3 - 2*y**4.
-2*y*(y - 2)*(y - 1)**2
Let d(a) = 44*a**3 + 35*a**2 - 53*a - 35. Let v(x) = 90*x**3 + 70*x**2 - 105*x - 70. Let h(t) = 5*d(t) - 3*v(t). Factor h(w).
-5*(w - 1)*(w + 1)*(10*w + 7)
Find y, given that -75/4*y - 39/4*y**2 - 37/4 - 1/4*y**3 = 0.
-37, -1
Let d(i) be the third derivative of -i**7/168 - i**6/288 - 2*i**4/3 + 14*i**2. Let g(m) be the second derivative of d(m). Factor g(s).
-5*s*(6*s + 1)/2
Let g(n) be the second derivative of -n**7/63 - n**6/9 + 5*n**5/6 + 5*n**4/18 - 8*n**3/3 - 35*n - 2. Solve g(b) = 0 for b.
-8, -1, 0, 1, 3
Let p(y) be the third derivative of y**7/945 - 7*y**6/90 + 481*y**5/270 - 70*y**4/9 + 400*y**3/27 - 97*y**2. Factor p(x).
2*(x - 20)**2*(x - 1)**2/9
Let t be (63/(-12))/((-24)/64). Suppose 21*o**2 + t*o**2 + 5*o**3 + 80*o + 8*o**2 - 3*o**2 = 0. Calculate o.
-4, 0
Let n(v) be the first derivative of -v**6/27 + 2*v**5/9 - v**4/3 - 14. Factor n(p).
-2*p**3*(p - 3)*(p - 2)/9
Let y be (12/16)/(207/(-2)). Let s = y + 347/276. Solve s*p + 3/4*p**2 + 1/2 = 0.
-1, -2/3
Let z = 2808 + -2806. Let -1/4*c**z - c - 3/4 = 0. Calculate c.
-3, -1
Let g be 4/16*3 - 78/(-24). Suppose 0 - 2/7*y**3 - 2/7*y**g + 2/7*y**2 + 2/7*y = 0. What is y?
-1, 0, 1
Let c(b) be the second derivative of -b**6/195 + 3*b**5/65 + 17*b**4/78 - 2*b**3/13 - 16*b**2/13 + 10*b + 12. Solve c(n) = 0.
-2, -1, 1, 8
Let u be (-19)/2 - (-189 - -178). Suppose -3/4 + 3/2*l**3 + u*l**2 - 3/4*l - 3/4*l**5 - 3/4*l**4 = 0. What is l?
-1, 1
Let p(k) be the third derivative of -5/192*k**4 + 0 + 1/24*k**3 + 1/120*k**5 - 1/960*k**6 - 6*k**2 + 0*k. What is s in p(s) = 0?
1, 2
Let i(u) = -6*u**5 - 4*u**4 + 10*u**3 + u + 4. Let j(b)