f) + 2*g(f). Factor j(i).
-3*(i - 2)*(i - 1)**2
Let b(s) be the second derivative of s**8/2240 + s**7/1120 + 19*s**3/6 - 7*s. Let c(m) be the second derivative of b(m). Factor c(l).
3*l**3*(l + 1)/4
Let q(b) = -b**3 + 6*b**2 - b + 3. Let a be q(6). Let g = a + 7. Factor 3*v**2 - 3*v**4 - g*v**2 + 1 - 1 - 4*v**3.
-v**2*(v + 1)*(3*v + 1)
Let c(x) be the second derivative of x**4/18 - 34*x**3/3 + 867*x**2 + 286*x. Find t, given that c(t) = 0.
51
Factor 14/9*t**2 + 0 - 2/9*t**3 + 16/9*t.
-2*t*(t - 8)*(t + 1)/9
Let r(s) = s**3 + 4*s**2 + s - 2. Let y be r(-2). Let f(p) be the first derivative of y*p - p**2 + p**2 - 5 - 5*p - 2*p**2 - p**3. What is a in f(a) = 0?
-1, -1/3
Let h(t) be the first derivative of 5*t**4/4 - 95*t**3/3 + 495*t**2/2 - 405*t - 36. Determine b, given that h(b) = 0.
1, 9
Factor -45*x**2 - 6*x**3 - 47 + 27*x + x**3 - 102*x + 12.
-5*(x + 1)**2*(x + 7)
Let -170*d**4 - 19*d**2 + 54*d + 85*d**4 + 84*d**4 + 11*d**3 - 45*d = 0. What is d?
0, 1, 9
Let l(n) be the third derivative of 1/6*n**5 + 0*n**3 + 0 + 22*n**2 + 0*n + 1/60*n**6 - 1/2*n**4. Determine g so that l(g) = 0.
-6, 0, 1
Let b(u) be the second derivative of u**6/45 + u**5/5 + 11*u**4/18 + 2*u**3/3 - 3*u + 64. Factor b(y).
2*y*(y + 1)*(y + 2)*(y + 3)/3
Suppose 0*u = -o + 3*u + 12, 2*o - 2*u = 12. Suppose -5*l = -o*l - 8. Find d such that 7*d**2 + l - 5*d + 2*d + 19*d = 0.
-2, -2/7
Let p(o) be the first derivative of -o**6/90 + 2*o**5/15 - 2*o**4/3 + 2*o**3/3 + 1. Let x(t) be the third derivative of p(t). Suppose x(k) = 0. What is k?
2
Let h be 2/(40/1127) - (-3)/12. Let x = 57 - h. Factor -4/5 + x*c**4 - 2*c + 2/5*c**3 - 6/5*c**2.
2*(c - 2)*(c + 1)**3/5
Let x be ((-14)/6 + -1)/(56/(-126)). Let v(u) be the first derivative of -x*u**2 + 2*u**3 + 6*u + 5. Find a such that v(a) = 0.
1/2, 2
Let g(c) be the second derivative of -2*c**7/21 + 2*c**5/5 - 2*c**3/3 + 20*c - 1. Determine d, given that g(d) = 0.
-1, 0, 1
Let d(x) be the second derivative of 0*x**2 - 14/15*x**6 + 49/10*x**5 + 0*x**4 + 0*x**3 + 0 - 28*x + 1/21*x**7. What is q in d(q) = 0?
0, 7
What is h in -3/10*h + 3/10*h**3 - 1/10*h**4 + 1/5 - 1/10*h**2 = 0?
-1, 1, 2
Suppose -90 = -5*r - 3*z, -r - 3*r - z = -72. Suppose -3*g = -0 - r. Factor -2*s - 8 - s**2 + 3*s - 4*s + g.
-(s + 1)*(s + 2)
Let z(v) be the third derivative of -3/80*v**5 + 1/16*v**4 + 0*v + 0 - 11*v**2 - 1/24*v**3. Factor z(a).
-(3*a - 1)**2/4
Let a = 191 - 191. Let u(x) be the first derivative of -1/9*x**6 + a*x**2 - 1/2*x**4 + 2/9*x**3 + 2/5*x**5 + 0*x - 4. Let u(y) = 0. What is y?
0, 1
Let f be 2 + (0 - (2 - 0)). Let m(a) be the first derivative of 0*a**3 - 3 + 0*a + 3/20*a**5 - 1/8*a**6 + 0*a**2 + f*a**4. Suppose m(w) = 0. Calculate w.
0, 1
Let a(r) be the first derivative of 2*r**3/3 - 3*r**2/2 + r - 8. Let x be a(3). Factor 6*b**3 - 7*b**3 + 4*b + x*b**2 - b**5 - 4*b**4 - 4 - 1 - 3.
-(b - 1)**2*(b + 2)**3
What is d in 2/5*d**2 + 12/5*d - 224/5 = 0?
-14, 8
Let b(y) be the third derivative of 0 - 9*y**2 + 1/9*y**3 + 0*y + 7/72*y**4 - 7/360*y**6 - 1/90*y**5. What is s in b(s) = 0?
-1, -2/7, 1
Let b(j) be the third derivative of 0 + 32*j**2 - 1/36*j**4 + 2/9*j**3 - 1/90*j**5 + 0*j. Find g, given that b(g) = 0.
-2, 1
Let h(i) = i**2 - 9*i - 8. Let b be h(10). Determine p, given that 0*p**2 - 97*p + 3*p**b + 18 + 42*p + 40*p = 0.
2, 3
Let a(d) be the first derivative of -d**6/240 - d**5/40 - d**4/16 - d**3/12 - d**2/16 - 15*d - 5. Let v(x) be the first derivative of a(x). Factor v(s).
-(s + 1)**4/8
Let d(c) be the third derivative of -c**5/12 - 25*c**4/3 - 1000*c**3/3 - 191*c**2. Factor d(k).
-5*(k + 20)**2
Let l(h) be the second derivative of h**4/48 - 29*h**3/3 + 1682*h**2 + 21*h + 2. Solve l(b) = 0.
116
Let f(t) = 2*t**2 + 4*t. Suppose -2*w = 3*y - 5*w + 12, 0 = 4*y + 3*w + 16. Let x = -6 - y. Let b(r) = -8*r**2 - 15*r. Let c(o) = x*b(o) - 9*f(o). Factor c(i).
-2*i*(i + 3)
Let q = -30 - -32. Determine j, given that -7*j**4 - 8*j**4 - q*j**4 - 8*j**3 + 12*j**5 - 3*j**4 = 0.
-1/3, 0, 2
Factor -269*i - 460*i**3 + 688*i**2 + 445*i + 5*i**4 + 31*i**4.
4*i*(i - 11)*(i - 2)*(9*i + 2)
Let z(n) be the second derivative of -n**7/210 + 29*n**6/150 - 219*n**5/100 + 59*n**4/60 + 448*n**3/15 + 294*n**2/5 - 80*n. Find f such that z(f) = 0.
-1, 3, 14
Let l(i) be the first derivative of i**7/350 + i**6/600 - i**5/100 - i**4/120 + 9*i**2 - 10. Let f(n) be the second derivative of l(n). Factor f(d).
d*(d - 1)*(d + 1)*(3*d + 1)/5
Let c = -17 + 17. Let n be 14 + (-4)/12*c. Factor -7 + n*o**2 + o**2 - 6*o + 7.
3*o*(5*o - 2)
Let p be (-4)/(-3)*(-2 + (-1389)/(-6)). Factor -6*j**2 + j**3 - 303*j + 2*j**3 + p*j.
3*j*(j - 1)**2
Suppose 2*q - 3 = q. Solve 2*l**q + 3*l**3 - 4 + 4 + 5*l**4 = 0 for l.
-1, 0
Let i(o) be the first derivative of o**9/756 - o**8/420 + 4*o**3/3 - 17. Let d(w) be the third derivative of i(w). Factor d(h).
4*h**4*(h - 1)
Let u(t) = 64*t**3 - 32*t**2 - 33*t - 4. Let c(j) = -320*j**3 + 160*j**2 + 164*j + 20. Let q(b) = 5*c(b) + 24*u(b). Solve q(y) = 0.
-1/4, 1
Let s(a) be the second derivative of -a**6/396 - 2*a**5/165 + a**4/33 + 11*a**3/6 - 13*a. Let x(t) be the second derivative of s(t). Factor x(m).
-2*(m + 2)*(5*m - 2)/11
Let f(a) be the first derivative of -2*a**5/5 - 7*a**4/2 - 4*a**3 + 91. Let f(q) = 0. What is q?
-6, -1, 0
Let l(x) = -x**3 + 8*x**2 - 7*x + 4. Let k be l(7). Suppose 1 - 16 = -4*w - 3*v, -w + k*v - 1 = 0. Solve -4*d**w + 9*d**3 - 2*d - 3*d = 0 for d.
-1, 0, 1
Let y(t) be the third derivative of t**9/3780 - 2*t**7/315 + 11*t**4/24 + 12*t**2. Let c(i) be the second derivative of y(i). Factor c(z).
4*z**2*(z - 2)*(z + 2)
Let t(s) be the second derivative of s**6/20 + 9*s**5/20 + 9*s**4/8 - s**3 - 9*s**2 - 64*s. Factor t(i).
3*(i - 1)*(i + 2)**2*(i + 3)/2
Let k be 1 + -4 + 3564/13 + 3. Let n = k + -274. Factor 2/13*s - n*s**2 + 0.
-2*s*(s - 1)/13
Let o(u) be the first derivative of u**5/100 - 7*u**4/40 + 3*u**3/5 - 17*u**2/2 + 26. Let g(a) be the second derivative of o(a). Find i, given that g(i) = 0.
1, 6
Let o(u) = -7*u**2 + 1262*u - 133571. Let h(r) = r**2 + r + 2. Let p(a) = -4*h(a) - o(a). Solve p(x) = 0.
211
Let l be 5 - (10/(-5) + 1). Let x be 12/72 - (-2)/l. Suppose -1/2 - m - x*m**2 = 0. What is m?
-1
Let u = -11 + 17. Solve -3*m**3 + 2*m**2 - u*m**2 - m**3 = 0.
-1, 0
Let k be (-836)/(-99) - 9 - -1. Suppose 0 + 2/9*x**2 - 2/9*x**4 + k*x**3 - 4/9*x = 0. What is x?
-1, 0, 1, 2
Let m(z) be the second derivative of z**5/3 - 85*z**4/24 + 10*z**3/3 - 15*z**2 + 37*z. Let w(o) be the first derivative of m(o). Factor w(s).
5*(s - 4)*(4*s - 1)
Let t = -5120 - -46120/9. Factor 16/9 + 4*j**2 + 14/9*j**3 + t*j + 2/9*j**4.
2*(j + 1)*(j + 2)**3/9
Let v be 3*((-39)/(-9) + 2). Determine u, given that -v*u**2 - 17*u**2 - 525*u**4 + 128*u**3 - 292*u**3 - 147*u**5 - 100*u**3 = 0.
-3, -2/7, 0
Let g be -6 - (2530/(-77))/5. Suppose 3*u - u - 1 = 3*l, -5*u = -4*l - 13. Determine s so that -g - 2/7*s + 4/7*s**2 + 2/7*s**l = 0.
-2, -1, 1
Suppose -6 = -5*s - 31. Suppose j - u = -4, -4*j - u - 1 = -2*u. Let d(f) = -f**2 + f. Let k(q) = -17*q**2 + q + 8. Let h(a) = j*k(a) + s*d(a). Factor h(m).
-4*(m + 1)*(3*m - 2)
Let w = -14 - -25. Let x = w + -9. Suppose -13*o**2 - 21*o**3 - 6*o**x + 4*o + 135*o**4 - o**2 = 0. What is o?
-2/5, 0, 2/9, 1/3
Let y(o) be the first derivative of -o**4/18 - 10*o**3/27 - o**2/3 + 2*o + 91. What is b in y(b) = 0?
-3, 1
Let g(j) be the third derivative of 1/210*j**6 + 0 + 0*j**4 + j**2 + 0*j + 0*j**5 - 1/735*j**7 + 0*j**3. Suppose g(w) = 0. What is w?
0, 2
Suppose 460*x = -5*n + 462*x + 10, 5*n + 25 = -5*x. Factor 3/7*c**3 + 0*c + 6/7*c**2 + n.
3*c**2*(c + 2)/7
Let w(j) be the third derivative of -j**6/24 + 65*j**4/24 + 10*j**3 - 593*j**2. Let w(f) = 0. Calculate f.
-3, -1, 4
Let l be -6*(-3)/(-6) - 1. Let b be 1 + (-2 - l)/2. Factor -3/5*n**3 - 2/5*n**b + 0*n - 1/5*n**4 + 0.
-n**2*(n + 1)*(n + 2)/5
Suppose -243 + 234 = -4*s + 3*a, 3*a - 6 = -s. Suppose 0*y**2 + 0 + 0*y**4 - y**s + 1/2*y + 1/2*y**5 = 0. What is y?
-1, 0, 1
Let c(x) be the second derivative of x**10/15120 + x**9/3780 + x**8/3360 + 2*x**4/3 + 15*x. Let a(r) be the third derivative of c(r). Find o such that a(o) = 0.
-1, 0
Determine l, given that 60/7*l - 2/7*l**2 - 450/7 = 0.
15
Let k = -11976 - -11976. Let g**2 - g**4 + k + 1/2*g**5 + 0*g**3 - 1/2*g = 0. What i