**4.
b*(b - 1)**2*(7*b + 2)/4
Let j(r) = 3*r**2 + 2*r - 1. Let s(z) = -z. Let v be s(-4). Let k(p) = 16*p**2 + 11*p - 5. Let d(i) = v*k(i) - 22*j(i). Factor d(b).
-2*(b - 1)*(b + 1)
Let d(f) be the second derivative of -f**5/90 + f**4/6 - 5*f**3/9 + 7*f**2/9 - 25*f. Let d(l) = 0. What is l?
1, 7
Let h = -133 - -1467/11. Find d, given that 0*d**2 + 0*d + 2/11*d**4 + h*d**3 + 0 = 0.
-2, 0
Determine j so that 3/4*j**2 - 3*j + 0 = 0.
0, 4
Let k(l) be the third derivative of l**8/336 - l**7/210 - l**6/120 + l**5/60 - 11*l**2. Factor k(h).
h**2*(h - 1)**2*(h + 1)
Let n be 40/100*(-10)/(-42). Let z(x) be the first derivative of 1 - n*x**3 + 0*x**2 + 2/7*x. Factor z(h).
-2*(h - 1)*(h + 1)/7
Let u(c) be the first derivative of -5*c**6/6 + c**5 + 5*c**4/4 - 5*c**3/3 + 5. Factor u(b).
-5*b**2*(b - 1)**2*(b + 1)
Let n be 11*(6/(-33))/(-1). Let 1/3 + a**n + 1/3*a**3 + a = 0. What is a?
-1
Suppose -2*s + 6 = 2. Let u(n) be the first derivative of 1/3*n**6 - 1/2*n**4 - 2/5*n**5 + 0*n + 2 + 2/3*n**3 + 0*n**s. Find c such that u(c) = 0.
-1, 0, 1
Let x(t) be the first derivative of t**6/24 + t**5/10 - t**4/4 - t**3/6 + 3*t**2/8 - 11. Let x(i) = 0. Calculate i.
-3, -1, 0, 1
Factor -226*o**2 - 49 + 66*o**2 + 13 - 132*o - 64*o**3.
-4*(o + 1)*(4*o + 3)**2
Let q(f) be the third derivative of f**5/15 + f**4 + 6*f**3 - 27*f**2. Factor q(s).
4*(s + 3)**2
Let o be 8 - (-1 + -4 + 9). Determine z so that -28*z**5 - 8*z**2 + 28*z**3 + 2*z**o + 8*z**4 - 2*z**4 = 0.
-1, 0, 2/7, 1
Let p be (63/18 + -3)*1*8. Let l(s) be the second derivative of 1/2*s**2 + 0 - 1/3*s**3 + 1/12*s**p + 4*s. Solve l(m) = 0 for m.
1
Let l(v) be the first derivative of 1/6*v**3 - 1/8*v**4 + 0*v + 1/4*v**2 - 1/10*v**5 + 1. Factor l(m).
-m*(m - 1)*(m + 1)**2/2
Let g(c) be the first derivative of 3*c**5/5 + 3*c**4/2 + c**3 + 2. Determine v, given that g(v) = 0.
-1, 0
Suppose 0 = v - 5 + 1. Let m = v - 2. Factor -6*c - m - 2 - 4*c**2 + 2*c**2.
-2*(c + 1)*(c + 2)
Find j, given that 54*j - 30*j - 164 - 16 + 36*j - 5*j**2 = 0.
6
Suppose -8 = 15*b - 68. Solve 1/5*f - 1/5*f**b - 3/5*f**2 + 3/5*f**3 + 0 = 0.
0, 1
Let a(n) be the first derivative of 0*n**3 - 2 + 1/10*n**5 - 1/6*n**4 - n + 0*n**2. Let k(l) be the first derivative of a(l). Suppose k(p) = 0. Calculate p.
0, 1
Let b(i) be the second derivative of -i**5/90 + i**4/6 - 5*i**3/9 - 25*i**2/9 - 7*i. Factor b(z).
-2*(z - 5)**2*(z + 1)/9
Let f(l) = l + 14. Let a be f(-10). Let q(y) = y**3 - 3*y**2 - 4*y - 4. Let r(g) = -g**3 + 4*g**2 + 5*g + 5. Let t(h) = a*r(h) + 5*q(h). Factor t(j).
j**2*(j + 1)
Let 1/5*u**4 + 0*u + 0 - 1/5*u**2 - 1/5*u**3 + 1/5*u**5 = 0. What is u?
-1, 0, 1
Suppose 2*u = 0, v - 4*u + 0*u = 2. Find y such that -2*y**v - 12*y**2 + 11*y**2 - 9*y = 0.
-3, 0
Let x(b) be the second derivative of 0 + 0*b**3 + 0*b**2 + 2*b + 1/21*b**7 - 1/10*b**5 + 1/15*b**6 - 1/6*b**4. Factor x(q).
2*q**2*(q - 1)*(q + 1)**2
Suppose 0 = 31*h - 32*h, 0 = 3*p + h. Solve p*i + 1/5*i**2 + 0 - 2/5*i**3 + 1/5*i**4 = 0 for i.
0, 1
Let n(r) = 26*r**4 + 41*r**3 + 26*r**2 + 11*r + 11. Let m(d) = 5*d**4 + 8*d**3 + 5*d**2 + 2*d + 2. Let y(v) = -11*m(v) + 2*n(v). Factor y(g).
-3*g**2*(g + 1)**2
Let t(b) be the second derivative of -1/42*b**7 + 1/2*b**2 + 1/2*b**3 - 1/10*b**6 - 1/10*b**5 - 4*b + 1/6*b**4 + 0. Solve t(y) = 0.
-1, 1
Factor 0 - 6/5*y**2 + 3/5*y**3 + 3/5*y.
3*y*(y - 1)**2/5
Let j = 355/5313 - 1/161. Let y = 3/11 + j. Let -y*r**2 - 2*r - 3 = 0. Calculate r.
-3
Let l(g) = -g + 11. Let o be l(9). Factor 2/5*k**3 + o*k - 8/5*k**2 - 4/5.
2*(k - 2)*(k - 1)**2/5
Let a(f) be the second derivative of -f**6/40 - f**2/2 - f. Let v(c) be the first derivative of a(c). Factor v(h).
-3*h**3
Let u(x) = -7*x**3 + 5*x**2 + 2*x - 5. Let r = -13 + 17. Let w(k) = 3*k**3 - 2*k**2 - k + 2. Let q(a) = r*u(a) + 10*w(a). Factor q(i).
2*i*(i - 1)*(i + 1)
Let p = 790/297 + 2/297. Solve 4/9*c + 0 - 16/9*c**3 - 26/9*c**4 + 14/9*c**2 + p*c**5 = 0.
-2/3, -1/4, 0, 1
Let n be (-12)/10*(-50)/15. Suppose -4*h - 12 = 0, 2*y = -3*y - n*h + 3. Let -9*z**4 - 2*z**5 - z + 9*z**2 + 3*z - 5*z**5 + 5*z**y = 0. What is z?
-1, -2/7, 0, 1
Let z(f) = f + 14. Let b be z(-10). Solve -7/2*s**2 + 7/2*s**b - s**3 + 0 + s = 0 for s.
-1, 0, 2/7, 1
Let o(n) be the second derivative of -n**6/30 - n**5/10 - n**4/12 - 6*n. What is k in o(k) = 0?
-1, 0
Factor 0 + 2/9*b**3 - 2/9*b + 0*b**2.
2*b*(b - 1)*(b + 1)/9
Let k(m) be the second derivative of m**4/48 - m**3/8 - m**2/2 - 10*m. Factor k(i).
(i - 4)*(i + 1)/4
Let p(b) be the third derivative of b**7/280 + b**6/480 - b**5/120 - 6*b**2. Factor p(l).
l**2*(l + 1)*(3*l - 2)/4
Let q(f) be the third derivative of f**10/302400 - f**8/20160 + f**6/1440 - f**5/12 - 2*f**2. Let j(d) be the third derivative of q(d). Factor j(r).
(r - 1)**2*(r + 1)**2/2
Let n be 4 - 1/(-1)*-2. Suppose 8 = -3*x + 7*x. Factor -j**x + n*j**3 - j**4 + 0*j**2 + 0*j**4.
-j**2*(j - 1)**2
Suppose 0 = -2*j + 7*j. Suppose 0 = -j*r - 5*r + 35. Find h such that 1 - h**2 - 3*h**4 + r*h**2 - 3*h**3 - 1 = 0.
-2, 0, 1
Let k be 1/4 + 9/12. Let s be 1 - 1/(k/15). Let o(p) = p**3 - p**2 + p - 1. Let d(a) = -8*a**3 + 10*a**2 - 10*a + 8. Let n(r) = s*o(r) - 2*d(r). Factor n(v).
2*(v - 1)**3
Suppose -s + 24 = b, 2*s - 78 = -3*b + 5*s. Let n be 30/b + 6/(-15). Factor n - 2/5*j**2 + 2/5*j.
-2*(j - 2)*(j + 1)/5
Let o(k) be the first derivative of -2/33*k**3 - 2 + 2/11*k**2 - 2/11*k. Solve o(w) = 0.
1
Let f(u) = 6*u + 0*u - 13*u + 10 + u**2. Let w be f(6). Factor 0*o**3 - 2/9*o**w + 0*o + 0 + 2/9*o**2.
-2*o**2*(o - 1)*(o + 1)/9
Let d = -10 + 12. Suppose 18*j**4 - 9*j + 9*j**3 + 6*j**d - 24*j**2 + 6*j**3 + 8 - 2 = 0. Calculate j.
-1, 1/2, 2/3
Suppose 2*c + 7 = 23. Let f be (c/20)/((-2)/(-30)). Determine l, given that -6*l - f*l**2 + 5*l**2 - 2*l**2 - 3 = 0.
-1
Suppose 12 = y + 2*y. Suppose -q = -y*l - 0*l + 18, -2*q + 5*l = 21. Determine j, given that 3/5 + 3/5*j**q - 6/5*j = 0.
1
Let k(j) be the second derivative of j**5/80 - j**3/24 + 3*j - 2. Let k(g) = 0. What is g?
-1, 0, 1
Suppose 1 - 5 = -2*m. Let v(c) be the second derivative of 0 - 5/42*c**4 - 8/21*c**3 - 1/70*c**5 + 3*c - 4/7*c**m. Suppose v(r) = 0. What is r?
-2, -1
Let k(u) = -u**3 - 1. Let c(v) = 3*v**4 - 6*v**3 - 12. Let h(t) = c(t) - 12*k(t). Let h(l) = 0. What is l?
-2, 0
Let k be 6*(-3)/(-12) + (-36)/24. Let -1/2*t + k - t**2 - 1/2*t**3 = 0. Calculate t.
-1, 0
Let z = 141 + -137. Let x(k) be the first derivative of 25/2*k**z - 10/3*k**3 - 1 + 0*k - 2*k**2. Factor x(n).
2*n*(5*n - 2)*(5*n + 1)
Let r(z) be the first derivative of -z**3/9 + 5*z**2/6 + 17. What is o in r(o) = 0?
0, 5
Let z be 0/(-2) + 0 + 2. Let a be (-1)/z*0/6. Suppose -2/7*i**2 - 2/7*i + a = 0. Calculate i.
-1, 0
Let j(y) be the second derivative of -y**4/4 - y**3/2 - 24*y. Solve j(z) = 0 for z.
-1, 0
Let k(m) be the first derivative of -m**6/48 - m**5/40 + m**4/24 + m**2 + 1. Let s(t) be the second derivative of k(t). Solve s(w) = 0.
-1, 0, 2/5
What is t in 0 - 3/5*t + 1/5*t**2 + 3/5*t**3 - 1/5*t**4 = 0?
-1, 0, 1, 3
Let v be (2 + -3)/(-1 + 2). Let r be 3*(v - -2) - 1. Find q, given that 5*q**3 - 5*q**2 + q**2 - q**4 + r*q**3 - 3*q**3 = 0.
0, 2
Let q(c) = 1. Let g(i) = i - 3. Let d(n) = g(n) + 4*q(n). Let t be d(1). Find l, given that 2*l**2 - 16*l**3 + 10*l**4 + 2*l**2 - 2*l**t + 4*l = 0.
-2/5, 0, 1
Let a(n) be the first derivative of 0*n - 1 + 1/14*n**4 + 0*n**2 - 2/21*n**3. Factor a(q).
2*q**2*(q - 1)/7
Let v = -1 + 5. Suppose -37*i**3 - 8*i**5 - 21*i**2 - 6*i + 10*i**3 - 15*i**4 + v*i**5 + i**5 = 0. Calculate i.
-2, -1, 0
Find u, given that 8*u**2 + 2/3 + 2*u**4 - 4*u - 20/3*u**3 = 0.
1/3, 1
Let h(r) be the first derivative of -r**5/15 + r**4/4 - 2*r**2/3 - 13. Solve h(a) = 0 for a.
-1, 0, 2
Suppose u - 2*c = 0, 5 = -5*u + c + 14. Solve -6*v - 6*v**3 - u*v + 2*v**4 + 6*v + 6*v**2 = 0 for v.
0, 1
Let o(g) be the first derivative of 2*g**6/3 - 4*g**5 + 9*g**4 - 28*g**3/3 + 4*g**2 + 24. Suppose o(i) = 0. Calculate i.
0, 1, 2
Suppose 0*z + 12 = z. Let y be (-12)/(-15)*z/16. Factor 1/5 + 1/5*j**5 + 2/5*j**3 + 2/5*j**2 - 3/5*j**4 - y*j.
(j - 1)**4*(j + 1)/5
Let y(x) be the first derivative of 0*x - 1/4*x**4 + 0*x**3 + 1/30*x**5 - 2*x**2 + 4. Let u(q) be the second derivative of y(q). Find j such that u(j) = 0.
0, 3
Let h(v) be the second derivative of v**5/5 + 2*v**4/3 + 2*v**3/3 - v. Let 