 4. Let z(u) be the first derivative of -43/10*u**4 + k + 0*u + 56/25*u**5 + 34/15*u**3 - 2/5*u**2. Solve z(b) = 0 for b.
0, 1/4, 2/7, 1
Suppose -5*v - 2 = -12. Factor -5*t + 4*t**v - 7*t - 3*t**3 - 16*t**2.
-3*t*(t + 2)**2
Let s(g) be the first derivative of -g**4/26 - 4*g**3/39 + 7*g**2/13 - 8*g/13 - 16. Let s(u) = 0. What is u?
-4, 1
Suppose 3*m - 30 + 11 = -5*c, 23 = 4*c + 5*m. Factor 1/2*i**c + 1/3*i**3 - 1/3 - 1/2*i.
(i - 1)*(i + 2)*(2*i + 1)/6
Let m(f) be the third derivative of f**5/390 - f**3/39 + 4*f**2. Find k such that m(k) = 0.
-1, 1
Let k(u) be the second derivative of -u**5/20 + u**4/4 - u**3/2 + u**2/2 + 4*u. Factor k(f).
-(f - 1)**3
Suppose -8 = 23*k - 27*k + 2*d, 5*d + 20 = 2*k. Factor 0*n + k - 1/2*n**2 + n**3.
n**2*(2*n - 1)/2
Let z be ((12/(-3))/(-1920))/1. Let d(n) be the third derivative of 0*n**3 + 0*n - n**2 - 1/120*n**5 + 1/96*n**4 + 0 + z*n**6. Factor d(k).
k*(k - 1)**2/4
Let 0 + 0*z**2 + 0*z**3 + 0*z - 1/3*z**4 - 1/3*z**5 = 0. Calculate z.
-1, 0
Let n(r) = r**2 - 1. Let u(b) = -2*b**2 + 8*b - 6. Suppose 0 = -y + 9 - 3. Suppose -y*k - 5 = -k. Let p(c) = k*u(c) + 4*n(c). Factor p(g).
2*(g - 1)*(3*g - 1)
Let q(x) be the first derivative of x**3/6 + x**2/4 + x/8 + 2. Factor q(d).
(2*d + 1)**2/8
Let m(j) be the third derivative of -3*j**2 + 1/20*j**6 + 0 + 1/70*j**7 + 0*j**4 + 0*j + 1/20*j**5 + 0*j**3. Find x such that m(x) = 0.
-1, 0
Let o(z) be the first derivative of z**4/78 + 2*z**3/39 + z**2/13 - 8*z + 5. Let g(f) be the first derivative of o(f). Factor g(m).
2*(m + 1)**2/13
Let q(a) = -a**4 - 4*a**3 - a**2 + 2*a. Let b(x) = -x**3 + x. Let w = -2 + 4. Let n(h) = w*b(h) - q(h). Find i such that n(i) = 0.
-1, 0
Let t = 171/334 - 2/167. Factor t*m**2 - 1/2*m + 0 + 1/2*m**3 - 1/2*m**4.
-m*(m - 1)**2*(m + 1)/2
Let j(f) be the second derivative of -f**8/7560 - f**7/1260 - f**6/540 - f**5/540 + f**3/3 + f. Let k(g) be the second derivative of j(g). Factor k(i).
-2*i*(i + 1)**3/9
Suppose -3*v + 57 = -3*i, 2*i + 31 = v + 5*i. Suppose -3*z + 2*w = 2, 0 = -5*z + 2*w - 5*w + v. Factor -12/7*f**z - 2/7*f**3 - 24/7*f - 16/7.
-2*(f + 2)**3/7
Let l(x) = -4*x**2 - 2. Let d(w) = -5*w**2 - w - 3. Suppose -5*m = 3*a - 26, -5*m - a = 3*a - 28. Let y(r) = m*d(r) - 6*l(r). Factor y(i).
4*i*(i - 1)
Suppose -4*f + 9*f - 24 = -k, -2*f - 12 = -5*k. Suppose -11*i = -9*i - k. Determine a, given that 0 + 2/7*a**i + 2/7*a = 0.
-1, 0
Let v(c) be the second derivative of c**5/20 + c**4/2 - 7*c**3/6 + 3*c**2/2 - c. Let a be v(-7). Factor -3*t**2 - 1/2 + 2*t**a - 1/2*t**4 + 2*t.
-(t - 1)**4/2
Let k(f) be the second derivative of -2*f**7/9 + 2*f**6/5 - 2*f**5/15 + 7*f. What is l in k(l) = 0?
0, 2/7, 1
Let d be (-23 + -5)*(-3)/(-2). Let m be (d/7)/((-7)/1). Factor 2/7 + 6/7*u + 2/7*u**3 + m*u**2.
2*(u + 1)**3/7
Let n(f) be the third derivative of f**7/1890 - f**6/540 - f**5/45 - f**4/24 + 8*f**2. Let b(i) be the second derivative of n(i). Solve b(t) = 0 for t.
-1, 2
Let t = -2 - -6. Suppose 0 = -v + 3*z - 9, 0 = -t*v - z - 1 + 4. Factor 1/3*w**2 + v - 1/3*w.
w*(w - 1)/3
Let d(q) be the first derivative of -q**6/3 + 4*q**5/5 + q**4 - 8*q**3/3 - q**2 + 4*q + 6. Let d(r) = 0. Calculate r.
-1, 1, 2
Let y(f) be the first derivative of 4*f**3/3 + 4*f**2 - 22. Factor y(s).
4*s*(s + 2)
Let l = -10 + 16. Let d be -9*(-4 + 22/l). Determine z, given that -9/2*z - 8*z**2 - 1 - 1/2*z**5 - 3*z**4 - 7*z**d = 0.
-2, -1
Let v(n) be the second derivative of n**6/360 - n**5/40 + n**4/12 + n**3/2 + 3*n. Let o(j) be the second derivative of v(j). Factor o(u).
(u - 2)*(u - 1)
Suppose -3*y = -15, -2*f - y - 4*y = -31. Let n(w) be the second derivative of 1/4*w**4 + 1/2*w**3 + w + 0 - f*w**2. Factor n(a).
3*(a - 1)*(a + 2)
Suppose 0 = 6*o - 22*o. Factor o + 0*z - 2/7*z**4 - 4/7*z**3 - 2/7*z**2.
-2*z**2*(z + 1)**2/7
Factor 8/19 + 32/19*j + 42/19*j**2 + 18/19*j**3.
2*(j + 1)*(3*j + 2)**2/19
Suppose -22 + 13 = -3*n. Suppose 2/3*c + 7/3*c**3 + 0 + n*c**2 = 0. Calculate c.
-1, -2/7, 0
Factor 3/2*r**4 + 48*r + 16 + 45*r**2 + 29/2*r**3.
(r + 1)*(r + 4)**2*(3*r + 2)/2
Let p be (-10)/4*7/(-35). Suppose p*j**2 + 1/2*j + 0 = 0. Calculate j.
-1, 0
Let s = -1799/3 - -627. Let f = -27 + s. Suppose -1/3*q + 2/3*q**2 - 2/3 + f*q**3 = 0. Calculate q.
-2, -1, 1
Let h(b) = b + 1. Let p(k) = -5*k**2 - 15*k - 10. Let o(a) = -5*h(a) - p(a). Suppose o(r) = 0. Calculate r.
-1
Let g be 6/4 - 49/(-14). Factor 12/5*a**4 + 0*a + 3/5*a**g + 0*a**2 + 0 + 12/5*a**3.
3*a**3*(a + 2)**2/5
Let h(l) be the second derivative of -2*l + 0 - 1/90*l**6 + 0*l**2 - 1/20*l**5 + 1/126*l**7 + 1/9*l**3 + 1/36*l**4. Factor h(x).
x*(x - 2)*(x - 1)*(x + 1)**2/3
Let d(w) = -w**3 - 11*w**2 - 20*w - 13. Let c be d(-9). Let y(j) be the first derivative of 1/2*j**4 - 5/3*j**3 + 0*j - j**2 + j**c - 3. Factor y(l).
l*(l - 1)*(l + 1)*(5*l + 2)
Suppose 4*i - 4 = 2*w, -3*i = 5*w + 8 - 37. Let f = 0 + i. Find v such that -v**2 + v**4 - 3*v**3 + 4*v**f - v + 0*v**3 + 0*v**3 = 0.
-1, 0, 1
Let f be (-8508)/(-240) - (-8)/10. Let w = f - 36. Factor 0*t + w*t**5 + 0*t**4 - 1/2*t**2 - 3/4*t**3 + 0.
t**2*(t - 2)*(t + 1)**2/4
Let m(b) be the third derivative of -b**9/25200 - b**8/5600 - b**4/12 - 5*b**2. Let w(u) be the second derivative of m(u). Suppose w(h) = 0. Calculate h.
-2, 0
Let r be (-36)/8*(-1 - 5). Find m such that r*m**2 + 7 - 33*m - 1 + 4 - 4 = 0.
2/9, 1
Let l = -4517261/66 - -68445. Let z = -7/22 + l. Factor -2/3*w**2 + z*w - 2/3.
-2*(w - 1)**2/3
Let d(b) be the second derivative of -1/100*b**5 + 0 + 0*b**4 + 7*b + 1/210*b**7 + 0*b**2 + 0*b**6 + 0*b**3. Factor d(r).
r**3*(r - 1)*(r + 1)/5
Let f(s) be the first derivative of 3*s**4/2 - s**3 - 3*s**2/2 + 1. Let f(x) = 0. What is x?
-1/2, 0, 1
Let q(g) = -6*g**5 - 2*g**4 - 3*g**2 + 6*g. Let d(f) = -5*f**5 - 2*f**4 - 2*f**2 + 5*f. Let i(b) = 5*d(b) - 4*q(b). Find o such that i(o) = 0.
-1, 0, 1
Let s be 6/9*(-18)/(-4). Let -2 - 9*z**2 + 12 + 2 - s*z**3 = 0. Calculate z.
-2, 1
Let x(a) be the third derivative of -5*a**8/336 + a**7/21 + 11*a**2. Let x(s) = 0. What is s?
0, 2
Let s(u) be the third derivative of u**6/150 - u**5/25 + u**4/15 - 9*u**2. Find m, given that s(m) = 0.
0, 1, 2
Let g(f) be the first derivative of -4 + 1/2*f**2 - 2/3*f - 1/9*f**3. Solve g(l) = 0.
1, 2
Let u(f) = f**2 + f. Let v be u(0). Let o(w) = -w**3 + w**2. Let b be o(v). Factor -3*h**3 - 4*h**2 + h - h**4 + 5*h**2 + 2*h**3 + b*h**2.
-h*(h - 1)*(h + 1)**2
Let d be 1 - 8 - -3*1. Let n(f) = -2*f - 6. Let k be n(d). Factor 0 + 1/4*h - 1/4*h**k.
-h*(h - 1)/4
Let d = -143 + 145. Factor -1/3*j**d + 1/3 + 1/3*j - 1/3*j**3.
-(j - 1)*(j + 1)**2/3
Suppose 89 - 5*s**4 + 5*s**2 + 94 - 183 = 0. What is s?
-1, 0, 1
Let j(w) be the first derivative of w**6/6 - 2*w**5/5 + w**4/4 + 3. Find l such that j(l) = 0.
0, 1
Let i = 1179/4 - 292. Let j = 107/36 - i. Factor 2/3*t + 2/9*t**3 + 2/3*t**2 + j.
2*(t + 1)**3/9
Let c(d) be the third derivative of 19/100*d**6 - 4*d**2 + 8/25*d**5 + 0 + 13/40*d**4 + 11/175*d**7 + 1/112*d**8 + 1/5*d**3 + 0*d. Solve c(q) = 0.
-1, -2/5
Let c be ((-3)/(-7 + -2))/(-2 - -3). Let x(f) be the second derivative of 0*f**2 + c*f**4 + 3/10*f**5 + 3*f + 0 + 0*f**3 + 1/15*f**6. Factor x(b).
2*b**2*(b + 1)*(b + 2)
Let q(j) be the third derivative of 7*j**6/40 + 3*j**5/2 + 9*j**4/2 + 4*j**3 + 10*j**2. Factor q(h).
3*(h + 2)**2*(7*h + 2)
Let k(i) be the second derivative of -3*i**7/14 + i**6 - 9*i**5/20 - 3*i**4 + 2*i**3 - 16*i. Solve k(v) = 0.
-1, 0, 1/3, 2
Let q(z) be the first derivative of -5*z**4/4 - 5*z**3 - 15*z**2/2 - 5*z + 22. Determine a, given that q(a) = 0.
-1
Let h(b) be the second derivative of b**6/15 - b**5/10 - b**4/2 + 5*b**3/3 - 2*b**2 - 9*b. Factor h(x).
2*(x - 1)**3*(x + 2)
Let o be ((-1)/3)/(1/(-18)). Let l = o + -2. Determine q, given that 0*q + l*q + 0*q - 4*q**3 - 4*q**4 + q**4 + 2*q**2 + 1 = 0.
-1, -1/3, 1
Suppose 0 = 4*d - 2*w - 44, -w - 3*w + 20 = d. Suppose j - 9*j + 4*j**4 + 35*j**3 - 35*j**3 - d*j**2 = 0. What is j?
-1, 0, 2
Let z = -3126/7 - -447. Let z*v**2 + 6/7 - 9/7*v = 0. Calculate v.
1, 2
Let k(f) be the second derivative of -f**7/840 + f**5/120 - f**3/6 + 3*f. Let u(a) be the second derivative of k(a). Factor u(q).
-q*(q - 1)*(q + 1)
Let y(f) be the second derivative of -5*f**4/48 - f**3/8 + f**2/4 - f. Factor y(w).
-(w + 1)*(5*w - 2)/4
Let p be 4 - (-150)/(-36) - 6/(-2