*(z - 3)*(z - 1)**3
Suppose -48 = -13*t + 4. Let n(m) be the second derivative of -1/60*m**t + 1/150*m**6 - 1/100*m**5 + 0*m**2 + 1/30*m**3 + 2*m + 0. What is k in n(k) = 0?
-1, 0, 1
Let f = 197/5 + -4127/105. Let j(q) be the second derivative of -1/7*q**2 + q - 1/42*q**4 + 0 - f*q**3. Factor j(v).
-2*(v + 1)**2/7
Let v(x) = -6*x**4 - 2*x**3 + 12*x**2 - 4*x + 4. Let f(o) = 7*o**4 + 3*o**3 - 13*o**2 + 3*o - 5. Let k(b) = -4*f(b) - 5*v(b). Factor k(h).
2*h*(h - 2)*(h - 1)*(h + 2)
Let p(j) be the third derivative of -1/240*j**6 - 1/120*j**5 + 0 + 0*j**4 + 3*j**2 + 0*j**3 + 0*j. Factor p(f).
-f**2*(f + 1)/2
Suppose -j - 4 = -4*g, -g - 2*g = -j - 2. Factor 3*k**2 - 3*k**4 + 0*k**j + 0*k**4.
-3*k**2*(k - 1)*(k + 1)
Suppose -3*c + 92 - 98 = 5*f, 0 = 2*f + 2*c + 4. Suppose f*d**2 - 8/7*d**3 - 2/7 + 6/7*d = 0. Calculate d.
-1, 1/2
Let s be (0/(-3 - -2))/(-2). Let u be ((-6)/4)/((-2)/4). Factor 2*h**2 - 2*h**5 - h**3 + 6*h**4 + s*h**2 - 5*h**u.
-2*h**2*(h - 1)**3
Let v be (1 + 0)/(3 - 4). Let a = 1 + v. Factor 49/4*o**4 + 0*o + a + o**2 + 7*o**3.
o**2*(7*o + 2)**2/4
Let h be 6*-2*(-3)/12. Determine c, given that c**3 + 0*c**h - 4*c**3 = 0.
0
Let a = 87/7 + -11. Suppose 4/7*u**3 + 8/7*u + 2/7 + a*u**2 = 0. What is u?
-1, -1/2
Let q(k) be the third derivative of k**7/105 + k**6/60 - k**5/30 - k**4/12 + 4*k**2. Find f such that q(f) = 0.
-1, 0, 1
Let a be (-3535)/(-1400) - 1/8. Let 4/5*k**4 - a*k**2 + k + 1/5*k**3 + 2/5 = 0. What is k?
-2, -1/4, 1
Factor 1/2*b**3 + 0 + 1/2*b**2 - b**4 + 0*b.
-b**2*(b - 1)*(2*b + 1)/2
Let u(r) be the first derivative of -r**6/30 + r**4/12 + 3*r - 2. Let g(o) be the first derivative of u(o). Determine p so that g(p) = 0.
-1, 0, 1
Let x(o) = o**4 - o**3 + o. Let w(t) = -12*t**4 + 24*t**3 - 12*t**2 - 8*t + 4. Let l(v) = -w(v) - 4*x(v). Factor l(q).
4*(q - 1)**3*(2*q + 1)
Let v(m) be the second derivative of m**7/42 - m**6/15 + m**4/6 - m**3/6 - 5*m. Factor v(j).
j*(j - 1)**3*(j + 1)
Let y(x) = -2*x**2 - 5*x + 3. Let f(a) = -3*a**2 - 6*a + 4. Let p be 3/(-5)*10/2. Let z(q) = p*f(q) + 4*y(q). Factor z(i).
i*(i - 2)
Factor -4/9*n - 16/3 + 4/9*n**2.
4*(n - 4)*(n + 3)/9
Find g such that -14 + 3 - 4 + 3*g + 3*g**2 - 3 = 0.
-3, 2
Let w(x) be the second derivative of -x**7/63 - 2*x**6/45 - x**5/30 + 17*x. Factor w(r).
-2*r**3*(r + 1)**2/3
Let v = -11 + 17. Let j be ((-10)/(-15))/(2/v). Let y**2 - 1 - j*y**2 + 2*y + 0 = 0. What is y?
1
Let q(u) = 4. Let a(b) = -3. Let l(r) = -3*a(r) - 2*q(r). Let v(g) = -g**5 + 4*g**4 - 4*g**3 - 2*g**2 + 5*g + 5. Let c(x) = -14*l(x) + 2*v(x). Solve c(f) = 0.
-1, 1, 2
Let t(m) = m**3 - 10*m**2 + 17*m - 8. Let o be t(8). Let x(j) be the second derivative of 1/18*j**4 + o + 0*j**2 + j + 0*j**3. What is r in x(r) = 0?
0
Suppose b - 5 = 2. Suppose 0 = w + 4 - b. Factor 0*j**2 + 3*j**3 - 3*j**4 - 10*j**w - 2*j**2.
-j**2*(j + 2)*(3*j + 1)
Factor 1/4*o**2 + 0 + 5/8*o**3 + 1/2*o**4 + 0*o + 1/8*o**5.
o**2*(o + 1)**2*(o + 2)/8
Factor 1/3*q**3 + 0*q + 0 - 2/9*q**2 - 1/9*q**4.
-q**2*(q - 2)*(q - 1)/9
Let y(z) = -14*z**5 + 24*z**4 - 6*z**3 - 4*z**2 - 2. Let r(a) = -28*a**5 + 48*a**4 - 12*a**3 - 8*a**2 - 5. Let v(l) = 2*r(l) - 5*y(l). Factor v(i).
2*i**2*(i - 1)**2*(7*i + 2)
Let q(n) = -10*n**4 - 8*n**3 + 9*n**2 - 9*n + 9. Let m(t) = t**4 + t**3 - t**2 + t - 1. Let i(l) = 18*m(l) + 2*q(l). Factor i(h).
-2*h**3*(h - 1)
Let o(p) be the third derivative of -p**7/945 - p**6/135 + 23*p**2. Factor o(v).
-2*v**3*(v + 4)/9
Let f(s) be the third derivative of -s**5/140 - 5*s**4/56 + s**3 + 15*s**2 - 2*s. Factor f(g).
-3*(g - 2)*(g + 7)/7
What is b in -80*b**2 + 32*b + 4*b**5 + 59*b**3 + 5 + 13*b**3 - 5 - 28*b**4 = 0?
0, 1, 2
Let y(d) be the second derivative of 0 - d + 7/6*d**7 - 9/4*d**5 + 7/3*d**4 + 0*d**2 - 14/15*d**6 - 2/3*d**3. What is s in y(s) = 0?
-1, 0, 2/7, 1
Let s(i) be the second derivative of i**6/1620 - i**5/540 + i**3 - 4*i. Let f(t) be the second derivative of s(t). Factor f(b).
2*b*(b - 1)/9
Let t be (-2 + (-42)/15)/(9/(-40)). Factor -16/3*z + 32/3*z**4 + 2/3 - t*z**3 + 16*z**2.
2*(2*z - 1)**4/3
Let k(l) be the first derivative of -1 + 0*l**2 - 2/65*l**5 + 0*l**4 + 4/39*l**3 - 2/13*l. Factor k(t).
-2*(t - 1)**2*(t + 1)**2/13
Suppose 0 = 5*w - 8*w + 18. Suppose -18 + w = -6*h. Find o such that 1/3*o**4 + 0 - 1/3*o**h + 0*o + 0*o**3 = 0.
-1, 0, 1
Let d(s) be the second derivative of s**5/5 - 2*s**3/3 - s. Factor d(b).
4*b*(b - 1)*(b + 1)
Suppose 3*m = 8 - 5, -m - 27 = 4*d. Let o be 4 + d + (-22)/(-6). Find n such that o*n + 4/3*n**2 - 2/3 = 0.
-1, 1/2
Suppose 15 = -3*y, 0 = -3*l + 3*y - 0*y + 24. Factor 7*u**2 + 2*u**l + 6*u - 3*u**3 - u**2 + 2 + 3*u**3.
2*(u + 1)**3
Let i(o) = 147*o**4 + 84*o**3 + 15*o**2 - 3*o. Let g(v) = 294*v**4 + 168*v**3 + 29*v**2 - 5*v. Let m(u) = -3*g(u) + 5*i(u). Find x such that m(x) = 0.
-2/7, 0
Let t(h) be the first derivative of -7*h**6/480 - h**5/48 + h**4/48 - h**2 + 1. Let j(g) be the second derivative of t(g). Suppose j(o) = 0. Calculate o.
-1, 0, 2/7
Factor 0*k**2 - 6/5*k**4 + 0 + 0*k**3 - 3/5*k**5 + 0*k.
-3*k**4*(k + 2)/5
Let j(q) be the second derivative of -q**5/80 + q**3/24 + 8*q. Factor j(y).
-y*(y - 1)*(y + 1)/4
Let r(m) = -m + 17. Let h be r(7). Let 4*p + 1 - h*p + p**3 - p**2 + 5*p = 0. Calculate p.
-1, 1
Let k be (-68)/(-20) + (-9)/(-15). Let d(b) be the second derivative of 1/10*b**2 - b - 1/100*b**5 - 1/60*b**k + 1/30*b**3 + 0. Factor d(f).
-(f - 1)*(f + 1)**2/5
Let -2/7 + 3/7*m + 0*m**2 - 1/7*m**3 = 0. What is m?
-2, 1
Let y(c) be the second derivative of 0*c**3 + 1/10*c**5 + 1/6*c**4 - 1/15*c**6 + 0 + 0*c**2 + 5*c - 1/21*c**7. Factor y(g).
-2*g**2*(g - 1)*(g + 1)**2
Let j = 14 - -19. Let v = 33 - j. Factor -1/4*g - 1/4*g**2 + v.
-g*(g + 1)/4
Let s = -4 - -5. Let g(h) = 1 - 1 - h**2 + s - 10*h + 3*h**3. Let d(w) = w**3 - 3*w. Let p(n) = -7*d(n) + 2*g(n). Factor p(b).
-(b - 1)*(b + 1)*(b + 2)
Let r(x) = 7*x**3 + 27*x**2 + 48*x + 29. Let c(n) = 8*n**3 + 28*n**2 + 48*n + 28. Let z(t) = 3*c(t) - 4*r(t). Factor z(w).
-4*(w + 2)**3
Let y be 2/((-4)/(-1))*4. Let u = -44 - -44. Factor u*n - 2*n + y*n**2 - 3*n + n.
2*n*(n - 2)
What is y in 2*y**2 + y**2 - 6*y**2 + 0*y**2 + 12 = 0?
-2, 2
Factor 6*f - 9*f**3 - 6*f**3 + 3*f**4 - 18*f + 0*f**3 + 24*f**2.
3*f*(f - 2)**2*(f - 1)
Suppose 0 = -12*x - 6*x + 54. Factor 10*k**x + 0 + 8/9*k - 16/3*k**2 - 50/9*k**4.
-2*k*(k - 1)*(5*k - 2)**2/9
Let -1/2 + 5/12*x - 1/12*x**2 = 0. What is x?
2, 3
Let q(x) be the first derivative of 3*x**8/80 + 13*x**7/350 - 3*x**6/50 - x**5/25 - 2*x**2 - 2. Let w(i) be the second derivative of q(i). Solve w(v) = 0.
-1, -2/7, 0, 2/3
Let o(m) = m**2 - 3*m. Let g(d) = 2*d**2 - 8*d. Let v(z) = 9*z - 1. Let t be v(1). Let i(j) = t*o(j) - 3*g(j). Factor i(c).
2*c**2
Let t(d) be the first derivative of -4 + 0*d + 9/5*d**5 + 0*d**2 + d**3 - 9/4*d**4 - 1/2*d**6. Factor t(j).
-3*j**2*(j - 1)**3
Let s(a) be the third derivative of -3*a**2 + 0*a - 1/30*a**5 + 0 - 1/12*a**4 + 0*a**3 + 1/30*a**6. Factor s(f).
2*f*(f - 1)*(2*f + 1)
Let c be -6*(-1)/((-6)/(-2)). Let 15*x**2 + 14*x**c - 14*x**3 + 2 - 5*x**2 - 6*x - 6 = 0. What is x?
-2/7, 1
Let n be (12/15)/((-2)/10). Let t = -2 - n. Factor -q - 3*q**3 - q**4 + q**t + 2*q**3 + 2*q**3.
-q*(q - 1)**2*(q + 1)
Let d = 8/9 + -2/9. Let r be (-6)/4*8/(-6). Determine q, given that 2/9 - 2/3*q + d*q**r - 2/9*q**3 = 0.
1
Let g(u) be the third derivative of u**5/15 - 2*u**3/3 - 5*u**2. Suppose g(y) = 0. What is y?
-1, 1
Suppose 63/8*l**2 - 3/8*l**3 + 1029/8 - 441/8*l = 0. What is l?
7
Let o(y) = 2*y**5 - 5*y**4 - 3*y**3 - 3*y**2 - 3. Let k(s) = s**5 - 4*s**4 - 2*s**3 - 2*s**2 - 2. Let v(f) = 3*k(f) - 2*o(f). Find a, given that v(a) = 0.
-2, 0
Let i(h) be the first derivative of 1/6*h**2 + 0*h - 1/9*h**3 + 1/15*h**5 - 1/12*h**4 - 1. Factor i(j).
j*(j - 1)**2*(j + 1)/3
Suppose -2*p + 3*o - 2 = 2*o, 10 = -3*p + 5*o. Let l(d) be the first derivative of 4/21*d**3 + 2/35*d**5 + p*d + 0*d**2 + 2 - 3/14*d**4. Factor l(u).
2*u**2*(u - 2)*(u - 1)/7
Factor 20*z**4 - 30*z**3 + 0*z**5 - 9*z + 5*z - 5*z**5 - z + 20*z**2.
-5*z*(z - 1)**4
Suppose -4*l**3 - l**2 - 5*l**2 - 2*l**2 = 0. What is l?
-2, 0
Let d(y) be the first derivative of 1/18*y**3 - 2 + 1/30*y**5 + 0*y**2 + 1/12*y**4 + 0*y. Let d(k) = 0. What is k?
-1, 0
Suppose -5*r - 20 = 4*m, -3*r = 3*m + 21 - 6. Determine s so that 0*s + 2/11