e 3 + -3 + (3 - 1). Let -15*n + 3 - 17*n + 180*n**b + 192*n**4 - 7*n - 336*n**3 = 0. What is n?
1/4, 1
Let p(m) be the second derivative of -m**7/735 + m**5/70 - m**4/42 + 2*m**2 - 7*m. Let z(y) be the first derivative of p(y). What is l in z(l) = 0?
-2, 0, 1
Let s = -254 - -256. Factor -8/3*z**3 - 4/3*z + 0 - 10/3*z**s - 2/3*z**4.
-2*z*(z + 1)**2*(z + 2)/3
Let p(v) be the second derivative of 0*v**2 + 6*v - 3/50*v**5 - 1/6*v**4 + 0 - 2/15*v**3 + 1/105*v**7 + 1/75*v**6. Find c such that p(c) = 0.
-1, 0, 2
Let f = -33 - -33. Solve 0*w + f - 2*w**3 - 2/3*w**2 - 2/3*w**5 - 2*w**4 = 0 for w.
-1, 0
Suppose -5*v = -5*f - 21 + 1, 3*v = -4*f - 16. Suppose 5*c - 4*q - 9 = v, -c - c + 30 = 5*q. Factor 10/3*h**3 + 0*h + 0 + 8/3*h**4 + 2/3*h**c + 4/3*h**2.
2*h**2*(h + 1)**2*(h + 2)/3
Suppose v - 3*v - h + 3 = 0, 4*v - 10 = 2*h. Let a = 6 - 3. Factor -a - 1 - v*p**2 + 2 + 4*p.
-2*(p - 1)**2
Suppose -4*j + 15*a - 10*a - 15 = 0, -3*a + 9 = j. Suppose 0 - 1/6*z**3 + j*z - 1/6*z**2 = 0. What is z?
-1, 0
Let l(s) be the third derivative of -3*s**2 - 1/80*s**5 + 0*s**3 + 0 - 1/16*s**4 + 0*s. Factor l(k).
-3*k*(k + 2)/4
Let f = -1 + 1. Suppose f = 3*p - 32 + 8. Let 2*u + 2*u**2 - 10*u + 0*u + p = 0. What is u?
2
Let o = 46 + -28. Suppose -3*p + o = 3*k, -3*k + 4*p - 7 = 3. Solve 2/5*t**k - 6/5*t + 4/5 = 0 for t.
1, 2
Let a(h) = h + 2. Let n be a(6). Factor -n*u**5 - 33*u**2 + 33*u**2 - 2*u**4.
-2*u**4*(4*u + 1)
Solve -1/3*s**4 + s**2 - 2/3 + 1/3*s - 1/3*s**3 = 0 for s.
-2, -1, 1
Factor 0*t + 0 - 3/7*t**4 + 0*t**2 + 3/7*t**3.
-3*t**3*(t - 1)/7
Let r(t) be the third derivative of t**6/120 - t**5/20 + t**4/12 - 10*t**2. Factor r(v).
v*(v - 2)*(v - 1)
Let 9/4*f + 3/2 + 3/4*f**2 = 0. What is f?
-2, -1
Factor 1/4 + 1/2*u + 1/4*u**2.
(u + 1)**2/4
Factor -y**4 + y**5 + 3*y**4 - 3*y**5.
-2*y**4*(y - 1)
Factor -2/15*u + 0 + 2/15*u**2.
2*u*(u - 1)/15
Let d be 24/18 + -2 - -1. Factor 0 - 1/3*a**3 + a**2 - a**4 + d*a.
-a*(a - 1)*(a + 1)*(3*a + 1)/3
Let x = 25 + -123/5. Find k such that 0*k - x*k**2 + 8/5 = 0.
-2, 2
What is a in -1/2*a + 1/4*a**2 - 3/4 = 0?
-1, 3
Factor 0 + 0*v + 3/2*v**2.
3*v**2/2
Suppose -b - 12 = -4*f, 6 = -5*f + 9*b - 13*b. Factor 0 + 2/5*w + w**f.
w*(5*w + 2)/5
Let r(n) be the third derivative of 0*n + 0*n**3 + 1/12*n**4 - n**2 + 1/120*n**6 + 0 - 1/20*n**5. Determine j, given that r(j) = 0.
0, 1, 2
Let t(y) be the second derivative of -1/60*y**4 + 5*y + 1/5*y**2 + 0 + 1/30*y**3. Factor t(k).
-(k - 2)*(k + 1)/5
Let i = 260/3 + -86. Suppose 5*q - 4*g + 7 = 1, 20 = 2*q + 4*g. Factor 0*k - 8/3*k**3 + 0 - i*k**q.
-2*k**2*(4*k + 1)/3
Suppose -2 = -2*i + 2. Factor -2*t**3 + i*t**4 - 4*t**2 + 4*t**2.
2*t**3*(t - 1)
Let d(y) be the first derivative of 1/3*y**3 - 3 + 0*y + 1/2*y**2. Suppose d(z) = 0. Calculate z.
-1, 0
Let c(u) be the third derivative of 7*u**7/225 - 7*u**6/300 - 4*u**5/75 - u**4/45 - 9*u**2. Factor c(z).
2*z*(z - 1)*(7*z + 2)**2/15
Let r(t) = -t**3 + t**2 - 1. Let x(z) = 12*z**3 - 16*z**2 + 4*z + 18. Let c(g) = 36*r(g) + 2*x(g). Solve c(i) = 0.
-2/3, 0, 1
Suppose 15 + 21 = -2*w. Let l be w/(-75)*(-60)/(-18). Factor 3/5*g**5 + 0*g**2 + 0*g + 1/5*g**3 - l*g**4 + 0.
g**3*(g - 1)*(3*g - 1)/5
Let o(g) be the second derivative of 0 + 0*g**3 + 1/50*g**5 + 2*g - 1/105*g**7 - 1/30*g**4 + 0*g**2 + 1/75*g**6. Factor o(p).
-2*p**2*(p - 1)**2*(p + 1)/5
Solve -162 - 162*f**2 - 3*f**4 - 324*f + 64 + 2*f**3 - 145 - 38*f**3 = 0 for f.
-3
Suppose -4*p + 13 = -k, -2*k + 5*k - 1 = 2*p. Let v(c) be the second derivative of 1/40*c**5 + 0*c**3 - c + 1/24*c**p + 0*c**2 + 0. What is t in v(t) = 0?
-1, 0
Suppose 12 = -12*o + 16*o. Let m(w) be the second derivative of 12*w**2 + 75/2*w**4 + 75/4*w**5 + 0 + 30*w**o - w. Solve m(s) = 0.
-2/5
Let 9*t**3 - 25*t**2 + 4*t**2 + 14*t**2 + t**5 - 5*t**4 + 2*t = 0. What is t?
0, 1, 2
Let y be 20/2*3/6. Let l = y - -7. Determine g so that -8*g**2 + 2*g**5 - g + 3*g + l*g**3 + 0*g**4 - 8*g**4 = 0.
0, 1
Let a be (2 + -4 - -5) + -3. Factor 0 + a*n**2 - 2/5*n + 2/5*n**3.
2*n*(n - 1)*(n + 1)/5
Let m(d) be the third derivative of 1/210*d**7 - 1/60*d**5 + 0*d - d**2 + 0*d**4 + 0*d**3 + 0 + 0*d**6. Factor m(s).
s**2*(s - 1)*(s + 1)
Let u(m) = 9*m**5 - 11*m**4 + 7*m**3 + 18*m**2 - 2*m. Let o(w) = -3*w**5 + 4*w**4 - 2*w**3 - 6*w**2 + w. Let g(y) = -7*o(y) - 2*u(y). Factor g(r).
3*r*(r - 1)**3*(r + 1)
Let d(c) be the second derivative of 0*c**2 + 0 - 2*c + 1/12*c**3 - 1/24*c**4. Factor d(n).
-n*(n - 1)/2
Let i(n) = -n - 5. Let j be i(-8). Let -j*m**2 + 2*m**3 - 2*m - 5*m**2 + 10*m**2 - 2 = 0. Calculate m.
-1, 1
Let j(a) = -a**3 - a**2. Let t(o) = -5*o**3 - 2*o**2 - 3*o**2 + 2*o**3. Let z(d) = 4*j(d) - t(d). Determine b so that z(b) = 0.
0, 1
Let d(y) be the first derivative of 24/7*y**2 + 30/7*y**3 + 8/7*y - 2 + 25/14*y**4. Suppose d(b) = 0. What is b?
-1, -2/5
Suppose 0 = 3*g + 5*z - 19, -41*g + 1 = -40*g - z. Let -3/2*y**3 - 3/2*y + 0 - g*y**2 = 0. What is y?
-1, 0
Suppose -7*a - 2*d = -2*a - 65, 2*a - 4*d = 2. Let j = -9 + a. Determine z, given that 8/9*z**3 - 14/9*z**j + 0 - 4/9*z = 0.
-1/4, 0, 2
Let i(t) = 35*t**4 + 115*t**3 + 115*t**2 - 100*t - 135. Let f(j) = 9*j**4 + 29*j**3 + 29*j**2 - 25*j - 34. Let a(h) = 15*f(h) - 4*i(h). Solve a(o) = 0.
-3, -2, -1, 1
Let o(v) = v**5 - 29*v**4 + 12*v**3 + 19*v**2 - 13*v. Let d(l) = -15*l**4 + 6*l**3 + 9*l**2 - 6*l. Let w(c) = -5*d(c) + 3*o(c). Determine q so that w(q) = 0.
-1, 0, 1, 3
Factor 4/5*c**2 - 8/5*c - 32/5.
4*(c - 4)*(c + 2)/5
Let l = -315 - -317. Determine q so that -2/3*q**3 + 0*q**l + 0*q + 1/3*q**4 + 0 = 0.
0, 2
Suppose 7 = 5*k - 2*l, 4*k - 23 = -k - 2*l. Factor t**3 - 3*t**4 - 2*t**2 - 4*t**2 + t - 2 + 11*t**2 - 2*t**k.
-(t - 1)*(t + 1)**2*(3*t - 2)
Let x(n) be the first derivative of -14*n**6/3 + 48*n**5/5 - 3*n**4 - 8*n**3/3 - 2. Factor x(g).
-4*g**2*(g - 1)**2*(7*g + 2)
Let m = 1 + 4. Suppose -2*g + 8 = -4*t, g - 7 + 3 = -m*t. Find k such that 0 + 2/3*k**5 + 0*k**g + 0*k**2 - 4/3*k**3 + 2/3*k = 0.
-1, 0, 1
Let b(v) be the first derivative of -v**6/24 + v**5/4 - v**4/2 + v**3/3 + 2. Factor b(c).
-c**2*(c - 2)**2*(c - 1)/4
Solve 7*f**2 - 3*f**2 - 2*f**2 + 2*f - f**2 + 1 = 0.
-1
Let r = -4 - -4. Suppose r - 4 = -k. Factor -k*f**2 + f - f + f.
-f*(4*f - 1)
Let t(y) be the third derivative of -2*y**7/525 + y**6/30 - 8*y**5/75 + 2*y**4/15 + y**2. Factor t(v).
-4*v*(v - 2)**2*(v - 1)/5
Find d such that 80/7*d**4 - 4/7*d - 26/7*d**2 - 18/7*d**3 + 0 - 32/7*d**5 = 0.
-1/4, 0, 1, 2
Let n(b) be the first derivative of -b**6/270 + b**5/72 - b**4/72 - b**3 + 1. Let h(g) be the third derivative of n(g). Let h(l) = 0. What is l?
1/4, 1
Let j(l) be the second derivative of 3*l**6/40 - 3*l**5/80 - 5*l**4/48 - l**3/24 - 4*l. Suppose j(s) = 0. Calculate s.
-1/3, 0, 1
Suppose -112 = 4*f - 4*a, f - 3*a = -a - 29. Let u = f - -27. What is x in -2/3 + 2/3*x**2 + u*x = 0?
-1, 1
Let d(g) be the third derivative of -1/45*g**5 - 6*g**2 + 0*g**3 - 1/36*g**6 + 0*g + 0 + 0*g**4. Factor d(i).
-2*i**2*(5*i + 2)/3
Let w(t) be the second derivative of -t**7/14 - t**6/10 + 9*t**5/20 + 5*t**4/4 + t**3 - 29*t. Factor w(z).
-3*z*(z - 2)*(z + 1)**3
Let a(m) be the first derivative of -5*m**6/24 - 3*m**5/2 - 65*m**4/16 - 5*m**3 - 5*m**2/2 - 40. Factor a(y).
-5*y*(y + 1)**2*(y + 2)**2/4
Let r(b) = b**2 - 6*b - 4. Suppose 35 = 4*j + j. Let q be r(j). Find f such that -f**3 - 3*f**2 + f**2 + q*f**3 = 0.
0, 1
Solve 0 + 3/2*l**2 + l = 0.
-2/3, 0
Suppose 2*d + 0 + 4 = 0. Let a = d + 4. Factor s**2 - a*s**4 + s**2 + 0*s**2.
-2*s**2*(s - 1)*(s + 1)
Let f = -14 - -14. Let y(a) be the second derivative of 3*a + 0 + f*a**2 - 1/50*a**5 + 1/75*a**6 - 1/30*a**4 + 1/15*a**3. Determine q so that y(q) = 0.
-1, 0, 1
Let k(g) = -g**3 - 12*g**2 - g - 10. Let d be k(-12). Solve -1/5*f**3 + 0 + 2/5*f**d - 1/5*f = 0 for f.
0, 1
Let n(h) be the first derivative of 5 - 1/6*h**2 + 4/9*h**3 + 0*h. Factor n(c).
c*(4*c - 1)/3
Let p(q) be the third derivative of -q**7/210 - q**6/30 - q**5/10 - q**4/6 - q**3/6 - 8*q**2. Factor p(u).
-(u + 1)**4
Let w(l) be the first derivative of -3*l**4/4 - 4*l**3 - 9*l**2/2 - 3. Let w(h) = 0. What is h?
-3, -1, 0
Let f = -16 + 24. Let d be -1*-24*f/108. Determine j so that -4/9*j - d*j**4 + 10/9*j**2 + 2/3*j**3 + 0 - 8/9*j**5 = 0.
-2, -1, 0, 1/2
Suppose 2*b = -5*o - 4 + 13, -b - 5*o = -12. Let f(i) = i**2 + 2. Let 