 2
Suppose -4 - 6 = -5*a. Let o(n) be the first derivative of -1/2*n**2 + 1/12*n**3 - a + n. Factor o(p).
(p - 2)**2/4
Let i(f) = 17*f**2 - 9*f + 8. Let m(r) = 11*r**2 - 6*r + 5. Let n = -7 - -2. Let w(t) = n*i(t) + 8*m(t). Suppose w(h) = 0. Calculate h.
0, 1
Let v(t) be the second derivative of -2/3*t**2 + 3*t + 0 + 1/6*t**4 - 5/9*t**3. Factor v(d).
2*(d - 2)*(3*d + 1)/3
Solve -2/3*c**2 - 2/3*c + 2/3 + 2/3*c**3 = 0 for c.
-1, 1
Solve 6*l**2 - 77 + 36*l + 3*l**3 - 24*l**2 + 53 = 0 for l.
2
Let v(q) = -q**3 - 2*q**2 + 2*q - 1. Let t be v(-3). Suppose t*l - 1 = 3. Let -4*x + 2*x**2 + 0*x**l + 6*x = 0. Calculate x.
-1, 0
Suppose -5*b**3 - 9*b**4 - 121 + 186 + 47*b**3 - 97 - 4*b**2 - 72*b = 0. Calculate b.
-2/3, 2, 4
Let y(r) = 2 + 5*r**2 + 0 + 0 - 7*r. Let v be -5*5/(25/(-6)). Let t(n) = 11*n**2 - 15*n + 4. Let i(c) = v*t(c) - 13*y(c). Factor i(m).
(m - 1)*(m + 2)
Let s(m) be the third derivative of -m**5/15 - m**4/3 - 2*m**3/3 + 7*m**2. What is d in s(d) = 0?
-1
Let z = 1 + 2. Let u be ((-8)/(-24))/(2/12). Find w, given that -u*w**4 + 0*w**5 + w**5 - 2 - 3*w**5 + 0*w**5 + 4*w**z + 4*w**2 - 2*w = 0.
-1, 1
Solve -98 + 4*j + 10*j + 2*j**2 + 110 = 0.
-6, -1
Let i(k) be the first derivative of -2*k**5/15 + k**4/6 - 10. Factor i(m).
-2*m**3*(m - 1)/3
Let n(z) = 8 + 11*z**3 - 13 + 35*z**2 - z + 11. Let i(t) be the first derivative of -t**4/2 - 2*t**3 - t - 1. Let l(w) = 34*i(w) + 6*n(w). Factor l(a).
-2*(a - 1)**3
Let g(k) be the second derivative of 0*k**2 - 3*k + 1/180*k**6 + 1/6*k**4 - 1/20*k**5 + 0 + 2/3*k**3. Let o(r) be the second derivative of g(r). Factor o(x).
2*(x - 2)*(x - 1)
Let x = -2 - -14/5. Let a = -3 + 5. Factor 0*s**a - 2/5*s**4 + 4/5*s**3 + 2/5 - x*s.
-2*(s - 1)**3*(s + 1)/5
Let b(h) be the third derivative of 0 + 0*h - h**2 - 1/21*h**3 - 1/210*h**5 + 1/42*h**4. Determine s, given that b(s) = 0.
1
Factor -21/5*o + 3/5*o**3 - 18/5*o**2 + 0.
3*o*(o - 7)*(o + 1)/5
Let h(p) = p**3 + 12*p**2 + p - 10. Let c(y) = 4*y**3 + 61*y**2 + 5*y - 52. Let f(a) = 6*c(a) - 33*h(a). Factor f(s).
-3*(s + 1)*(s + 3)*(3*s - 2)
Let p(x) be the third derivative of -x**7/231 - 2*x**6/165 - x**5/330 + x**4/66 - 4*x**2. Factor p(h).
-2*h*(h + 1)**2*(5*h - 2)/11
Let s(c) be the first derivative of c**6/120 - c**4/16 + c**3/12 - 2*c + 1. Let t(m) be the first derivative of s(m). Determine g so that t(g) = 0.
-2, 0, 1
What is j in -58*j**3 - 35*j**2 - 60*j**3 + 123*j**3 = 0?
0, 7
Let u(j) = j**5 + j**2 - 1. Let g(z) = 2*z**5 - 3*z**4 + 2*z**3 + z**2 - 1. Let m(p) = 4*g(p) - 4*u(p). Determine v, given that m(v) = 0.
0, 1, 2
What is q in -q**4 - 17*q**3 + 37*q**3 - 22*q**3 = 0?
-2, 0
Let o(t) be the second derivative of 0*t**4 + 0 + 1/2*t**3 + t + 0*t**2 - 3/20*t**5. Determine w so that o(w) = 0.
-1, 0, 1
Let y(s) be the second derivative of 0 + 0*s**2 - s - 1/18*s**3 + 1/36*s**4. Factor y(o).
o*(o - 1)/3
Let f = -8 - -16. What is q in -7/2*q**2 - f*q - 2 = 0?
-2, -2/7
Determine o so that 0*o - 28/5*o**3 - 4*o**4 + 0 - 8/5*o**2 = 0.
-1, -2/5, 0
Suppose 2 = -2*a + 3*m, 3*a = a + 5*m - 6. Find o such that 2*o**a - o**2 + 2 + 4*o + 0 + 2 = 0.
-2
Suppose 2*d + 5 = 29. Let q be (-3)/d - 26/(-40). Factor -12/5*a**2 + 8/5*a + 8/5*a**3 - 2/5 - q*a**4.
-2*(a - 1)**4/5
Suppose 4*c - 2*f - 12 = 0, -c + 3*c - 10 = 3*f. Factor -117 - 2*l**3 + 117 - c*l**2.
-2*l**2*(l + 1)
Factor -8*n**2 - 4 + 6*n**2 + 4*n + 2.
-2*(n - 1)**2
Suppose 5*s = 4*j - 48, 2*s - 4*s - 3*j = 10. Let k = s + 11. Factor 0*y - 4/11*y**2 + 0 - 2/11*y**4 - 6/11*y**k.
-2*y**2*(y + 1)*(y + 2)/11
Let b(z) be the third derivative of 1/8*z**4 + 0*z**3 + 0*z + z**2 + 1/20*z**5 + 0. Factor b(v).
3*v*(v + 1)
Find x such that 1 - 5/2*x + x**2 = 0.
1/2, 2
Let i(q) be the second derivative of -3*q + 0 + 1/90*q**6 - 1/9*q**3 + 0*q**4 - 1/6*q**2 + 1/30*q**5. Determine s so that i(s) = 0.
-1, 1
Let g(x) be the first derivative of -x**7/210 + x**6/60 - x**5/60 - x**2/2 - 2. Let l(w) be the second derivative of g(w). Find q, given that l(q) = 0.
0, 1
Let j(k) = 4*k + 4 - 2*k - 3 - 3*k. Let l be j(-1). Solve -1/5*h**l + 0 + 0*h = 0 for h.
0
Let p(g) be the first derivative of 5*g**3/12 + 5*g**2/2 + 15*g/4 - 10. Find z, given that p(z) = 0.
-3, -1
Suppose 2/9 + 2/3*o**2 - 2/3*o - 2/9*o**3 = 0. Calculate o.
1
Let i(v) be the third derivative of v**7/70 + v**6/20 + v**5/20 - 7*v**2. Determine w, given that i(w) = 0.
-1, 0
Let k(y) = -y**5 + y**4 - y**3 + y**2 + y - 1. Let d = 2 - 1. Let c(j) = 9*j**5 - 9*j**4 + 3*j**3 - 3*j**2 - 6*j + 6. Let h(o) = d*c(o) + 6*k(o). Factor h(m).
3*m**2*(m - 1)**2*(m + 1)
Let n(k) be the third derivative of -k**7/210 - k**6/60 + k**4/12 + k**3/6 + 7*k**2. Factor n(q).
-(q - 1)*(q + 1)**3
What is d in -2/3*d**5 + 2/3*d + 4/3*d**4 - 4/3*d**2 + 0*d**3 + 0 = 0?
-1, 0, 1
Let m(w) be the third derivative of w**7/630 - w**5/90 + w**3/18 - 8*w**2. Determine p so that m(p) = 0.
-1, 1
Let p(w) be the first derivative of -w**3/7 - 3*w**2/7 - 3*w/7 - 14. Factor p(m).
-3*(m + 1)**2/7
Let c(p) be the first derivative of 6*p + 1 + 4*p**3 + 15/2*p**2 + 3/4*p**4. Suppose c(r) = 0. What is r?
-2, -1
Suppose 0*q + 2*q = 0. Solve 5*w - 2 + 7*w**4 + q - 5*w**3 + 4 - 9*w**2 = 0.
-1, -2/7, 1
Let h(t) be the third derivative of -5*t**2 - 1/5*t**3 + 0 + 0*t + 1/100*t**5 + 1/40*t**4. Factor h(u).
3*(u - 1)*(u + 2)/5
Let u(g) be the first derivative of -5*g**6/33 - 24*g**5/55 - 2*g**4/11 + 20*g**3/33 + 9*g**2/11 + 4*g/11 - 3. Determine x so that u(x) = 0.
-1, -2/5, 1
Let q be -6 - 4/(-2) - 80/(-18). Factor -2/9*l**2 + 0 + 2/9*l**3 - q*l.
2*l*(l - 2)*(l + 1)/9
Let q be (-6)/(-33) + 31/11. Solve -a**3 - a**2 - a**q + 3*a**3 - 3*a**2 + 5*a - 2 = 0.
1, 2
Let x(p) = -p**2 + 3*p + 2. Suppose 4*h - 4*l + 6 = 14, -3*h - 18 = 3*l. Let k(s) = -3*s**2 + 10*s + 7. Let q(j) = h*k(j) + 7*x(j). Factor q(z).
-z*(z - 1)
Suppose 10*t**2 + 31 - 31 + 2*t = 0. What is t?
-1/5, 0
Let r = -2638/5 + 530. Factor -8/5*o**3 - 2/5*o**4 - 2/5 - 8/5*o - r*o**2.
-2*(o + 1)**4/5
Suppose -2*d - 12 = -4*d. Let q be (-2)/(-1) + -5 + d. Find r, given that 6*r**3 + 5*r**2 + 3*r**4 - 2*r**q - 2*r**4 + 2*r = 0.
-2, -1, 0
Let z(i) be the third derivative of 0*i**3 + 7*i**2 - 3/32*i**4 + 0*i - 1/40*i**5 - 1/480*i**6 + 0. Factor z(p).
-p*(p + 3)**2/4
Let v(y) be the first derivative of -y**7/420 - 3*y**2/2 - 3. Let b(q) be the second derivative of v(q). Factor b(n).
-n**4/2
Let o(a) be the second derivative of -a**6/1980 - a**5/660 + a**4/66 - a**3 - a. Let b(g) be the second derivative of o(g). What is f in b(f) = 0?
-2, 1
Let h(w) be the third derivative of -49*w**6/270 - 203*w**5/270 - 23*w**4/27 - 4*w**3/9 + 32*w**2. Determine z so that h(z) = 0.
-3/2, -2/7
Let n(p) be the second derivative of -2*p**6/15 + 16*p**5/15 + 35*p**4/27 + 4*p**3/9 - 16*p. Suppose n(d) = 0. Calculate d.
-1/3, 0, 6
Let b(o) be the second derivative of 1/15*o**5 - 1/180*o**6 + 1/6*o**3 - 1/3*o**4 + 2*o + 0*o**2 + 0. Let v(l) be the second derivative of b(l). Factor v(d).
-2*(d - 2)**2
Let w(j) be the second derivative of 1/12*j**3 - j**2 + 3*j + 1/120*j**5 - 1/24*j**4 + 0. Let s(o) be the first derivative of w(o). Factor s(b).
(b - 1)**2/2
Let h(k) be the first derivative of 2*k**3/9 - k**2 + 4*k/3 + 2. Determine v so that h(v) = 0.
1, 2
Let i(c) be the second derivative of 0*c**4 + 0*c**2 - 6*c + 1/48*c**3 + 0 - 1/160*c**5. Find y such that i(y) = 0.
-1, 0, 1
Suppose -5*z + 18 = 2*r + 1, 3*z - 12 = -3*r. Let m(o) = 2*o + 14. Let w be m(-6). Factor -1 + 8*f**w + 3 - z - 6*f - 1.
2*(f - 1)*(4*f + 1)
Let l(c) = c**2 - c - 1. Let g(a) = 4*a**2 - 14*a + 16. Let p(k) = -2*g(k) + 4*l(k). Solve p(i) = 0 for i.
3
Let r(f) be the second derivative of -f**9/20160 - f**8/26880 + f**7/5040 - f**4/12 + 2*f. Let q(z) be the third derivative of r(z). Factor q(v).
-v**2*(v + 1)*(3*v - 2)/4
Let u(r) be the third derivative of r**5/30 - r**4/4 + 2*r**3/3 + 8*r**2. Factor u(w).
2*(w - 2)*(w - 1)
Solve a - 1/2*a**2 - 1/4*a**4 - a**3 + 3/4 = 0 for a.
-3, -1, 1
Let w be (-3 + 2)*2 - 9. Let v(y) = 4*y**2 - 79*y + 146. Let q(m) = m**2 - 16*m + 29. Let d(f) = w*q(f) + 2*v(f). Determine a, given that d(a) = 0.
3
Let x(j) = -j. Let y(i) = i**4 - 3*i**3 + 3*i**2 + 5*i. Let l(n) = 6*x(n) + y(n). Factor l(m).
m*(m - 1)**3
Let f(u) be the third derivative of u**6/20 + u**5/20 - u**4/8 + 6*u**2. Factor f(r).
3*r*(