*m**4 + i*m**2. Solve q(n) = 0.
-1, 0
Let l(s) = s**2 + 4. Let b be l(0). Let q(g) = -g**2 + 4*g. Let p be q(b). Find v such that -2/3*v**3 + p*v**2 + 2/3*v - 1/3*v**4 + 1/3 = 0.
-1, 1
Let b(a) = 76*a**4 - 208*a**3 + 224*a**2 - 100*a + 16. Let o(i) = -i**4 - i**3. Let s(u) = b(u) + 4*o(u). Find z such that s(z) = 0.
4/9, 1/2, 1
Let r be -2 + 4 - (-8 + 6). Determine x so that -8*x**2 - 2*x + 2 - r*x**3 + 4*x - x = 0.
-2, -1/2, 1/2
Let c(s) = -s - 2. Let w be c(0). Let i be 6/(-2) + 3 - w. Solve -4/7*a - 2/7*a**i - 2/7 = 0 for a.
-1
Let n be 42/8 - 6/24. Suppose -n + 2 = -u. Factor -2*t + 2*t**4 - 2/5*t**5 + 4*t**2 - 4*t**u + 2/5.
-2*(t - 1)**5/5
Suppose 25*b + 8 = 29*b. Suppose -2*y + y - 7 = -4*x, -2*x + b*y = 4. Factor -1/2*n**x + 0*n**2 + 0*n + 1/2*n**4 + 0.
n**3*(n - 1)/2
Factor 16*b**3 + 35*b + 13*b - 2*b**4 - 12*b - 22*b**2 - 20*b**2.
-2*b*(b - 3)**2*(b - 2)
Factor -7*u**2 + 2*u**4 + u**2 - 31 + 31 + 4*u.
2*u*(u - 1)**2*(u + 2)
Let v(o) be the third derivative of -o**5/80 - 3*o**4/16 + 7*o**3/8 + 9*o**2. Let v(w) = 0. Calculate w.
-7, 1
Let m(b) = 3*b**3 - b**2 + 3*b + 7. Let n(p) = 3*p**3 + 3*p + 6. Let i(u) = 6*m(u) - 7*n(u). Find l, given that i(l) = 0.
-1, 0
Let b = 46 + -43. Let d(c) be the third derivative of 0*c**4 + 0*c**b + 0*c - 1/120*c**6 + 0 - 3*c**2 + 1/30*c**5. What is i in d(i) = 0?
0, 2
Let g(p) be the first derivative of 1/2*p**2 + 3 + 0*p - 1/3*p**3. Solve g(a) = 0 for a.
0, 1
Let v(t) be the third derivative of t**2 + 0*t**4 + 0*t + 0 - 1/90*t**5 + 0*t**3 - 1/180*t**6. Find k such that v(k) = 0.
-1, 0
Suppose 8 = 5*z - 2. Let h(j) be the second derivative of 1/21*j**7 + z*j + 1/25*j**6 + 0 + 0*j**2 - 1/25*j**5 + 0*j**3 + 0*j**4. Factor h(b).
2*b**3*(b + 1)*(5*b - 2)/5
Suppose -5*u + 3 = -z - 8*u, 0 = 2*z - 4*u - 4. Let w(h) be the second derivative of 0*h**4 - 1/90*h**6 + 0*h**3 + 0 - 1/60*h**5 + z*h**2 - 3*h. Factor w(c).
-c**3*(c + 1)/3
Determine h, given that 2*h**2 - 9*h**4 + 6*h**2 + 5*h**4 - 4 = 0.
-1, 1
Let o be 3/5 + 72/(-420). Factor -6/7 + 9/7*k**2 + o*k.
3*(k + 1)*(3*k - 2)/7
Let p(n) = 7*n**3 - 6*n**2 - n. Let k(u) = -20*u**3 + 17*u**2 + 3*u. Let o(d) = -6*k(d) - 17*p(d). Factor o(c).
c*(c - 1)*(c + 1)
Let u(a) be the first derivative of 4*a**3/3 + 12*a**2 - 40. Find q, given that u(q) = 0.
-6, 0
Let o(x) be the third derivative of 0*x + 1/96*x**4 + 0*x**3 - 1/120*x**5 + 1/480*x**6 + 0 - 2*x**2. Factor o(j).
j*(j - 1)**2/4
Let i be (-9)/(-6) - (-77)/(-66). Suppose -1/3*b**2 - 1/3*b + i + 1/3*b**3 = 0. What is b?
-1, 1
Factor -g**2 - 3 + 1 - 3*g**2 + 6.
-4*(g - 1)*(g + 1)
Let c(v) be the third derivative of v**7/210 - v**5/30 + v**3/6 - 5*v**2. Let c(g) = 0. Calculate g.
-1, 1
Let d be (-17)/(-51) - (-266)/(-834). Let g = d + 260/1251. Factor 0*j**4 + 4/9*j**3 + 0*j**2 - g*j**5 + 0 - 2/9*j.
-2*j*(j - 1)**2*(j + 1)**2/9
Let r(j) be the first derivative of 1/24*j**4 - j + 0*j**3 + 1 - 1/4*j**2. Let b(o) be the first derivative of r(o). Suppose b(t) = 0. What is t?
-1, 1
Let s(l) = 18*l**3 + 33*l**2 + 30*l + 6. Let q(z) = -53*z**3 - 100*z**2 - 89*z - 18. Let p(t) = 3*q(t) + 8*s(t). Factor p(y).
-3*(y + 1)**2*(5*y + 2)
Let c(d) be the first derivative of d**2 + d + 1/3*d**3 - 4. Factor c(q).
(q + 1)**2
Let n(r) = -r**3 + r**2 - r - 1. Let g(o) = -5*o**3 + o**2 + o - 3. Let f(u) = g(u) - 3*n(u). Determine a, given that f(a) = 0.
-2, 0, 1
Let z = -24 - -24. Factor 5/4*f**4 - 1/2*f**3 + z + 0*f**2 + 0*f.
f**3*(5*f - 2)/4
Suppose 28 = -7*m + 28. Let a(n) be the second derivative of m*n**2 - 3/4*n**4 + 0 - 1/3*n**3 - n. Find x such that a(x) = 0.
-2/9, 0
Let i(v) be the second derivative of 0*v**5 - 1/4*v**4 - 1/7*v**7 + 0*v**3 + 0 + 5*v + 3/10*v**6 + 0*v**2. Determine z so that i(z) = 0.
-1/2, 0, 1
Let c be (-45)/(-27) - 8/(-6). Factor 4/5*j + 2/5 - 2/5*j**4 + 0*j**2 - 4/5*j**c.
-2*(j - 1)*(j + 1)**3/5
Let m(v) = -9*v**2 - v. Let z be m(1). Let c be (-9)/8*z/15. Find b such that -1/2 - c*b - 1/4*b**2 = 0.
-2, -1
Let z(t) = -t**3 + 4*t**2 + 6*t - 1. Let j be z(5). Let p be 2*-1 + -2 + j. Determine v so that 0 + 1/2*v**3 + p*v**2 - 1/2*v = 0.
-1, 0, 1
Suppose -8*u - 13*u - 43 + 3*u**2 + 19 = 0. What is u?
-1, 8
Let z(d) = 10*d**4 - 8*d**3 + 12*d**2 - 16*d - 6. Let t(h) = h**4 - h - 1. Let q(m) = 8*t(m) - z(m). Factor q(o).
-2*(o - 1)**4
Factor 7/4*n + 1/4*n**3 - 5/4*n**2 - 3/4.
(n - 3)*(n - 1)**2/4
Let c = -9 + 4. Let o(g) = g**2 - 1. Let x(l) be the second derivative of -l**4/6 - l**3/6 + l**2/2 + l. Let q(v) = c*x(v) - 6*o(v). Factor q(d).
(d + 1)*(4*d + 1)
Let a(o) = -o**2 - 2*o. Let i(g) = -g**2 - 6*g - 7. Let b be i(-5). Let h be a(b). What is m in m**5 - 5*m**2 + h*m**5 + 0*m**4 + m**4 + 4*m**2 - m**3 = 0?
-1, 0, 1
Let s = -13 - -16. Let a(b) be the third derivative of -1/525*b**7 - b**2 - 1/60*b**4 - 1/50*b**5 + 0*b + 0 + 0*b**s - 1/100*b**6. Factor a(i).
-2*i*(i + 1)**3/5
Let h(y) be the first derivative of y**4/4 + 4*y**3 - 3*y**2 + 10*y + 1. Let v(q) = q**2 - q + 1. Let o(a) = -2*h(a) + 18*v(a). Find x, given that o(x) = 0.
-1
What is i in 11*i**2 + 4*i**4 + 13*i**2 - 31 - 4*i + 15*i**5 + 31 - 39*i**3 = 0?
-2, 0, 1/3, 2/5, 1
Let s = -3 + 2. Let y be (-1 + (0 - -1))/s. Determine i so that -2*i**4 - 4/3*i + y + 8/3*i**3 + 2/3*i**2 = 0.
-2/3, 0, 1
Let r(p) = 6*p**5 + 18*p**4 + 28*p**3 + 6*p**2. Let q(f) = 2*f**5 + 6*f**4 + 9*f**3 + 2*f**2. Let h be 20/(-6) + 4/12. Let s(m) = h*r(m) + 10*q(m). Factor s(t).
2*t**2*(t + 1)**3
Let q(n) be the second derivative of 1/30*n**6 - 1/18*n**4 - 1/126*n**7 - 1/30*n**5 + 0 - 1/6*n**2 - 6*n + 1/6*n**3. Suppose q(p) = 0. Calculate p.
-1, 1
Factor -2/9*c**2 - 2/3*c**4 - 2/9*c**5 + 0 + 0*c - 2/3*c**3.
-2*c**2*(c + 1)**3/9
Let n(w) be the second derivative of w**7/21 - w**6/4 + 2*w**5/5 - w**4/8 - w**3/6 + 2*w. Solve n(r) = 0.
-1/4, 0, 1, 2
Let z = 8 - -6. Factor 10*t**2 + t**2 - z*t**2.
-3*t**2
Factor 0 - 2/17*c**3 - 4/17*c**2 - 2/17*c.
-2*c*(c + 1)**2/17
Suppose -4/3*f + 2/3*f**3 + 0 + 2/3*f**2 = 0. What is f?
-2, 0, 1
Determine t, given that -t**5 + 0*t**5 - t**4 + 30*t**2 - 29*t**2 + 0*t**3 + t**3 = 0.
-1, 0, 1
Let y(p) be the third derivative of -5*p**6/36 + p**5/6 + p**4/4 + p**3/9 + 9*p**2. Let y(w) = 0. Calculate w.
-1/5, 1
Suppose 13 = 5*u + 3. Factor -t**u - 7 + 0 - t + 9.
-(t - 1)*(t + 2)
Let t = 3 - -1. Solve -2*f**3 + 2*f**t + 2*f**2 - 2*f**2 = 0 for f.
0, 1
Let l(p) be the second derivative of -p**5/30 - p**4/9 - p**3/9 + 9*p. Factor l(t).
-2*t*(t + 1)**2/3
Let v(s) = 10*s**2 + 11*s - 11. Suppose 3*j = j. Let r = j - -6. Let q(k) = -9*k**2 - 10*k + 10. Let y(g) = r*v(g) + 7*q(g). Factor y(w).
-(w + 2)*(3*w - 2)
Factor -15*c**3 + 5*c**3 + 5*c**4 + 5*c**2 + 0*c**3.
5*c**2*(c - 1)**2
Let s(k) be the third derivative of k**5/20 + 13*k**4/24 + 2*k**3/3 - 3*k**2. Factor s(i).
(i + 4)*(3*i + 1)
Let j(c) = 3*c**4 + c**3 - c**2 + c + 2. Let q(z) = z**3 + 3 + 4*z**4 - 3*z**4 - 2. Let i(l) = -j(l) + 2*q(l). Factor i(f).
-f*(f - 1)**2*(f + 1)
Let b(x) = -x**4 + x + 1. Let r(c) = 12*c**4 - 4*c**3 + 5*c**2 - 13*c - 11. Let p(q) = 44*b(q) + 4*r(q). Find f, given that p(f) = 0.
0, 1, 2
Let s(o) be the first derivative of -o**7/224 + o**6/80 - o**5/160 - 2*o**3/3 - 1. Let i(l) be the third derivative of s(l). Determine j so that i(j) = 0.
0, 1/5, 1
Let r(f) be the third derivative of f**8/6720 + f**7/840 + f**6/240 + f**5/15 - f**2. Let p(n) be the third derivative of r(n). What is h in p(h) = 0?
-1
Let -14 - 2 + 112*k**3 - 254*k**2 + 74*k**2 - 15*k - 97*k + 196*k**4 = 0. What is k?
-1, -2/7, 1
Suppose 3*f = 2*v - 11, 7*v - 2*f - 11 = 2*v. Let r be 5/25 + v/(-5). Factor -2/3*o**3 + 0*o - 2/3*o**2 + r.
-2*o**2*(o + 1)/3
Let x(r) be the first derivative of r**6/3 + 6*r**5/5 + 3*r**4/2 + 2*r**3/3 - 7. Factor x(w).
2*w**2*(w + 1)**3
Determine q, given that -3/2 - 15/8*q - 3/8*q**2 = 0.
-4, -1
Let h(g) be the third derivative of g**7/180 - g**6/72 - g**5/30 - g**4/8 - 3*g**2. Let i(v) be the second derivative of h(v). Solve i(p) = 0.
-2/7, 1
Let h = -42 - -169/4. Let u = -859/4 - -215. Solve -1/4 - 1/4*w**3 + h*w + u*w**2 = 0 for w.
-1, 1
Suppose 3*y**3 - 3*y**2 - 9*y + 1 - 8 - 6*y - 2 = 0. Calculate y.
-1, 3
Let p(y) = -8*y + 2. Let q be p(-3). Suppose -8 + x**3 - 5*x**3 - 9*x**3 - q*x**2 - 2*x**4 - 24*x + x**3 = 0. Calculate x.
-2, -1
Let r(f) be the first derivative of -1/6*f**4 +