
0, 1
Let j(k) be the third derivative of -k**7/420 + k**5/60 - k**3/12 + 2*k**2. Solve j(g) = 0.
-1, 1
Let l = 21 - 14. Suppose -4*m + 15 = l. Factor 5*k**5 + 4*k**4 - m*k**5 + k**2 + 3*k**4 + 5*k**3.
k**2*(k + 1)**2*(3*k + 1)
Let g be (-4 - (-84)/20)*4. Factor -2/5*b**4 - g*b + 0*b**2 + 2/5 + 4/5*b**3.
-2*(b - 1)**3*(b + 1)/5
Let z be (-10)/(-4) - (-7)/14. Factor 5*c**2 - c**2 - 24*c**4 + 7*c**z - 2*c**3 + c**3 + 14*c**5.
2*c**2*(c - 1)**2*(7*c + 2)
Let w = 7 - 5. Factor -6*u**2 + u**w + 2*u + 3*u**2.
-2*u*(u - 1)
Let v = -2 + 2. Suppose v = -5*a + 2*t + 298, 3*t - 33 - 30 = -a. Factor 30*u - a*u**4 + 14*u**5 + 6*u**3 - 30*u**2 - 50*u**2 + 94*u**3 - 4.
2*(u - 1)**4*(7*u - 2)
Let m(d) be the second derivative of -d**5/60 - d**4/24 - 5*d**2/2 - 2*d. Let u(p) be the first derivative of m(p). Factor u(n).
-n*(n + 1)
Suppose 0*y + y = 0. Factor -21*z**2 + 2*z**4 + 6*z + y*z**5 + 27*z**3 + 3*z**5 - 17*z**4.
3*z*(z - 2)*(z - 1)**3
Let v = 105 - 313/3. Factor v*d**3 + 0 + 0*d + 0*d**2 - 2/3*d**4.
-2*d**3*(d - 1)/3
Let r be 1/(-42)*(-4)/(2/2). Let n(d) be the first derivative of 2/7*d - 1/7*d**2 + 1/14*d**4 - r*d**3 - 1. Factor n(m).
2*(m - 1)**2*(m + 1)/7
Let z(c) be the second derivative of 2*c**7/63 + 17*c**6/90 + 7*c**5/15 + 11*c**4/18 + 4*c**3/9 + c**2/6 - c. What is u in z(u) = 0?
-1, -1/4
Suppose -u - 1 = 9*n - 8*n, 2*n - 18 = 3*u. Factor 0*q**2 + 0*q + 0 + 1/4*q**n.
q**3/4
Let q be 3/((-135)/(-10))*3/1. Let z(w) be the first derivative of -3/16*w**4 - 7/8*w**2 + q*w**3 + 1/2*w + 1. What is t in z(t) = 0?
2/3, 1
Let h(v) be the third derivative of v**5/15 + 2*v**4/3 - 8*v**3 - 36*v**2. Determine w, given that h(w) = 0.
-6, 2
Let s(w) be the first derivative of w**3/3 + 8*w**2 + 64*w + 9. Factor s(t).
(t + 8)**2
Let r = -2/57 + 61/114. Let k(f) be the second derivative of r*f**2 + 1/2*f**4 + 0 + 1/30*f**6 - 1/5*f**5 - 2/3*f**3 - 2*f. Factor k(h).
(h - 1)**4
Let f(r) = -r. Let n be f(-2). Suppose -2*u - n = -6. Factor 1/3*l**u - 1/3*l + 0.
l*(l - 1)/3
Let s(c) be the third derivative of -c**5/40 - 3*c**4/32 + 23*c**2. Let s(r) = 0. What is r?
-3/2, 0
Let w(n) = n. Suppose -3*q - 7 = -5*x - 3, 6 = -q - 3*x. Let i = q + 2. Let h(b) = -2*b**2 + 5*b + 2. Let p(v) = i*h(v) + 5*w(v). Let p(z) = 0. Calculate z.
-1, 1
Suppose 24 = 3*r + r. Suppose -6*t + 3*t - 4*z = r, 12 = -4*z. Determine y, given that -2*y**2 - 2*y**3 - y**3 - 2*y**4 - t*y**3 + y**3 = 0.
-1, 0
Let j be (-17)/(-5) - (-19 - -22). Factor 0 + 6/5*y**3 - 6/5*y**4 - 2/5*y**2 + 0*y + j*y**5.
2*y**2*(y - 1)**3/5
Let h = 1517/5 - 303. Factor 0*p + h*p**2 + 0.
2*p**2/5
Factor 4/15*o - 2/5 + 2/15*o**2.
2*(o - 1)*(o + 3)/15
Factor -4/3*s**2 + 2/3 - 7/3*s.
-(s + 2)*(4*s - 1)/3
Let v = -5 - -5. Factor 6*d + v*d**2 + 7 - 4 + d + 4*d**2.
(d + 1)*(4*d + 3)
Let d(q) be the first derivative of -q**3/12 - q**2/4 + 3*q/4 - 3. Find l, given that d(l) = 0.
-3, 1
Let f(a) be the first derivative of -3*a**4/16 - a**3/2 + 3*a**2/8 + 3*a/2 + 25. Solve f(z) = 0 for z.
-2, -1, 1
Let s(l) = 2*l**5 - 11*l**4 - 15*l**3 + 2*l**2 + 13*l - 9. Let h(u) = -u**4 - u**3 + u - 1. Let t(p) = -18*h(p) + 2*s(p). Find x such that t(x) = 0.
-1, 0, 1, 2
Let p be (140/(-8))/7*(-2)/15. Suppose 1/3*s**3 - 1/3*s**2 + p*s**4 - 1/3*s + 0 = 0. Calculate s.
-1, 0, 1
Solve -4/5*w**3 - 1/5*w**4 + 0 - w**2 - 2/5*w = 0.
-2, -1, 0
Suppose -8 = -10*c - 8. Let k(v) be the second derivative of 0 + 0*v**3 + 1/6*v**4 - 1/30*v**6 + 3*v - 1/2*v**2 + c*v**5. Factor k(l).
-(l - 1)**2*(l + 1)**2
Let l be 0 + (-1 - -3) - -1. Let r(t) be the second derivative of 0*t**2 + 0*t**4 + 0*t**l + 1/20*t**5 - 2*t + 0. Suppose r(z) = 0. Calculate z.
0
Let n = 213 + -3194/15. Let u(c) be the second derivative of 0*c**2 - 2*c - 1/105*c**7 + 0 - n*c**3 + 0*c**4 + 1/25*c**5 + 0*c**6. Solve u(i) = 0 for i.
-1, 0, 1
Suppose 0*v + 5*v = 15. Factor -4*g**2 - 1 + 3 + 5*g - v*g**2.
-(g - 1)*(7*g + 2)
Solve 3/2*x + 0 - 3*x**4 + 3*x**2 - 3/2*x**5 + 0*x**3 = 0.
-1, 0, 1
Find h, given that -53*h + 64*h**3 + 32 + 48*h**2 - 18*h**5 - 17*h**4 - 43*h - 9*h**4 - 4*h**4 = 0.
-2, 2/3, 1
Let z = 102 + -102. Let 1/2*g**4 + 0*g**2 + 0*g + 1/4*g**3 + z + 1/4*g**5 = 0. Calculate g.
-1, 0
Let y = 5 + -4. Let q be -5*(2 + -3)*y. Factor 3*f - q*f + 0*f + 2*f**2.
2*f*(f - 1)
Let x(n) be the third derivative of -n**5/15 - n**4/2 + 3*n**2. Determine h, given that x(h) = 0.
-3, 0
Let g be 12/(-4)*(-2)/3. Suppose 0*b + g*b - 4 = 0. Find t such that -b*t**2 - 6*t**3 - 4 + 5*t + 5*t + 2*t**3 = 0.
-2, 1/2, 1
Let j(y) = -y**2 + 21*y + 164. Let a be j(27). Factor 1/2*w**3 + 2*w + 0 - a*w**2.
w*(w - 2)**2/2
Suppose -5 = -3*s + 4. Factor -o**5 + 5*o + 5*o**3 - 6*o - s*o**3.
-o*(o - 1)**2*(o + 1)**2
Let p(m) be the second derivative of -1/2*m**2 - 1/36*m**5 - 1/36*m**4 + 0 + 0*m**3 - m. Let q(c) be the first derivative of p(c). Factor q(j).
-j*(5*j + 2)/3
Let y = 242/5 + -48. Factor -2/5*f**3 + y*f + 2/5*f**2 - 2/5.
-2*(f - 1)**2*(f + 1)/5
Let b(m) be the third derivative of m**6/360 + m**5/90 - m**4/18 - 4*m**3/9 + 24*m**2. Factor b(q).
(q - 2)*(q + 2)**2/3
Let q(a) be the second derivative of a**4/90 + 2*a**3/45 - a**2/5 - 17*a. Let q(v) = 0. Calculate v.
-3, 1
Let f(y) be the second derivative of -y - 2/105*y**7 - 1/15*y**4 - 2/25*y**6 + 0 - 3/25*y**5 + 0*y**3 + 0*y**2. Factor f(v).
-4*v**2*(v + 1)**3/5
Let c = 755/6 - 119. Let d = -251/42 + c. Factor -6/7*f**2 + d*f**3 - 2/7*f**4 + 2/7*f + 0.
-2*f*(f - 1)**3/7
Let r(m) = m**4 + 2*m**3 + 8*m**2 - m. Let h(n) = n**3 + n**2. Suppose 3 = j + p + p, -3*p + 8 = 5*j. Let t(q) = j*r(q) - 5*h(q). Factor t(v).
v*(v - 1)**3
Let u(g) be the second derivative of g**5/10 - g**4/6 - g**3/3 + g**2 + g. Factor u(k).
2*(k - 1)**2*(k + 1)
Suppose 9*s = 6*s + 9. Solve -5*i**2 + 1 - 3 - 10*i - s*i**2 = 0.
-1, -1/4
Let d be 10/((-40)/(-70)*(-21)/(-6)). Let 0 - y**2 + d*y**3 + y**5 - 17/4*y**4 + 0*y = 0. What is y?
0, 1/4, 2
Let f(r) = 5*r**3 + 145*r**2 + 1615*r + 1475. Let d(c) = -c**2 + 1. Let o(w) = 30*d(w) - f(w). Find b such that o(b) = 0.
-17, -1
Let n(h) be the first derivative of h**7/168 - h**6/40 + h**5/40 + h**4/24 - h**3/8 + h**2/8 + 2*h + 3. Let a(x) be the first derivative of n(x). Factor a(r).
(r - 1)**4*(r + 1)/4
Let i(n) be the first derivative of 5*n**3/3 - 5*n**2 - 40*n - 5. Factor i(g).
5*(g - 4)*(g + 2)
Factor 3/4 - v + 1/4*v**2.
(v - 3)*(v - 1)/4
Let k = -6 + -1. Let h = k - -7. Let y - 1/2*y**2 + h = 0. Calculate y.
0, 2
Suppose 22 = 8*d - 10. Let s(w) be the first derivative of -2/3*w**3 + 0*w - 1/3*w**6 + 2/5*w**5 + 3 + 0*w**2 + 1/2*w**d. Factor s(i).
-2*i**2*(i - 1)**2*(i + 1)
Let v(y) be the third derivative of -y**7/3780 + y**5/540 + y**3/2 - 2*y**2. Let x(l) be the first derivative of v(l). Suppose x(z) = 0. What is z?
-1, 0, 1
Let i(j) = -j + 11. Let g be i(9). Let r(x) be the third derivative of 0*x**3 + 2*x**g - 1/50*x**5 + 1/60*x**4 + 0*x - 1/75*x**6 + 0. Factor r(a).
-2*a*(a + 1)*(4*a - 1)/5
Let y = -1/14 - -3/14. Let k be 25/14*10/25. Suppose k*z - 4/7*z**2 + y*z**3 - 2/7 = 0. What is z?
1, 2
Determine q, given that 3/5*q**3 + 8/5*q**2 + 7/5*q + 2/5 = 0.
-1, -2/3
Let t(f) be the third derivative of f**6/120 + f**5/20 - f**4/4 - 4*f**3/3 - 31*f**2. Determine c, given that t(c) = 0.
-4, -1, 2
Suppose -3*g - 1 = -10. Factor 1 + 3*f + 2*f**2 - 3 - 2*f**g + 0*f**3 - f**3.
-(f - 1)*(f + 1)*(3*f - 2)
Let j(h) be the first derivative of 7*h**6/3 + 18*h**5/5 - 5*h**4/2 - 6*h**3 - 2*h**2 + 14. Solve j(n) = 0.
-1, -2/7, 0, 1
Let t(n) be the second derivative of -1/96*n**4 + 7*n + 0 + 1/8*n**2 + 1/48*n**3. Factor t(s).
-(s - 2)*(s + 1)/8
Let l = -1131/11 - -103. Let i(m) = m**3 + 6*m**2 + 2*m - 11. Let c be i(-5). What is w in 0*w - l*w**3 - 2/11*w**c + 0*w**2 + 0 = 0?
-1, 0
Let l = 176 + -173. Let y(m) be the first derivative of -1/5*m**4 + 1 - 2/5*m - 14/25*m**5 + 4/15*m**6 - 2/5*m**2 + 16/15*m**l. Find n, given that y(n) = 0.
-1, -1/4, 1
Let r(z) be the first derivative of z**6/9 + 4*z**5/15 - 4*z**3/9 - z**2/3 - 21. Let r(x) = 0. What is x?
-1, 0, 1
Suppose -3*k = -7 + 1. Factor j**2 + 4*j - k*j + 2 + j.
(j + 1)*(j + 2)
Factor 4/5*l + 2/5*l**2 + 2/5.
2*(l + 1)**2/5
Factor 4/5 + 13/5*p**2 - 6/5*p**3 - 12/5*p + 1/5*p**4.
(p - 2)**2*(p - 1)**2/5
Let m(a) be the first derivative of 0*a + 1/24*a**4 + 0*a**3 - 1/12*a**2 - 2. Factor m(i).
i*(i - 1)*