(w) be the first derivative of c(w). Factor n(r).
-2*r*(r - 2)*(r + 1)**3/7
Let n = -107 - -109. Let c(j) be the second derivative of -1/42*j**7 + j + 0*j**n + 1/15*j**6 + 0*j**5 + 1/6*j**3 - 1/6*j**4 + 0. Factor c(h).
-h*(h - 1)**3*(h + 1)
Let h be ((-1)/(-10))/(13/104). Let f = 9 + -9. Factor 2/5*d**3 + f + 0*d + 2/5*d**5 + 0*d**2 + h*d**4.
2*d**3*(d + 1)**2/5
Let d(k) = k**3 - 3*k**2 + 2*k + 3. Let b(g) = -g**3 + 2*g**2 - g - 2. Let u(w) = -3*b(w) - 2*d(w). Factor u(i).
i*(i - 1)*(i + 1)
Let l be (-8)/(-16)*1/24. Let u(c) be the third derivative of 1/60*c**5 + 1/240*c**6 + c**2 + l*c**4 + 0*c**3 + 0 + 0*c. Suppose u(b) = 0. Calculate b.
-1, 0
Let c(i) be the third derivative of i**4/24 - i**3 + i**2. Let a be c(9). Factor -1/3*r - 1/3*r**a + 0 - 2/3*r**2.
-r*(r + 1)**2/3
Let c(t) = t**3 + 13*t**2 + 13*t + 16. Let p be c(-12). Factor 3*v**p + 8*v**3 - 7*v**2 - 5*v**3 + v**2.
3*v**2*(v - 1)*(v + 2)
Solve 4*w**2 - 11/4*w**3 - 9/4*w**4 + 0 + w = 0 for w.
-2, -2/9, 0, 1
Let j(m) be the second derivative of m**4/16 + 7*m**3/4 + 147*m**2/8 + 29*m. Let j(t) = 0. What is t?
-7
Let y(f) be the third derivative of 0*f + 1/20*f**5 + 5*f**2 + 0*f**4 + 0*f**6 + 0*f**3 + 0 - 1/70*f**7. Factor y(l).
-3*l**2*(l - 1)*(l + 1)
Factor 0*y + 0*y**3 + 0*y**2 + 0 - 3/7*y**4.
-3*y**4/7
Let b be 4/(-22) - (-4670)/275. Let z = 17 - b. Let 0 - z*o**3 + 1/5*o**5 + 1/5*o**2 + 0*o - 1/5*o**4 = 0. Calculate o.
-1, 0, 1
Let f(k) be the first derivative of 1/40*k**5 + 3*k - 1/12*k**3 - 1/4*k**2 + 1/24*k**4 + 3. Let n(x) be the first derivative of f(x). Factor n(c).
(c - 1)*(c + 1)**2/2
Let m be 10/(-6) + (-14)/(-8). Let a(y) be the third derivative of 0*y + 0 - m*y**3 - y**2 + 0*y**4 + 1/120*y**5. Let a(n) = 0. What is n?
-1, 1
Let p(u) be the first derivative of 8*u + 2*u**3 + 2 + 5/2*u**4 - 12*u**2. Let p(j) = 0. Calculate j.
-2, 2/5, 1
Suppose -2 - 8 = 5*q. Let u = 2 - q. Factor -p**2 + u - 2 - 1.
-(p - 1)*(p + 1)
Let z(f) be the third derivative of -f**6/300 - f**5/150 + 4*f**2. Find y such that z(y) = 0.
-1, 0
Let n(d) be the first derivative of 27*d**6/4 + 63*d**5/5 + 13*d**4/8 - 14*d**3/3 + d**2 + 7. Factor n(p).
p*(p + 1)**2*(9*p - 2)**2/2
Suppose -3*r**3 + 9*r**3 - 2*r**2 - 6*r + 2*r**4 + 0*r**3 = 0. What is r?
-3, -1, 0, 1
Let s(b) = 34*b**4 + 44*b**3 + 10*b**2 - 2*b + 2. Let u(y) = 67*y**4 + 88*y**3 + 21*y**2 - 5*y + 5. Let t(v) = 5*s(v) - 2*u(v). Suppose t(l) = 0. What is l?
-1, -2/9, 0
Let r(w) be the first derivative of w**4/8 + 47. Factor r(p).
p**3/2
Suppose -4*n - 4*i + 10 - 130 = 0, 0 = -3*i - 3. Let h = -21 - n. Factor 5*b**2 - 3*b**2 - h*b**3 - 2*b**3.
-2*b**2*(5*b - 1)
Let s(w) = -2*w**2 + 1. Let q be s(-1). Let h = 2 - q. Factor 0*m**3 + m**h - m - 3*m**3 + 3*m**2.
-m*(m - 1)*(2*m - 1)
Let w be 10/3 + 4/6. What is g in w*g**4 + 8*g**2 + 0*g + 3*g**3 - 2*g - 13*g**3 = 0?
0, 1/2, 1
Let r(m) be the second derivative of m**5/42 - m**4/63 - 5*m**3/63 + 2*m**2/21 + 25*m. Factor r(o).
2*(o - 1)*(o + 1)*(5*o - 2)/21
Factor 25*q**3 - 13*q + 0 - 5*q**2 + 1 - 3*q - 5.
(q - 1)*(5*q + 2)**2
Let o(v) = -162*v**3 + 540*v**2 - 249*v + 21. Let t(m) = -m**3 + m**2 + m - 1. Let k be 0 + -3 - (1 - 19). Let i(q) = k*t(q) - o(q). Factor i(d).
3*(d - 3)*(7*d - 2)**2
Let v = 2 - -1. Suppose 14*i**4 + 7*i**3 - 4*i**2 - 6*i**2 + 17*i**v - 4 - 18*i - 6*i**3 = 0. Calculate i.
-1, -2/7, 1
Let b(g) be the third derivative of -g**7/189 + 2*g**6/135 - g**5/270 - g**4/54 + 4*g**2. Find d, given that b(d) = 0.
-2/5, 0, 1
Let t(z) be the first derivative of 7/10*z**5 + 25/6*z**3 - 4*z**2 - 19/8*z**4 - 1/12*z**6 + 3 + 2*z. Factor t(j).
-(j - 2)**2*(j - 1)**3/2
Let a(w) be the first derivative of -w**5/35 - 2*w**4/7 - 22*w**3/21 - 12*w**2/7 - 9*w/7 + 15. Find x such that a(x) = 0.
-3, -1
What is o in 2/15*o**4 + 26/15*o**2 + 8/5*o + 4/5*o**3 + 8/15 = 0?
-2, -1
Let i(t) be the third derivative of 3*t**8/448 - 2*t**7/105 + t**6/96 + t**5/120 + 33*t**2. Determine s so that i(s) = 0.
-2/9, 0, 1
Let g = -404/3 + 136. What is w in 0 - g*w**2 + 2/3*w = 0?
0, 1/2
Let g(h) = 4*h**3 + 6*h**2 + 4. Let p(d) = -5*d**3 - 7*d**2 + d - 4. Let m(k) = -7*g(k) - 6*p(k). Factor m(x).
2*(x - 2)*(x + 1)**2
Let i(j) = -2*j**5 + 6*j**3 + j**2. Let f(r) = -8*r**5 + 24*r**3 + 5*r**2. Let d(q) = -6*f(q) + 22*i(q). Find t, given that d(t) = 0.
-1, 0, 2
Let p(k) = -k + 3*k - 4*k + 3*k. Let l be p(4). Solve -2*t**3 + 0*t**l - 3*t**5 + 0*t**5 + 4*t**4 + t**5 = 0.
0, 1
Let c(n) = -10*n**5 + 15*n**3 - 10*n**2 - 5*n. Let z(b) = b**5 + b**4 - b**3 + 1. Let g(v) = -c(v) - 5*z(v). Factor g(f).
5*(f - 1)**3*(f + 1)**2
Let h(x) be the third derivative of 0 - 1/54*x**4 - x**2 - 1/27*x**3 + 0*x - 1/270*x**5. Determine i, given that h(i) = 0.
-1
Determine d, given that -1/6*d**4 + 0*d + 1/3*d**3 + 0 - 1/6*d**2 = 0.
0, 1
Let d = -12 - -49/4. Suppose d*i + 0 - i**4 - 1/4*i**3 + i**2 = 0. What is i?
-1, -1/4, 0, 1
Let l(q) be the second derivative of q**6/2 - q**5/4 - 5*q**4/4 + 5*q**3/6 - 31*q. Factor l(x).
5*x*(x - 1)*(x + 1)*(3*x - 1)
Suppose 0 = 4*g - 0*g + 4*r - 16, 2*g + 3*r = 10. Let w(x) be the first derivative of -2/15*x**3 + 0*x + 2/5*x**2 - g. Determine u so that w(u) = 0.
0, 2
Factor -5*j**2 + 284*j - 3*j**3 - 131*j - 4*j**2 - 141*j.
-3*j*(j - 1)*(j + 4)
Suppose 2*o - 8 = m, -3 = -3*o - 2*m - 5. Let d be 4/9*(-27)/(-18). Solve 0 + 0*p**o + 0*p + d*p**3 = 0.
0
Let o(v) be the first derivative of -v**3/2 + 3*v**2 - 6*v + 9. Factor o(q).
-3*(q - 2)**2/2
Factor 0*l**3 + 0*l + 2/3*l**4 - 4/3*l**2 + 2/3.
2*(l - 1)**2*(l + 1)**2/3
Solve 8*s**3 + 41*s + 15*s**2 + s**2 - 12*s**3 + 3*s + 24 = 0 for s.
-1, 6
Let q(z) = -7*z**4 - 11*z**3 + 7*z**2 + z - 5. Let r(t) = 4*t**4 + 6*t**3 - 4*t**2 + 3. Let m(a) = 3*q(a) + 5*r(a). Let m(s) = 0. Calculate s.
-3, -1, 0, 1
Let o(w) be the first derivative of 4*w**3/15 + 2*w**2/5 - 2. Determine n so that o(n) = 0.
-1, 0
Let s(j) be the third derivative of -j**8/1120 + j**7/315 - j**6/270 - j**4/12 - j**2. Let h(d) be the second derivative of s(d). Factor h(z).
-2*z*(3*z - 2)**2/3
Let s(i) = -i**3 + 3*i**2 + 2*i - 3. Let q be s(3). Factor 4*n - 8*n - 4*n**q + 10*n**2 - 2*n**2.
-4*n*(n - 1)**2
Let t(k) = -2*k**5 + 5*k**3 + 4*k**2 + k + 1. Let b(f) = f**3 - f - 1. Let l(r) = 2*b(r) + 2*t(r). Solve l(x) = 0 for x.
-1, 0, 2
Let m(x) be the first derivative of x**6/420 - x**5/210 - x**2 - 2. Let f(r) be the second derivative of m(r). Factor f(u).
2*u**2*(u - 1)/7
Suppose 5*m - 3 = 4*m. Let l(g) be the first derivative of g + m + g**2 + 1/3*g**3. Factor l(n).
(n + 1)**2
Let s(r) = r**3 + r**2 + 2*r + 1. Let l(a) = a**4 - 7*a**3 - 6*a**2 + 4*a + 5. Let h(z) = -l(z) - 3*s(z). Factor h(f).
-(f - 4)*(f - 2)*(f + 1)**2
Let a = -5 + 7. Suppose 2*i - 8 + a = 0. Factor 0 + 1/3*s**i + 0*s + 0*s**2.
s**3/3
Let b(p) = 6*p**2 - 17*p. Let a(x) = 3*x**2 - 9*x. Let z(d) = 5*a(d) - 3*b(d). Determine t so that z(t) = 0.
0, 2
Let n = -38 - -42. Let g(i) be the third derivative of 0*i**3 - 1/180*i**6 + 0*i + 0 - 2*i**2 - 1/45*i**5 - 1/36*i**n. Factor g(l).
-2*l*(l + 1)**2/3
Let t(r) be the first derivative of -r**3/12 + 2. Suppose t(a) = 0. Calculate a.
0
Let m(o) = -o**3 + 2*o**2 + 4*o - 3. Let v be m(3). Factor v*a**3 + 3/2*a**2 - a + 0 - 1/2*a**4.
-a*(a - 1)**2*(a + 2)/2
Factor -4/3*k**2 + 32/3 + 28/3*k.
-4*(k - 8)*(k + 1)/3
Let u = -27 - -24. Let c(n) = -6*n**3 + 6*n. Let z(i) = -i**4 - 6*i**3 + i**2 + 6*i. Let h(k) = u*z(k) + 4*c(k). Factor h(j).
3*j*(j - 2)*(j - 1)*(j + 1)
Let b be (-28)/4 + (-364)/(-49). Find t such that 0 - b*t**2 + 3/7*t = 0.
0, 1
Let f(o) = o**3 - 10*o**2 - 5*o + 2. Let a(m) = -m**2. Let b(p) = -6*a(p) + f(p). Let t be b(5). Factor t*g**2 - 3*g**2 + g + 0*g**2.
-g*(g - 1)
Let n(i) be the first derivative of 2*i**6/9 - 2*i**5/3 + i**4/2 + 2*i**3/9 - i**2/3 + 7. Factor n(c).
2*c*(c - 1)**3*(2*c + 1)/3
Let c(j) = -2*j**2 - 7*j + 4. Let x be c(-4). Suppose x - 2/3*f**2 + 4/3*f - 2/3*f**3 = 0. What is f?
-2, 0, 1
Find c such that 1/4*c**4 + 0*c + 0*c**3 + 0 + 0*c**2 = 0.
0
Factor 100*a**4 - 51*a**3 - 25*a**5 + 17*a**2 + 10*a**4 - 89*a**3 + 23*a**2.
-5*a**2*(a - 2)**2*(5*a - 2)
Let b(c) be the second derivative of -3*c**6/10 - 3*c**5/5 + c**4 + 7*c. Suppose b(t) = 0. What is t?
-2, 0, 2/3
Suppose 5*w = -p + 13, 4*w - 2*w = -2*p + 10. Let r = -150 - -154. Suppose 2/5*j**2 + 6/5*j**5 - w*j**3 + 0