2
Let j(s) be the second derivative of -1/20*s**4 - 2*s + 0 - 3/10*s**2 - 1/5*s**3. Factor j(i).
-3*(i + 1)**2/5
Let q(b) be the first derivative of -3*b**5/5 - 3*b**4/2 - b**3 + 1. Factor q(z).
-3*z**2*(z + 1)**2
Let f(p) = 2*p**2 - 3*p. Suppose -b = 2*b + s - 10, 0 = -5*b + 4*s - 6. Let g be f(b). Factor -6*a + a + 4*a - a**3 - 2*a**g.
-a*(a + 1)**2
Let v(h) be the third derivative of -1/12*h**4 + 0*h + 0*h**3 + 1/168*h**8 - 2*h**2 + 2/105*h**7 + 0 + 0*h**6 - 1/15*h**5. Suppose v(a) = 0. What is a?
-1, 0, 1
Factor u**2 + 2/3*u + 1/3*u**3 + 0.
u*(u + 1)*(u + 2)/3
Let s(v) be the first derivative of v**5/40 - v**4/12 + v**3/12 - 4*v - 3. Let k(c) be the first derivative of s(c). Let k(r) = 0. What is r?
0, 1
Let h(l) be the third derivative of 3*l**6/8 - l**5 + 5*l**4/6 + 18*l**2. Determine t so that h(t) = 0.
0, 2/3
Let m(n) be the third derivative of 7*n**6/540 - n**5/36 - n**4/18 + n**3 - 2*n**2. Let k(t) be the first derivative of m(t). Find x such that k(x) = 0.
-2/7, 1
Let v(m) = -12*m**2 - 308*m - 408. Let s(f) = -f**2 - 28*f - 37. Let c(q) = 32*s(q) - 3*v(q). Factor c(i).
4*(i + 2)*(i + 5)
Let o = 308/9 - 100/3. Factor 2/9*x**5 + 8/9*x**3 - o*x**4 + 4/9*x**2 + 4/9 - 10/9*x.
2*(x - 2)*(x - 1)**3*(x + 1)/9
Let h(o) be the second derivative of o**6/120 + o**5/80 - o**4/48 - o**3/24 + 6*o. Find y such that h(y) = 0.
-1, 0, 1
Suppose -2*q + 5*q + 3 = -3*m, -m + 5*q = -23. Solve w + 23*w**2 + m*w + 8*w**3 - w**2 + 10*w**3 = 0 for w.
-1, -2/9, 0
Let i(m) = 162*m**2 + 62*m - 26. Let n(a) = -18*a**2 - 7*a + 3. Suppose -3*w - 2*l = 166, -w + 2*l = 3*l + 57. Let v(g) = w*n(g) - 6*i(g). Factor v(f).
-4*f*(9*f + 2)
What is l in l**2 - 3*l + 15*l - 10*l + l**3 - 2*l**3 = 0?
-1, 0, 2
Find p, given that 14 + 4*p + 2/7*p**2 = 0.
-7
Let r(o) be the first derivative of 2 + 1/4*o**3 - 1/4*o + 1/4*o**2. Let r(u) = 0. Calculate u.
-1, 1/3
Let o(a) be the second derivative of 0*a**2 + 0 + 10*a - 1/14*a**4 + 0*a**3 - 1/70*a**6 + 9/140*a**5. Factor o(p).
-3*p**2*(p - 2)*(p - 1)/7
Let g(k) be the first derivative of k**4/8 - k**3/3 + k**2/4 + 1. What is y in g(y) = 0?
0, 1
Factor b**2 + b**3 - 5*b**2 - 4*b - 3*b**3 - 2*b**2.
-2*b*(b + 1)*(b + 2)
Let y = -1/6 - -19/42. Find c such that -4/7*c + 2/7 + y*c**2 = 0.
1
Let d(h) be the first derivative of -2*h**5/15 + 11*h**4/18 - 10*h**3/9 + h**2 - 4*h/9 - 6. Find x such that d(x) = 0.
2/3, 1
Let m = 21 - 83/4. Let r = 0 + 2. Determine j, given that 1/4*j**5 - m*j**4 + 0*j - 1/4*j**3 + 1/4*j**r + 0 = 0.
-1, 0, 1
Factor 6*l**2 - 13*l**3 + 34*l**3 - 4*l - 11*l**3.
2*l*(l + 1)*(5*l - 2)
Suppose 16*n - 12*n = 0. Factor 4/7*b**3 + n - 2/7*b**4 - 2/7*b**2 + 0*b.
-2*b**2*(b - 1)**2/7
Let n be (-24)/6 - (-52)/10. Factor 0*m + 0*m**4 + 3/5*m**5 - n*m**2 - 9/5*m**3 + 0.
3*m**2*(m - 2)*(m + 1)**2/5
Let m(u) be the third derivative of -u**8/1680 - u**7/315 - u**6/180 - 5*u**4/24 + 2*u**2. Let d(x) be the second derivative of m(x). Factor d(k).
-4*k*(k + 1)**2
Let z(b) be the first derivative of -b**5/70 + b**4/21 - 3*b - 1. Let k(t) be the first derivative of z(t). Determine s, given that k(s) = 0.
0, 2
Factor -y**4 - 8*y**3 - 15*y**2 - 3*y**4 + 11*y**2.
-4*y**2*(y + 1)**2
Let g(r) = r**4 + 7*r**2 - 2*r - 10. Let n(o) = -5*o**4 + o**3 - 27*o**2 + 8*o + 41. Let v(x) = -18*g(x) - 4*n(x). Solve v(j) = 0.
-2, -1, 1, 4
Factor 56*k**3 - 14*k**4 - 2*k**5 + 19*k**4 + 6*k**5 + 8 + 19*k**4 + 64*k**2 + 36*k.
4*(k + 1)**4*(k + 2)
Let r(p) be the first derivative of -2*p + 2 + 0*p**3 - 1/7*p**2 + 1/42*p**4. Let j(n) be the first derivative of r(n). Solve j(g) = 0 for g.
-1, 1
Let a(w) be the second derivative of -w**5/40 + w**4/12 + w**3/12 - w**2/2 - 17*w. Determine b, given that a(b) = 0.
-1, 1, 2
Let b(g) = -g**3 + g**2 - g. Let q(m) = -4*m**3 - 2*m**2 + 4. Let h(i) = -2*b(i) + q(i). Solve h(k) = 0.
-2, -1, 1
Let z(a) = a**2 + 10*a - 11. Let h be z(-11). Factor -6/5*n**3 + h + 2/5*n**2 - 2/5*n**5 + 6/5*n**4 + 0*n.
-2*n**2*(n - 1)**3/5
Let j be (-3 + (-10)/(-4))/((-2)/8). Let r = -1 + 8/3. Solve r*h**j + 2 - 17/3*h = 0.
2/5, 3
Let r(s) be the third derivative of -2/9*s**3 + 3*s**2 - 2/15*s**5 + 0*s + 1/36*s**6 + 0 + 1/4*s**4. Determine d, given that r(d) = 0.
2/5, 1
Let k be (-88)/(-42) - (2 + (-22)/14). Factor -k*a**3 + 5/3*a - a**2 - 1/3 + 4/3*a**4.
(a - 1)**2*(a + 1)*(4*a - 1)/3
Let o(q) be the first derivative of 1/14*q**4 - 1 + 0*q + 0*q**2 + 0*q**3. Factor o(a).
2*a**3/7
Suppose 4*d - 3*d = 0. Let k(w) be the second derivative of 0*w**2 + 1/25*w**5 - 1/15*w**3 + d + 0*w**6 + 0*w**4 + 2*w - 1/105*w**7. Factor k(z).
-2*z*(z - 1)**2*(z + 1)**2/5
Let f(h) be the third derivative of -h**5/3 + 2*h**4/3 + 2*h**3/3 + 6*h**2. Find j, given that f(j) = 0.
-1/5, 1
Let l(v) be the first derivative of -v**4/16 - v**3/12 + v**2/8 + v/4 - 11. Factor l(b).
-(b - 1)*(b + 1)**2/4
Factor -8/3*b - 4/3*b**3 - 14/3*b**2 + 2/3*b**4 + 0.
2*b*(b - 4)*(b + 1)**2/3
Let a(j) be the second derivative of -j**4/108 - j**3/27 + j**2/6 - 7*j. Factor a(c).
-(c - 1)*(c + 3)/9
Let g(b) be the first derivative of b**6/1260 + b**5/105 + b**4/28 - 3*b**3 - 5. Let o(h) be the third derivative of g(h). Factor o(q).
2*(q + 1)*(q + 3)/7
Let g = 1108 - 12186/11. Determine j so that 6/11*j**3 - 4/11*j**2 - g*j + 0 = 0.
-1/3, 0, 1
Let y(h) be the first derivative of 0*h**5 + 0*h + 0*h**2 - 1/1260*h**6 - 2 + 0*h**4 + 2/3*h**3. Let q(o) be the third derivative of y(o). Factor q(g).
-2*g**2/7
Let d = 4 + -2. Suppose -8*k**2 - 18*k**d + 4*k + 4*k**2 = 0. Calculate k.
0, 2/11
Let x(h) be the third derivative of 7*h**8/192 + h**7/5 + 137*h**6/480 - 13*h**5/120 - 3*h**4/8 + h**3/3 - 21*h**2. Find s such that x(s) = 0.
-2, -1, 2/7
Let m(d) be the first derivative of -d**6/4 - d**5/2 + d**4/4 + d**3 + d**2/4 - d/2 - 5. Determine b so that m(b) = 0.
-1, 1/3, 1
Factor 4*t**5 - 152 - 4*t**3 + 152.
4*t**3*(t - 1)*(t + 1)
Let d = -91138521/350 - -260396. Let y = d + 3/50. Determine j, given that 0 + 2/7*j**4 + 2/7*j - y*j**3 - 2/7*j**2 = 0.
-1, 0, 1
Let o be -3*(-3)/3 - 1. Let n be o - (-3 - -6) - -3. Suppose -8/7*k + 2/7*k**n + 8/7 = 0. What is k?
2
Factor n + 1/6*n**2 + 5/6.
(n + 1)*(n + 5)/6
Let s be 465/(-20)*(-1)/3. Let g = s + -89/12. Determine x so that 1/3 + g*x**3 + x**2 + x = 0.
-1
Let p(r) be the second derivative of -484/3*r**4 - 16/3*r**2 + 0 + 352/9*r**3 - 4*r + 5324/15*r**5 - 14641/45*r**6. Factor p(z).
-2*(11*z - 2)**4/3
Suppose -13*j = -7*j - 12. Factor 0 - 3*y**3 - 1/2*y - 1/2*y**5 + 2*y**4 + 2*y**j.
-y*(y - 1)**4/2
Suppose -13 = -2*c - 4*r + 13, -25 = -5*r. Suppose -5*b**5 - b**5 + c*b**5 + b**5 + 4*b**4 - 2*b**3 = 0. What is b?
0, 1
Let r = -71 - -73. Determine i, given that -3/4 - 9/4*i**r + 3/4*i**3 + 9/4*i = 0.
1
Let a be 5/(-2)*(2 + -4). Let s = a - 2. Find q such that 2*q**s - 4/3*q**4 - 4/3*q**2 + 0 + 1/3*q + 1/3*q**5 = 0.
0, 1
Determine a so that 4/15*a**2 - 2/5*a**4 + 0 + 0*a + 2/5*a**3 - 4/15*a**5 = 0.
-2, -1/2, 0, 1
Let s(m) = 3*m**5 - 13*m**4 + 2*m**3 + 2*m**2 - 5*m + 3. Let d(o) = 15*o**5 - 66*o**4 + 9*o**3 + 9*o**2 - 24*o + 15. Let y(k) = -4*d(k) + 21*s(k). Factor y(i).
3*(i - 1)**4*(i + 1)
Let 3/4 + 2*t**4 - 21/4*t**2 - 2*t + 9/2*t**3 = 0. Calculate t.
-3, -1/2, 1/4, 1
Let a be (-4)/(-6) - (-5)/(-30). Factor a*p + 1/2*p**2 + 0.
p*(p + 1)/2
Let r(l) be the first derivative of l**5 - 5*l**4/2 - 20*l**3/3 + 5*l**2 + 15*l + 25. Factor r(c).
5*(c - 3)*(c - 1)*(c + 1)**2
Let 3/2*t**2 + 3*t + 0 = 0. What is t?
-2, 0
Let j(t) = -3*t**4 - 11*t**3 - 8*t**2 - 2. Let q(l) = -9*l**4 - 34*l**3 - 25*l**2 - 7. Let x(n) = -7*j(n) + 2*q(n). Factor x(f).
3*f**2*(f + 1)*(f + 2)
Let p(l) be the second derivative of l**6/120 - l**5/10 + l**4/2 + 5*l**3/6 + 3*l. Let o(g) be the second derivative of p(g). Solve o(u) = 0 for u.
2
Let j(l) be the first derivative of -7*l**6/360 - l**5/90 - l**2/2 + 3. Let m(s) be the second derivative of j(s). Factor m(h).
-h**2*(7*h + 2)/3
Determine g, given that -5*g**3 - 35*g**3 + 7*g**4 + 28*g**4 - 2 - 10*g**5 - 3 + 10*g + 10*g**2 = 0.
-1/2, 1
Suppose -21 = -d - 6*d. Let j(p) be the second derivative of -1/10*p**6 + 0 - 1/12*p**4 - 2*p + 0*p**2 + 0*p**d - 1/5*p**5. Determine l so that j(l) = 0.
-1, -1/3, 0
Let k(p) = p**2 - 6 + 11*p + 3 - 6 - 1. Let s be k(-12). Suppose s*q**2 - 2/3*q**3 - 2*q + 2/3 = 0. Calculate q.
1
Factor 0*t**3 - 3*t**4 