- 1/5*n**v - 23/15*n**4 + 4/5*n**3. Factor t(u).
-2*(u - 1)**2*(5*u - 1)**2/5
Let t(s) be the third derivative of -s**6/60 - s**5/15 - 4*s**2. Find y such that t(y) = 0.
-2, 0
Suppose -2*h + 2 = 0, -5*b + h + 4*h + 10 = 0. Let v(s) be the third derivative of 1/60*s**5 + 1/3*s**b + 0 - 2*s**2 + 1/8*s**4 + 0*s. Factor v(t).
(t + 1)*(t + 2)
Let w(o) = o**3 - 10*o**2 + 17*o - 8. Let b be w(8). Let v(u) be the third derivative of 0 + 1/150*u**5 + u**2 - 1/15*u**4 + b*u + 4/15*u**3. Solve v(a) = 0.
2
Determine v so that 3*v**2 + 8*v + v - 6*v**2 - 6 = 0.
1, 2
Let p(s) = -s**3 + 8*s**2 - 8*s + 9. Let d be p(7). Factor -6*m - 2 - 9*m**2 + 9*m**d + 2*m**2 + 6.
2*(m - 2)*(m - 1)
Let c(d) be the first derivative of -d**4/21 + 2*d**3/21 + d - 3. Let h(i) be the first derivative of c(i). Factor h(u).
-4*u*(u - 1)/7
Let d(k) be the second derivative of k**4/102 - 4*k**2/17 - 11*k. Factor d(w).
2*(w - 2)*(w + 2)/17
What is y in -16*y + 2*y**3 - 7*y**2 - 3 + y**3 + 25*y - 2*y**2 = 0?
1
Let t**5 + 292*t**4 - 142*t**4 + 36*t - 148*t**4 - 11*t**3 - 12*t**2 = 0. What is t?
-3, 0, 2
Let j = 125/1356 - 1/113. Let t(r) be the first derivative of 0*r - 3 + 0*r**2 + 2/9*r**3 - 1/15*r**5 - j*r**4. What is u in t(u) = 0?
-2, 0, 1
Suppose 3*v - i = -2*i - 18, 4*i = 0. Let b be 9/v*(-8)/18. Let -2/3*c + 0 + b*c**2 = 0. Calculate c.
0, 1
Let c be ((-99)/(-44))/(1/(-8)). Let o be ((-1)/(-6))/((-6)/c). Factor -1/2*f - 1/2*f**2 + 1/2*f**3 + o.
(f - 1)**2*(f + 1)/2
Suppose 0 = 11*g - 6*g. Suppose -b + 0*b = g. Factor 1/3*z**3 + 0 + b*z**2 + 0*z.
z**3/3
Let a(r) be the first derivative of -r**5/20 + r**4/3 - 2*r**3/3 + 2*r + 3. Let b(t) be the first derivative of a(t). Factor b(l).
-l*(l - 2)**2
Factor 0*q**4 + 0*q + 0 + 0*q**3 - 1/4*q**5 + 0*q**2.
-q**5/4
Let f(b) be the third derivative of -1/36*b**6 + 0*b**3 + 2*b**2 + 0 + 0*b - 1/90*b**5 + 0*b**4 - 4/315*b**7. Factor f(m).
-2*m**2*(m + 1)*(4*m + 1)/3
Let b(g) = g**2 + g. Let p be b(1). Factor 0 + 1/8*x**4 + 3/8*x**3 + 1/4*x**p + 0*x.
x**2*(x + 1)*(x + 2)/8
Let f(m) be the third derivative of -m**6/120 - m**4/24 - 3*m**2. Let b(z) = -2*z**2. Let q(y) = b(y) - f(y). Factor q(j).
j*(j - 1)**2
Suppose -9*m = -11*m + 6. Factor 4*j**m - 4*j**3 - j - j + j**2 + 3*j**3.
j*(j + 1)*(3*j - 2)
Let p(h) = -h**2 - 8*h + 2. Suppose 0*f = 5*f + 40. Let k be p(f). Solve -10*n**2 + 4*n + 2*n**2 - k*n = 0 for n.
0, 1/4
Factor 9 + 1/4*x**2 + 3*x.
(x + 6)**2/4
Let l(k) be the third derivative of -1/72*k**4 - 1/180*k**5 + 0 + 0*k**3 - k**2 + 0*k. Factor l(a).
-a*(a + 1)/3
Let q(u) be the second derivative of u**8/20160 + u**4/3 - u. Let t(j) be the third derivative of q(j). Factor t(s).
s**3/3
Let b(k) be the third derivative of k**8/588 - 2*k**7/245 + k**6/105 + 25*k**2. What is c in b(c) = 0?
0, 1, 2
Let z(m) = 8*m**3 - 6*m**2 + 8*m - 5. Let a(k) = -33*k**3 + 24*k**2 - 33*k + 21. Let r = 38 + -57. Let l = 2 - r. Let n(i) = l*z(i) + 5*a(i). Factor n(t).
3*t*(t - 1)**2
Let q be 0 - (-2 + 2 + -2). Suppose 3*p**3 - 4*p**2 + q*p - 6*p**3 + 5*p**3 = 0. Calculate p.
0, 1
Let s = 417/70 - 51/10. Factor 2/7*c + 6/7*c**3 + 0 + s*c**2 + 2/7*c**4.
2*c*(c + 1)**3/7
Let m(z) be the first derivative of -z**5/5 + 3*z**4/2 - 13*z**3/3 + 6*z**2 - 4*z - 4. Factor m(o).
-(o - 2)**2*(o - 1)**2
Let m(o) be the third derivative of o**7/2100 - o**6/900 - o**5/300 + o**4/60 - o**3/6 + 2*o**2. Let t(i) be the first derivative of m(i). Factor t(u).
2*(u - 1)**2*(u + 1)/5
Let b(x) = -x**3 + 11*x**2 + x - 8. Let v be b(11). Suppose -11 = -v*h + 4. Find w, given that -16*w**4 - 4*w**h + 12*w**3 + 10*w**5 - 5*w + 3*w = 0.
-1/3, 0, 1
Let k(h) = h**3 + 4*h**2 + 2*h - 1. Let u be k(-3). Suppose 5*a - 1 - 5*a + 4 - 3*a**u = 0. Calculate a.
-1, 1
Determine s, given that -3/2*s + 0 + 1/2*s**2 = 0.
0, 3
Let h be (12/(-9))/((-4)/9). Suppose b + 4*t - 20 = -3*b, 0 = h*t - 6. Factor -2/3*z**4 + 0 - 2/3*z - 1/3*z**b + 5/3*z**2.
-z*(z - 1)*(z + 2)*(2*z - 1)/3
Let x(f) be the third derivative of -f**8/168 - f**7/35 + f**6/60 + 7*f**5/30 - 4*f**3/3 + 8*f**2. Solve x(q) = 0.
-2, -1, 1
Let k = 1423/7 - 203. Find u, given that k + 0*u**2 - 4/7*u**3 + 4/7*u - 2/7*u**4 = 0.
-1, 1
Let p(f) = -2*f**2 - 2. Let o(z) = 3*z**2 - z + 3. Let h(n) = 4*o(n) + 7*p(n). Factor h(l).
-2*(l + 1)**2
Let d = 3/16 + -1/48. Let v(i) be the second derivative of 0*i**3 + 0*i**2 + 0 + d*i**4 - 3*i. Factor v(p).
2*p**2
Solve 0*l + 14/5*l**4 + 24/5*l**5 - 14/5*l**3 + 0 - 4/5*l**2 = 0.
-1, -1/4, 0, 2/3
Let r be (1 + 3)/(0 + 2). Let v = 10 - 5. Determine z, given that z - z**r + 6*z**3 + z + 3*z**4 - v*z**4 - 5*z**2 = 0.
0, 1
Let 2/13*p**2 - 16/13*p + 0 = 0. Calculate p.
0, 8
Let a(w) be the first derivative of -2*w**6/21 + 4*w**5/7 - 2*w**4/7 - 8*w**3/3 + 6*w**2/7 + 36*w/7 - 20. Let a(h) = 0. What is h?
-1, 1, 3
Let u(w) = -2*w**2 + w. Let v(y) = 11*y**2 - 16*y + 4. Let n(q) = 40*u(q) + 5*v(q). Find c such that n(c) = 0.
-2, 2/5
Factor 6*a**3 + 48*a + 72 - 16*a**2 + 0*a - 4*a**3 - 6*a**2.
2*(a - 6)**2*(a + 1)
Let o be ((-27)/36)/((-3)/8). Let 2*d - 4/3 - 2/3*d**o = 0. What is d?
1, 2
Let u = 7 + -5. Let h(n) = n**4 + 3*n**3 + 4*n**2 - 2*n. Let f(x) = 2*x**3 + 5*x**2 - 3*x. Let a(t) = u*f(t) - 3*h(t). What is j in a(j) = 0?
-1, -2/3, 0
Factor -4/9 - 2/9*s + 2/9*s**2.
2*(s - 2)*(s + 1)/9
Factor -3/7*d + 6/7 - 6/7*d**2 + 3/7*d**3.
3*(d - 2)*(d - 1)*(d + 1)/7
Let s(c) be the third derivative of -1/105*c**7 - 4/15*c**5 - 1/12*c**6 + 0*c**3 + 0*c - 1/3*c**4 - 8*c**2 + 0. Solve s(x) = 0 for x.
-2, -1, 0
Let h(f) be the third derivative of 1/108*f**4 + 0*f + 0 - 1/270*f**5 + 0*f**3 + f**2. Factor h(y).
-2*y*(y - 1)/9
Let i(a) = -2*a - a**2 + 2*a**2 + 2 - 2. Let c be i(-2). Solve 0*y**3 - 6*y**5 - 2*y**3 + c*y**5 = 0 for y.
-1, 0, 1
Let q(z) be the second derivative of z**6/120 + z**5/120 + z**3/6 - z. Let u(l) be the second derivative of q(l). Factor u(v).
v*(3*v + 1)
Let -4*c**3 + 3*c + 3*c**3 - 2*c**2 - 2*c**3 + 5*c**2 - 3*c**4 = 0. Calculate c.
-1, 0, 1
Let z = -168 - -673/4. Factor -1/4*n**3 + z*n + 1/2*n**2 - 1/2.
-(n - 2)*(n - 1)*(n + 1)/4
Factor -6/5*d**2 - 6/5 + 1/5*d**3 + 11/5*d.
(d - 3)*(d - 2)*(d - 1)/5
Let r(s) = 2*s + s**2 - 5*s**2 + 5*s**2. Let z be r(-3). Factor -1/3*v**4 - 1/3*v**5 + 1/3*v**z + 0*v + 0 + 1/3*v**2.
-v**2*(v - 1)*(v + 1)**2/3
Let s(f) be the first derivative of 0*f + 0*f**2 + 2/45*f**5 - 1/18*f**4 - 4 + 1/27*f**6 - 2/27*f**3. Let s(b) = 0. Calculate b.
-1, 0, 1
Let m(p) be the second derivative of -p**4/54 - p**3/27 + 2*p**2/9 + 6*p. Find l such that m(l) = 0.
-2, 1
Let n(d) = -7*d**4 + 3*d**3 - 3*d**2 - 7*d. Let k(l) = 6*l**4 - 2*l**3 + 3*l**2 + 6*l. Let x(b) = -6*k(b) - 5*n(b). Determine p, given that x(p) = 0.
-1, 0
Let o be (-66)/(-14) + 4/14. Let q be 1*(-1 - (-7 + -1)). Factor 2*k - q*k**3 + k**3 - k**3 - o*k**2.
-k*(k + 1)*(7*k - 2)
Suppose 0 = -2*s + 1202 + 84. Let a = s - 1913/3. Solve 32/3*d**4 + 2/3*d + a*d**2 + 0 + 40/3*d**3 = 0.
-1/2, -1/4, 0
Let x(d) be the second derivative of d**7/24 + d**6/60 - 21*d**5/80 + d**4/6 + d**3/6 - 29*d. What is t in x(t) = 0?
-2, -2/7, 0, 1
Let a(r) = -r**2 - 22*r + 48. Let h be a(-24). Let u(l) be the second derivative of h - 1/20*l**5 + 1/6*l**3 + 1/4*l**2 - l + 0*l**4 - 1/60*l**6. Factor u(d).
-(d - 1)*(d + 1)**3/2
Suppose 2/3*f**4 - 1/3*f**5 + 0 + 1/3*f**3 + 0*f - 2/3*f**2 = 0. What is f?
-1, 0, 1, 2
Factor 6*u + 6 + 12 + u**3 - 10*u**2 + u**3.
2*(u - 3)**2*(u + 1)
Let o(b) be the third derivative of -b**7/1155 - b**6/330 + 4*b**2. Let o(m) = 0. What is m?
-2, 0
Suppose 5*l = 28 - 8. Solve t**l - 2*t + 3*t - 10*t**3 + 2*t**2 + t + 5*t**4 = 0 for t.
-1/3, 0, 1
Let c(j) be the second derivative of 3*j**5/100 + 3*j**4/20 + j**3/5 + 15*j. Factor c(p).
3*p*(p + 1)*(p + 2)/5
Let n(i) be the second derivative of 0*i**2 + 4*i - 1/72*i**4 + 1/180*i**6 + 1/36*i**3 - 1/120*i**5 + 0. Factor n(b).
b*(b - 1)**2*(b + 1)/6
Let y = 0 - -7. Let k be -2 + (2 - (-2)/y). Solve 0*z**3 + 2/7*z**2 - k*z**4 + 0 + 0*z = 0 for z.
-1, 0, 1
Let j(m) = m**5 + m**4 - 3*m**3 - 2*m**2 + m + 1. Let z(g) = -g**3. Let u(p) = -3*j(p) + 3*z(p). Determine r so that u(r) = 0.
-1, 1
Let n be 6 - -1*12/(-3). Suppose -5*u + 21 = n*u. Solve 2/3*k + 0 + 0*k**2 - 2/3*k**u = 0.
-1, 0, 1
Let x(q) = 175*q**2 + 990*q - 550. Let f(y) = -8*y**2 - 45*y + 25. Let v(t) = -45*f(t) - 2*x(t). Solve