*h**3*(3*h - 1)*(3*h + 2)
Let g(n) be the first derivative of 1/3*n + n**3 + n**2 + 1/3*n**4 + 4. Factor g(p).
(p + 1)**2*(4*p + 1)/3
Let f(y) = y**2 + 19*y + 20. Let c be f(-18). Solve 0*n + 1/4*n**c + 0 = 0.
0
Let k = -401/30 + 67/5. Let m(f) be the third derivative of 0*f**3 + 0 - 1/24*f**4 + 1/40*f**6 + f**2 - k*f**5 + 0*f. Find s such that m(s) = 0.
-1/3, 0, 1
Let k(w) = w**2 + 7*w - 5. Let p be k(-8). Factor 0*y**2 - p*y + 2*y**2 - y**2 + y - 3.
(y - 3)*(y + 1)
Suppose 44 = 29*q - 18*q. Find t such that 4*t**3 - 9/2 - 1/2*t**q + 12*t - 11*t**2 = 0.
1, 3
Let g(k) be the second derivative of k**6/90 - k**4/18 + k**2/6 - 7*k. What is r in g(r) = 0?
-1, 1
Let y(l) = -l**2 + 3*l - 3. Let g be y(3). Let p be ((-3 - g)/2)/1. Factor p*q + 1/3 - 2/3*q**2 + 0*q**3 + 1/3*q**4.
(q - 1)**2*(q + 1)**2/3
Let p(u) be the first derivative of 0*u**5 - 2*u**4 + 1/3*u**6 + 4*u + 3*u**2 + 2 - 4/3*u**3. Determine c, given that p(c) = 0.
-1, 1, 2
Let o(t) = 5*t**3 - 2*t + 1. Let d be o(1). Let n be d*(1 - (-1)/(-2)). Factor 2/3 - 7/3*y - 3*y**n.
-(y + 1)*(9*y - 2)/3
Let o(y) be the second derivative of y**4/15 - y**3/3 + 2*y**2/5 - 5*y. Factor o(r).
2*(r - 2)*(2*r - 1)/5
Suppose -4*x + 6 = -6. Suppose -2*f**3 + 3 - 3*f**2 + 12*f**2 + 7*f**3 + 10*f**x - 15*f - 12*f**4 = 0. Calculate f.
-1, 1/4, 1
Let d(m) be the second derivative of -m**7/735 + m**5/105 - m**3/21 + m**2/2 + m. Let k(v) be the first derivative of d(v). Factor k(z).
-2*(z - 1)**2*(z + 1)**2/7
Let t(p) be the second derivative of -7*p**6/15 - 5*p**5/3 - 11*p**4/6 + 4*p**2/3 + 5*p. Suppose t(y) = 0. Calculate y.
-1, -2/3, 2/7
Let j(b) = b + 3. Let v be j(-1). Let 2*p**v + 1/2*p + 2*p**4 + 1/2*p**5 + 0 + 3*p**3 = 0. What is p?
-1, 0
Let a(t) = -5*t**3 + 35*t**2 - 78*t + 48. Let w(b) = -10*b**3 + 70*b**2 - 155*b + 95. Let l(x) = 5*a(x) - 3*w(x). Factor l(p).
5*(p - 3)**2*(p - 1)
Let d(t) be the third derivative of t**2 - 1/2*t**3 + 0*t - 3/16*t**4 + 0 - 1/40*t**5. Factor d(g).
-3*(g + 1)*(g + 2)/2
Let c(o) = 4*o - 14. Let q be c(5). Let i(d) be the third derivative of 1/24*d**4 + 0*d**5 + 0 + 0*d**3 - d**2 - 1/120*d**q + 0*d. Let i(y) = 0. Calculate y.
-1, 0, 1
Let d(w) be the third derivative of -w**8/336 + w**7/210 + w**6/120 - w**5/60 - 6*w**2. Suppose d(t) = 0. Calculate t.
-1, 0, 1
Let r be ((-525)/(-20))/(2/(-8)). Let y be (-46)/r + 18/135. Find a such that -2/7 - 6/7*a + y*a**3 + 2/7*a**5 - 4/7*a**2 + 6/7*a**4 = 0.
-1, 1
Let q = 2622/5 + -524. Factor 0*o - 2/5*o**3 + 0 + q*o**2.
-2*o**2*(o - 1)/5
Let o = -18 + 21. Suppose -4 = -o*b + 2*b. Factor 1/4 + 1/4*t**b + t + 3/2*t**2 + t**3.
(t + 1)**4/4
Factor t**2 + 70*t**5 - 71*t**5 - 2 - t**4 + t**3 + 2.
-t**2*(t - 1)*(t + 1)**2
Let v(d) be the second derivative of -d**5/10 - 5*d**4/9 + 23*d**3/27 - 4*d**2/9 + 8*d. Factor v(c).
-2*(c + 4)*(3*c - 1)**2/9
Let f(y) be the first derivative of -5*y**4 - 32*y**3/3 - 2*y**2 + 8*y - 9. Determine v, given that f(v) = 0.
-1, 2/5
Let t be (70/18 - -1) + -2. Let p = -20/9 + t. Suppose -2/3*s**4 + p*s**3 + 0 - 2/3*s + 2/3*s**2 = 0. Calculate s.
-1, 0, 1
Determine h, given that 0*h + 0 + 2/3*h**5 - 1/3*h**4 + 1/3*h**2 - 2/3*h**3 = 0.
-1, 0, 1/2, 1
Factor -54*z + 145*z**2 + 30 + 142*z + 67*z + 20*z**3.
5*(z + 1)*(z + 6)*(4*z + 1)
Let f(s) = -3*s - 12. Let m be f(-4). Let l(w) be the third derivative of 3*w**2 + 0 - 1/96*w**4 + m*w**3 - 1/240*w**5 + 0*w. Factor l(n).
-n*(n + 1)/4
Let u(z) be the third derivative of -z**7/21 - 7*z**6/24 - z**5/2 + 5*z**4/24 + 5*z**3/3 - 43*z**2. What is q in u(q) = 0?
-2, -1, 1/2
Let d(h) be the third derivative of h**9/80640 - h**8/20160 - h**7/5040 - h**5/30 + 2*h**2. Let u(w) be the third derivative of d(w). Factor u(c).
c*(c - 2)*(3*c + 2)/4
Let p be 5 + -1 - (-2 + 2). Determine y so that y**3 + 2*y**2 + y**3 + y**p - y**2 = 0.
-1, 0
Let o(i) be the third derivative of 1/70*i**5 - 1/420*i**6 + 1/21*i**3 + 0 + 0*i + i**2 - 1/28*i**4. Factor o(d).
-2*(d - 1)**3/7
Let l be 21/(-6) + (3 - -1). Factor 0*d + l*d**2 - 1/2*d**5 - 1/2*d**4 + 1/2*d**3 + 0.
-d**2*(d - 1)*(d + 1)**2/2
Let n(k) = 2*k**2 + 35*k + 17. Let o be n(-17). Factor 8*q**3 + 22/3*q**2 + o + 4/3*q.
2*q*(3*q + 2)*(4*q + 1)/3
Let t(d) be the third derivative of 11/36*d**4 - 14/135*d**5 - 9*d**2 + 1/108*d**6 + 0 + 0*d + 2/3*d**3. Let t(p) = 0. What is p?
-2/5, 3
Let p(q) be the first derivative of -q**4/22 - 4*q**3/33 - 1. Factor p(z).
-2*z**2*(z + 2)/11
Let g be (-1)/4 + 455/480. Let o = g - 1/32. Factor o*t**4 - 4/9*t**2 - 2/9 + 2/3*t - 2/9*t**5 - 4/9*t**3.
-2*(t - 1)**4*(t + 1)/9
Let h(b) be the first derivative of 27*b**6/14 - 27*b**5/7 - 135*b**4/14 - 50*b**3/7 - 5*b**2/2 - 3*b/7 - 2. Determine c, given that h(c) = 0.
-1/3, 3
Let i(j) be the third derivative of 1/12*j**4 - 1/6*j**3 + 0*j + 0 + 1/20*j**5 - 3*j**2. Suppose i(r) = 0. Calculate r.
-1, 1/3
Let f(y) = -2*y**2 + 8*y + 5. Let s(o) = o**2 - o - 1. Let m(n) = f(n) + 5*s(n). What is g in m(g) = 0?
-1, 0
Let j(l) = 10*l**2. Let r be j(1). Let a be ((-4)/(-5))/(4/r). Factor -3*s**a + 4*s + 5*s**2 - s**2 + 4 + 0*s**2.
(s + 2)**2
Let b(x) be the first derivative of x**5/60 - x**4/18 + x**3/18 + 3*x + 6. Let u(d) be the first derivative of b(d). Suppose u(j) = 0. Calculate j.
0, 1
Let f(b) = b**3 - 6*b**2 + 7*b - 7. Let m be f(5). Factor -w**3 - 3*w**m + 2*w**3 - 12*w**2 - 7*w**3 - 4*w.
-w*(3*w + 2)**2
Let c be 4/2 - (0 - 0). Suppose 3*h + 1 = 7. Find d, given that -c*d + 2*d + h*d + d**2 = 0.
-2, 0
Let r(n) be the first derivative of n**6/120 + n**5/60 - 3*n**2/2 + 7. Let s(o) be the second derivative of r(o). Factor s(a).
a**2*(a + 1)
Let r be 4*(1 - (1 - 1)). Suppose 0 = -5*c + 3*k + 12, -7 = r*c + 2*k + 1. Factor c - 2/9*b**2 + 0*b.
-2*b**2/9
Let j(b) be the third derivative of -b**6/60 + b**5/30 + 7*b**2. Let j(n) = 0. What is n?
0, 1
Factor 1/5 - 2/5*i**3 - 1/5*i**2 + 2/5*i.
-(i - 1)*(i + 1)*(2*i + 1)/5
Let r(a) be the first derivative of 3*a**4/20 - 7*a**3/5 + 21*a**2/5 - 24*a/5 + 16. Solve r(x) = 0.
1, 2, 4
Let f(v) = 13*v**3 + v - 1. Let j be f(1). Suppose 2*o + 3 = j. Solve 2*k**4 - o*k**2 + 3*k**2 - 5*k + k**5 + 0*k**5 + 4*k = 0.
-1, 0, 1
Let b be 3/18*-3 + (-5)/(-4). Find y, given that 0 - 1/4*y**3 - b*y**2 - 1/2*y = 0.
-2, -1, 0
Let v(j) = 2*j**2 - 2*j - 1. Let p be v(2). Solve -x**4 - 14*x**4 - p*x**3 - 2 + 2 - 12*x**5 = 0 for x.
-1, -1/4, 0
Let u(l) be the first derivative of l**3/3 - 3*l**2/2 - 10. Factor u(g).
g*(g - 3)
Let s = 9 - 7. Factor 17*l**5 + 4*l - 8*l**5 - 6*l**s - 24*l**4 + 21*l**3 - 4*l.
3*l**2*(l - 1)**2*(3*l - 2)
Let t(a) = -a**3 - 3*a**2 + 3*a - 3. Let u be t(-5). Factor -12*w**3 + u*w - 11*w - 4 - 2 + 15*w**2.
-3*(w - 2)*(w + 1)*(4*w - 1)
Let c(l) be the first derivative of 3*l**4/16 - 9*l**3/4 + 45*l**2/8 + 75*l/4 + 19. Suppose c(h) = 0. What is h?
-1, 5
Suppose -s + 3*h - 6 = -18, 4*s + 4 = -h. Let r(t) be the second derivative of s*t**3 - 1/2*t**2 - 2*t + 1/12*t**4 + 0. Factor r(j).
(j - 1)*(j + 1)
Let s(u) = u**2 + 3*u + 3. Let p be s(-2). Let k(q) = 3*q**3 - q**2 + q - 1. Let g be k(p). Factor -t**2 - 3 + 3 + g - t**2.
-2*(t - 1)*(t + 1)
Let o(j) be the second derivative of -j**6/120 - 3*j**5/40 - 3*j**4/16 + 57*j. Factor o(t).
-t**2*(t + 3)**2/4
Let g(a) be the first derivative of -a**6/180 + a**5/10 - 3*a**4/4 - a**3 - 3. Let h(v) be the third derivative of g(v). Factor h(j).
-2*(j - 3)**2
Suppose 2 = u - 3. Factor 8*s**4 + u*s**5 - s**5 + 4*s**3 + 0*s**4.
4*s**3*(s + 1)**2
Let n(r) be the third derivative of r**7/420 - r**6/96 + r**5/60 - r**4/96 + 13*r**2. Solve n(v) = 0 for v.
0, 1/2, 1
Let u be 3/(-12) + 92/240. Let m(w) be the first derivative of -u*w**3 + 0*w - 3 - 1/5*w**2. Factor m(f).
-2*f*(f + 1)/5
Let v(a) be the first derivative of -a**2 - 1 + 1/2*a**4 + 2/3*a**3 - 2*a. Factor v(w).
2*(w - 1)*(w + 1)**2
Let t(r) be the third derivative of -r**6/144 - r**5/120 + r**4/12 - r**3/9 + 10*r**2. Factor t(o).
-(o - 1)*(o + 2)*(5*o - 2)/6
Let m(u) be the third derivative of u**6/135 - u**5/270 - u**4/27 + u**3/27 - 4*u**2. Factor m(r).
2*(r - 1)*(r + 1)*(4*r - 1)/9
Factor 4/9*s**2 - 2/9*s**4 + 0 + 0*s + 2/9*s**3.
-2*s**2*(s - 2)*(s + 1)/9
Let y(r) be the second derivative of 0*r**2 + 27/5*r**5 + 8/3*r**3 - 6*r**4 - 9/5*r**6 - 3*r + 0. Factor y(i).
-2*i*(3*i - 2)**3
Let c(l) = l**2 + 3*l. Let s(y) = 4*y**2 + 10*y - 1. 