Factor -4*z**r - 1 - 3*z**i + z - z**4 + 2*z**3 + 4*z**2 + z**5 + z**2.
(z - 1)**3*(z + 1)**2
Let m(y) be the first derivative of -3/2*y**2 - 2 + 0*y - 2*y**3 + 6/5*y**5 + 0*y**4 + 1/2*y**6. Find a such that m(a) = 0.
-1, 0, 1
Let i = -1 + 5. Factor -5*f**2 + i*f**3 - 5*f**3 + 4*f**2.
-f**2*(f + 1)
Let j(f) be the third derivative of f**5/60 + f**4/24 - f**3/3 - 15*f**2. Suppose j(n) = 0. Calculate n.
-2, 1
Let y(a) be the second derivative of a**7/140 - a**6/20 + a**5/10 + 4*a**2 - 8*a. Let p(o) be the first derivative of y(o). Find h such that p(h) = 0.
0, 2
Let y(c) be the first derivative of c**4/4 + c**3/3 - 2*c**2 + 2*c - 3. Let h(q) = -7*q**3 - 5*q**2 + 25*q - 13. Let x(m) = 6*h(m) + 39*y(m). Factor x(z).
-3*z*(z - 2)*(z - 1)
Let t = 1 + 1. Solve -1 - t*x**2 + 0 - 6*x - 1 + 2*x = 0.
-1
Let s be 4*(-3 - (-20)/8). Let i(t) = -t**3 - 5*t - 3. Let n(y) = y**3 + y**2 + 4*y + 2. Let k(q) = s*i(q) - 3*n(q). Suppose k(p) = 0. Calculate p.
-2, -1, 0
Let d(r) be the second derivative of 5*r**4/84 - r**3/21 + 3*r. Factor d(f).
f*(5*f - 2)/7
Suppose -9 = -5*g + 6. Let c = g - 1. Suppose -3*t**2 + t**c - t - t**4 - t**2 - 3*t**3 = 0. Calculate t.
-1, 0
Let h(b) be the second derivative of 0*b**2 + 0 - 1/12*b**3 - 5*b - 1/24*b**4. Factor h(f).
-f*(f + 1)/2
Let l = 21 + -20. Let n(x) be the first derivative of -1/9*x**3 - 1/3*x + 1/3*x**2 - l. What is p in n(p) = 0?
1
Factor -38*f**2 + 0 - 2 - 4*f + 37*f**2 + 7*f.
-(f - 2)*(f - 1)
Factor -3*n**2 - 3*n + 4*n**4 + 0*n - n**4 + n**5 + n**3 + n.
n*(n - 1)*(n + 1)**2*(n + 2)
Let o(z) be the first derivative of -z**6/135 - z**5/90 - 9*z + 3. Let g(v) be the first derivative of o(v). Solve g(s) = 0 for s.
-1, 0
Let a(t) be the third derivative of -t**6/540 - t**5/60 - t**4/18 + 5*t**3/3 + 10*t**2. Let n(g) be the first derivative of a(g). Find i, given that n(i) = 0.
-2, -1
Let o = 125 + -371/3. Factor 0 + o*p - 2/3*p**3 + 2/3*p**2.
-2*p*(p - 2)*(p + 1)/3
Suppose 4 = 4*u - 28. Let p be (-64)/(-10) - u/20. Suppose -a**3 + 0 - 5*a + p*a**3 + 2 - 2*a**2 = 0. Calculate a.
-1, 2/5, 1
Let u(s) be the first derivative of s**7/3360 - s**6/360 + s**5/96 - s**4/48 + s**3 + 6. Let m(n) be the third derivative of u(n). Solve m(l) = 0.
1, 2
Suppose 3*r - 5 = -2*n, -4*r - 1 = 4*n - 5. Factor 1 - r*p**2 + 0 + 2*p**2 + 0.
-(p - 1)*(p + 1)
Let s(o) be the first derivative of -4 + 0*o**3 + 1/3*o**5 + 0*o - 1/6*o**4 + 0*o**2. Factor s(i).
i**3*(5*i - 2)/3
Let v(x) = -x**2 + 8*x + 4. Let k be v(8). Let 2*f**3 + 14*f**2 + 2*f**4 - k*f + 2*f**3 - 16*f**4 = 0. Calculate f.
-1, 0, 2/7, 1
Let j = -14507/36 + 403. Let u(y) be the third derivative of 0*y + 1/18*y**3 + 1/180*y**5 + j*y**4 - 2*y**2 + 0. Find t, given that u(t) = 0.
-1
Suppose 2 = 3*u - 0*b + 4*b, 5*u - b - 11 = 0. Suppose u*d + 3*a = -6, -10 = -d + 5*a - 0*a. Solve d - l**2 - 2/3*l - 1/3*l**3 = 0.
-2, -1, 0
Suppose 0*f - 5 = -f. Factor -4*l**4 - 2 - 4*l**3 + 4 + 6*l**2 + 3*l**f + l - 4.
(l - 1)**3*(l + 1)*(3*l + 2)
Suppose -2*m = m - 15, 0 = 3*r + 2*m - 31. Let x(t) = -t**2 + 6*t - 3. Let j be x(4). Solve -5*h**j + h**2 - r*h**2 - 3*h + 6*h**4 + 8*h**5 = 0 for h.
-1, 0, 1
Let j = -34 - -4081/120. Let g(o) be the third derivative of 0 + 4*o**2 + 2/75*o**5 - 1/15*o**3 - j*o**4 - 1/120*o**6 + 0*o. Factor g(f).
-(f - 1)**2*(5*f + 2)/5
Find g, given that 0*g**2 - 18/11*g + 6/11*g**3 - 12/11 = 0.
-1, 2
Let d(p) be the second derivative of p**5/20 + p**4/42 + 10*p. Factor d(o).
o**2*(7*o + 2)/7
Suppose -5*g = -0*g + 5. Let j be 2 - (1 - (2 + g)). Factor 3*c + c**2 + c**j - c.
2*c*(c + 1)
Let o(b) be the first derivative of -b**4/6 + 10*b**3/3 - 25*b**2 + 250*b/3 - 5. Factor o(k).
-2*(k - 5)**3/3
Let k(t) be the third derivative of t**5/60 + 3*t**4/8 + 5*t**3/6 + t**2. Let q be k(-9). Factor d**4 + 6*d**3 + 5*d**2 - d**2 + d + d**q + 3*d**4.
d*(d + 1)**4
Let w(l) be the second derivative of -l**6/105 - l**5/35 - 3*l. Factor w(n).
-2*n**3*(n + 2)/7
Let y be 2*((-4)/2 - (-18)/4). Determine h so that -2/3*h - 8/3*h**y + 10/3*h**3 + 0 + 2*h**4 - 2*h**2 = 0.
-1, -1/4, 0, 1
Let k(i) be the third derivative of -1/30*i**3 + 3*i**2 + 0 + 1/60*i**4 + 0*i - 1/300*i**5. Find b, given that k(b) = 0.
1
Let m be (-20)/(-30)*(-16)/(-30). Let y = -1/45 + m. Factor 0*v**3 - 1/6*v**5 - y*v**4 + 1/3*v**2 + 0 + 1/6*v.
-v*(v - 1)*(v + 1)**3/6
Let a = -8 + 15. Suppose a*n - 19 = 3*g + 2*n, -25 = -5*n. Find z such that -1/5*z**g + 3/5*z - 2/5 = 0.
1, 2
Let w(b) be the second derivative of 0*b**2 - b + 0*b**6 - 1/189*b**7 + 1/45*b**5 - 1/27*b**3 + 0 + 0*b**4. Determine g so that w(g) = 0.
-1, 0, 1
Suppose 81/4*a**2 + 3 + 18*a - 3/2*a**3 - 27/4*a**4 = 0. Calculate a.
-1, -2/9, 2
Let r(k) = 8*k**2 + 8*k. Let c(z) = -z**2 - z. Let p(b) = 51*c(b) + 6*r(b). Factor p(o).
-3*o*(o + 1)
Factor -8/9 + 8/9*c - 2/9*c**3 + 2/9*c**2.
-2*(c - 2)*(c - 1)*(c + 2)/9
Let j(c) be the first derivative of -1/15*c**3 - 2 + 1/10*c**2 + 2/5*c. What is r in j(r) = 0?
-1, 2
Let u(h) be the second derivative of 1/4*h**4 + 0 - 1/40*h**5 - 1/120*h**6 + 1/3*h**3 + h + 0*h**2. Let i(r) be the second derivative of u(r). Factor i(l).
-3*(l - 1)*(l + 2)
Solve 0 - 9*q**5 + 3/4*q**2 + 3/4*q - 75/4*q**4 - 39/4*q**3 = 0 for q.
-1, -1/3, 0, 1/4
Let x = 17 - 14. Let z(f) be the first derivative of 0*f**2 - 7/12*f**4 + 0*f - 1 + 2/9*f**x. Let z(w) = 0. What is w?
0, 2/7
Factor -1/4*w**2 + 0 + 3/4*w.
-w*(w - 3)/4
Let g = 107 + -103. Factor 5/4*o**g - 9/4*o**3 - 1/4*o**5 + 7/4*o**2 - 1/2*o + 0.
-o*(o - 2)*(o - 1)**3/4
Let b(s) be the first derivative of -2*s**5/45 - s**4/18 + 2*s**3/9 + s**2/9 - 4*s/9 + 8. Find n, given that b(n) = 0.
-2, -1, 1
Factor 8/5*z**2 - 12/5 + 16/5*z**3 + 4/5*z**4 - 16/5*z.
4*(z - 1)*(z + 1)**2*(z + 3)/5
Let k be (1/(-18))/((-4)/3). Let u(t) be the second derivative of -1/20*t**6 + k*t**4 + 0*t**5 + 1/42*t**7 + 0*t**2 + 0 + 0*t**3 + 2*t. Factor u(a).
a**2*(a - 1)**2*(2*a + 1)/2
Let g(o) be the second derivative of o**7/63 - o**5/15 + o**3/9 - 3*o. Factor g(c).
2*c*(c - 1)**2*(c + 1)**2/3
Let m(i) be the third derivative of 3*i**8/2240 - i**7/840 - i**4/24 - 3*i**2. Let y(x) be the second derivative of m(x). Find k, given that y(k) = 0.
0, 1/3
Let o = 9 - 5. Suppose -3*c**o - 6*c**3 - 6*c**2 - 3/5*c**5 - 3*c - 3/5 = 0. Calculate c.
-1
Let s(a) be the second derivative of a**5/8 - 5*a**4/12 - 5*a**3/3 + 10*a**2 + 50*a. Factor s(i).
5*(i - 2)**2*(i + 2)/2
Factor n**3 + 1/2*n**4 + 0*n**2 + 0 + 0*n.
n**3*(n + 2)/2
Let o(j) be the first derivative of -j**5/5 + j**4 - 2*j**3 + 2*j**2 - j + 7. Determine l, given that o(l) = 0.
1
Let v(j) = j - 8. Let z be v(10). Find w, given that 6*w**2 - 5*w**3 - w**3 + 0*w - w + z*w**4 - w = 0.
0, 1
Suppose -3*d - 2*h = -22, d - 4*h - 28 = -2*d. Determine w so that 5*w - 2*w**2 - w - d*w**2 = 0.
0, 2/5
Let w(k) = -17*k**3 + 29*k**2 - 13*k - 4. Let r(p) = -8*p**3 + 15*p**2 - 7*p - 2. Let h(y) = -10*r(y) + 4*w(y). Factor h(i).
2*(i - 2)*(i - 1)*(6*i + 1)
Let u(m) be the first derivative of -2*m**3/15 + 4*m**2/5 - 6*m/5 + 4. Factor u(j).
-2*(j - 3)*(j - 1)/5
Let b(j) be the third derivative of -j**7/210 + j**6/30 - j**5/10 + j**4/6 - j**3/6 + 10*j**2. Suppose b(o) = 0. What is o?
1
Let h be 1/6 - (-25)/300. Factor h*y + 0 + 1/4*y**2.
y*(y + 1)/4
Let k = -51 - -21. Let r be k/(-7) - 2/7. Solve -8/7*j**3 + 6/7*j**2 + 8/7*j + 2/7*j**r - 8/7 = 0.
-1, 1, 2
Suppose -6*b**4 + 3*b**5 - 67*b + 67*b = 0. What is b?
0, 2
Let m(d) = -d**3 - 3*d**2 - 2*d - 3. Let h(r) = -3*r**3 - 8*r**2 - 5*r - 8. Let t(s) = 3*h(s) - 8*m(s). Factor t(n).
-n*(n - 1)*(n + 1)
Let r be -2 + (3 - 26/10)*15. What is i in -9/5*i**r + 6/5*i**3 - 6/5*i + 9/5*i**2 + 0 = 0?
-1, 0, 2/3, 1
Suppose -4*t + 18 = 5*h, 2 = h + 5*t - 10. Let 28*f**h + 1 - 1 + f + f**3 - 30*f**2 = 0. Calculate f.
0, 1
Factor -2*b**5 + 4*b + 8*b**4 - 4*b**4 + 0*b**4 - 2*b - 4*b**2.
-2*b*(b - 1)**3*(b + 1)
Factor -67 - 1584*h**3 - 136*h**4 + 147 - 56*h**4 - 53 - 321*h + 1260*h**2.
-3*(h + 9)*(4*h - 1)**3
Let q(a) be the second derivative of 1/13*a**3 + 0 + a - 2/13*a**2 - 1/78*a**4. Determine v, given that q(v) = 0.
1, 2
Suppose 0*w + 46 = 2*w. Let -3*s + 26*s**3 - w*s**3 - 2 + 5 - 3*s**2 = 0. Calculate s.
-1, 1
Let o(p) be the third derivative of p**8/588 + 2*p**7/735 - p**6/210 - p**5/105 - 21*p**2. Let o(r) = 0. Calculate r.
-1, 0, 1
Let u(t) = -2*t**3 +