derivative of a - 1/2*q**3 - q**2 - 1/60*q**5 + 0*q - 1/6*q**4. Determine r so that i(r) = 0.
-3, -1
Factor 0 - 2*v - 1/3*v**3 - 5/3*v**2.
-v*(v + 2)*(v + 3)/3
Let c(s) be the first derivative of s**3 + 0*s + 3/4*s**4 - 3/5*s**5 - 4 - 3/2*s**2. Suppose c(y) = 0. What is y?
-1, 0, 1
Let r(t) be the third derivative of 1/80*t**5 + 0*t**4 + 0*t + 0*t**3 + 0 + 3*t**2. Determine j so that r(j) = 0.
0
Let z(k) be the first derivative of -3*k**2/2 - 15*k + 3. Let o be z(-6). Factor -2/5*q**o + 2/5*q + 2/5*q**4 + 4/5 - 6/5*q**2.
2*(q - 2)*(q - 1)*(q + 1)**2/5
Let f = 10 - 7. Determine c so that -1/4 - 3/2*c - 2*c**2 + 3/2*c**f + 9/4*c**4 = 0.
-1, -1/3, 1
Let z(s) be the third derivative of -s**5/120 - s**4/72 + 2*s**2. Factor z(i).
-i*(3*i + 2)/6
Let y(j) be the first derivative of -4/3*j**3 + 2/5*j**5 + j**2 - j**4 - 4 + 1/3*j**6 + 2*j. Determine l so that y(l) = 0.
-1, 1
Solve 4/5 - 6/5*u + 2/5*u**3 + 0*u**2 = 0 for u.
-2, 1
Suppose -i + 5 = -3*v - 0*i, v + 20 = 4*i. Let w(x) be the second derivative of 1/12*x**4 + 2*x - 2/3*x**3 + v + 2*x**2. Suppose w(z) = 0. What is z?
2
Let p be -3 + 2 + 28/21. Factor 1/3*f + 0*f**2 - 2/3*f**3 + p*f**5 + 0 + 0*f**4.
f*(f - 1)**2*(f + 1)**2/3
Let b(v) be the first derivative of v**3/3 + 2*v**2 - 9*v - 11. Let z be b(-6). Find i, given that 2/7*i - 2/7*i**2 - 2/7*i**z + 2/7 = 0.
-1, 1
Let w be (-5)/10 + 1 - 0. Factor 1/2*a**2 - 1/2*a**3 - 1/2 + w*a.
-(a - 1)**2*(a + 1)/2
Let n(u) = 3*u**2 + 4*u - 3. Let l(z) = 3*z**2 + 4*z - 2. Let g(h) = -4*l(h) + 3*n(h). Suppose g(m) = 0. Calculate m.
-1, -1/3
Suppose -512*x**3 + 11 - 84*x - 108*x**5 + 1048*x**2 - 3 - 736*x**2 + 384*x**4 = 0. What is x?
2/9, 1/3, 1
Suppose 2 = 3*r - 4. Let n be -1 + 2 - r*-1. Factor -4*m**2 + 0*m**3 + 2*m**n + 2*m + 0*m.
2*m*(m - 1)**2
Find b, given that 110*b - 110*b - 3*b**4 - 6*b**3 = 0.
-2, 0
Let z(c) = -9*c**2 + c. Let r(o) = 8*o**2. Suppose -2*p - 4*w + 8 = 0, p - 2*w = 2*w - 20. Let f(b) = p*z(b) - 5*r(b). Determine k so that f(k) = 0.
-1, 0
Factor 0 + r**2 - r - 1/4*r**3.
-r*(r - 2)**2/4
Suppose 0 = -3*f - 0*f + 6. Let u = 4/5 + -2/15. Factor 1/3*t**f - u*t + 1/3.
(t - 1)**2/3
Factor -57*v**3 + 4*v**2 + 21*v**3 + 32*v**3.
-4*v**2*(v - 1)
Let c = -13 + 19. Suppose 2*w - 2 = c. Suppose 0*s**4 + 5*s**3 - 11*s**3 + 2*s**w + 6*s**2 - 2*s = 0. Calculate s.
0, 1
Suppose -3*x + 168 = -2*x. Let q = 1178/7 - x. Factor 2/7*t**2 + 0 - 2/7*t**4 - 2/7*t**5 + 0*t + q*t**3.
-2*t**2*(t - 1)*(t + 1)**2/7
Let g be (25/10 - 3)*(-7 + -1). Solve 2/5*k**2 + 0*k + 0 - 1/5*k**g + 1/5*k**3 = 0.
-1, 0, 2
Let 2/13 + 2/13*n - 2/13*n**2 - 2/13*n**3 = 0. Calculate n.
-1, 1
Let s(l) = -3*l**3 - l**2. Let a be s(-1). Let i = a - 2. Factor i*p + 0 - 2/5*p**3 - 2/5*p**2.
-2*p**2*(p + 1)/5
Let x(p) = -1 + 1 + p - 3. Let y be x(7). Solve -2*d**2 - 14*d + 6*d**2 + 6*d**2 + y = 0 for d.
2/5, 1
Let z(j) be the third derivative of 1/480*j**6 + 0*j - 1/96*j**4 + 0 + 2*j**2 - 1/240*j**5 + 1/24*j**3. Suppose z(k) = 0. What is k?
-1, 1
Let p(j) = j - 1. Let y be p(5). Suppose 9 = -i + y*i. What is b in -2/3*b**i + 2/3*b + 0*b**2 + 0 = 0?
-1, 0, 1
Factor -2/7*g + 0*g**3 - 4/7*g**2 + 2/7*g**5 + 0 + 4/7*g**4.
2*g*(g - 1)*(g + 1)**3/7
Let w be (-4)/(-144) - (-7)/(63/2). Find u, given that w*u**4 + 0 - 1/4*u**2 + 1/4*u - 1/4*u**3 = 0.
-1, 0, 1
Let r(w) = -8*w**4 + 70*w**3 + 90*w**2 + 56*w - 22. Let y(n) = -n**4 + 10*n**3 + 13*n**2 + 8*n - 3. Let p(f) = 6*r(f) - 44*y(f). Factor p(z).
-4*z*(z + 1)*(z + 2)**2
Let m(k) = 3*k**3 + 3*k**2 - 40*k - 33. Let s(j) = -2*j**3 - 2*j**2 + 20*j + 17. Let a(b) = 3*m(b) + 7*s(b). Solve a(w) = 0.
-2, -1, 2
Suppose 5*z + 12 = -3*a, 0*z + 3*a = -2*z - 12. What is u in 0 - 2/7*u**5 - 4/7*u**4 + 2/7*u + z*u**3 + 4/7*u**2 = 0?
-1, 0, 1
Let p(c) be the third derivative of -c**6/90 - c**5/45 + 2*c**4/9 + 8*c**3/9 - 4*c**2. Determine h so that p(h) = 0.
-2, -1, 2
Let v be 4/(-18) - (-267)/1080. Let x(a) be the second derivative of -1/40*a**5 - 1/24*a**4 - a - 1/168*a**7 + 1/8*a**3 - 1/8*a**2 + 0 + v*a**6. Factor x(j).
-(j - 1)**4*(j + 1)/4
Suppose 4/5*q**2 + 2/5 - 2/5*q**5 - 4/5*q**3 - 6/5*q**4 + 6/5*q = 0. What is q?
-1, 1
Factor 0*b**4 + 4*b + 4*b**4 - 4*b**3 + 0*b**2 - 2*b**2 - 2*b**4.
2*b*(b - 2)*(b - 1)*(b + 1)
Let o(s) = -7*s**3 - 4*s**2 + 5*s + 6. Let k(y) = -27*y**3 - 15*y**2 + 21*y + 24. Let a(q) = 4*k(q) - 15*o(q). Suppose a(x) = 0. Calculate x.
-1, 2
Let r = 105 - 209/2. Find p, given that -p**3 - r*p**4 + 0*p**2 + p + 1/2 = 0.
-1, 1
Let m be 0/(1*(-2 - 0)). Factor 1/2*r + m - 1/4*r**3 - 1/4*r**2.
-r*(r - 1)*(r + 2)/4
Let n(t) = t**5 + 11*t**4 - 8*t**2 - 7*t + 3. Let x(r) = -12*r**4 + 8*r**2 + 8*r - 4. Let a(s) = 4*n(s) + 3*x(s). Factor a(l).
4*l*(l - 1)*(l + 1)**3
Suppose -8/3*k - 4/3*k**2 + 4/3*k**3 + 0 = 0. What is k?
-1, 0, 2
Let i(w) be the third derivative of -w**7/3780 - w**6/540 - w**5/180 + w**4/8 + 3*w**2. Let s(m) be the second derivative of i(m). Factor s(d).
-2*(d + 1)**2/3
Let l(d) = -2*d - 6. Let w(t) = -t**3 + 4*t**2 - 2*t + 3. Let y be w(4). Let h be l(y). Factor 2*r + h - r**2 - 2*r**2 + r**2.
-2*(r - 2)*(r + 1)
Let v(n) be the first derivative of 2/3*n**3 - n**2 + 0*n + 7. Factor v(i).
2*i*(i - 1)
Suppose 3 + 342*a + 4*a**2 - 3 - 350*a = 0. What is a?
0, 2
Factor 8/3*m - 4*m**2 + 4/3*m**3 + 0.
4*m*(m - 2)*(m - 1)/3
Let n(b) be the first derivative of -b**6/12 - b**5/5 + b**3/3 + b**2/4 - 8. Let n(t) = 0. What is t?
-1, 0, 1
Let a(x) be the third derivative of x**8/112 + 3*x**7/70 + 3*x**6/40 + x**5/20 - 11*x**2. What is j in a(j) = 0?
-1, 0
Suppose 2*i + 26 = 2*z, 0*z = 5*i - 2*z + 50. Let d be -2 + 1*i/(-2). Suppose 4/3 - 2/3*y**d - 2/3*y = 0. What is y?
-2, 1
Let a(l) be the first derivative of -l**6/6 - 4*l**5/5 - 5*l**4/4 - 2*l**3/3 + 3. Factor a(n).
-n**2*(n + 1)**2*(n + 2)
Let f(k) be the second derivative of -3*k + 0*k**2 + 1/21*k**3 + 0 - 1/42*k**4. Factor f(a).
-2*a*(a - 1)/7
Let d(x) be the second derivative of -81*x**4/14 - 12*x**3/7 - 4*x**2/21 + 25*x. Factor d(w).
-2*(27*w + 2)**2/21
Factor j**3 - 4*j + 6*j**2 + 2*j**2 - 5*j**3.
-4*j*(j - 1)**2
Solve 11/8*q - 3/8*q**2 - 3/4 = 0 for q.
2/3, 3
Determine s, given that 2*s**2 + 11*s**4 - 7*s**2 - 6*s**4 = 0.
-1, 0, 1
Let h(v) = 2*v**4 + 4*v**3 - 2*v**2 - 2*v + 2. Let p(f) = 2*f**4 + 5*f**3 - 3*f**2 - 3*f + 3. Let r(i) = 3*h(i) - 2*p(i). Factor r(b).
2*b**3*(b + 1)
Let b(a) be the third derivative of a**8/25200 + a**7/2100 + a**6/400 + a**5/20 - 5*a**2. Let m(f) be the third derivative of b(f). Factor m(y).
(2*y + 3)**2/5
Let b = 53/326 - -2/489. Find i, given that 0 + b*i**2 - 1/3*i + 1/6*i**3 = 0.
-2, 0, 1
Let g(x) be the second derivative of -3/100*x**5 + 3/10*x**2 - 1/20*x**4 + 1/10*x**3 + 0 - 3*x. Factor g(p).
-3*(p - 1)*(p + 1)**2/5
Factor -4/5*h**2 + 4/5*h**4 + 2/5*h - 2/5*h**5 + 0*h**3 + 0.
-2*h*(h - 1)**3*(h + 1)/5
Let c be (-4)/12 - (-62)/24. Let y = 179 + -176. What is k in -5/4*k**2 + 9/4*k + 7/4*k**4 - 1/2 - c*k**y = 0?
-1, 2/7, 1
Let m(s) be the first derivative of -s**4 - 8*s**3/3 - 2*s**2 + 48. What is k in m(k) = 0?
-1, 0
Suppose 0 = -s + 1 + 2. Suppose a**4 - 2*a**4 + 8*a**3 - 7*a**s = 0. What is a?
0, 1
Let x(b) be the first derivative of 1/3*b**3 + 2*b + 3/2*b**2 - 3. Factor x(o).
(o + 1)*(o + 2)
Factor a**2 - a**2 - 54*a**3 - 2*a**2 - 9*a**4 + 65*a**3.
-a**2*(a - 1)*(9*a - 2)
Let n(w) be the third derivative of -w**8/392 - 26*w**7/735 - 17*w**6/84 - 13*w**5/21 - 23*w**4/21 - 8*w**3/7 + 34*w**2. Solve n(a) = 0.
-3, -2, -1, -2/3
Let y(q) be the first derivative of 6 - 1/2*q**4 - 8*q**2 + 8*q + 10/3*q**3. Factor y(d).
-2*(d - 2)**2*(d - 1)
Let y(l) be the first derivative of -1/180*l**5 - l**2 - 1/72*l**4 + 0*l - 2 + 0*l**3. Let d(n) be the second derivative of y(n). Suppose d(v) = 0. What is v?
-1, 0
Suppose 3*l - 191 = 4*a, 171 = -4*a - 0*a - l. Let b be (-28)/a + 1 + 0. Factor -2/11*f - b*f**2 + 0 - 48/11*f**3 - 32/11*f**4.
-2*f*(f + 1)*(4*f + 1)**2/11
Let d(z) be the first derivative of z**3/3 - z**2 + z - 1. Solve d(m) = 0 for m.
1
Let a(k) = 2*k**5 + k**4 - 4*k**3 + 1. Let n(l) = -l**3 + l**2 - l + 1. Let m be (-6)/8 + (-14)/(-8). Let r(i) = m*a(i) - n(i). Factor r(y).
y*(y - 1)*(y + 1)**2*(2*y - 1)
Let k be 2/(-1 + (-8)/(-4)). Factor -19*h**k + 11*h**2 - 4*h + 6*h**2.
-2*h*(h + 2)
Let h(y) = -5*y**3 - y + 1 + 2*y**3 + y**2 + 4*y**3. Let l(n) = 8