w + 57 - 11*w**3 - 3*w**2 - 3*w + 8*w**3. Let z(u) = -5*q(u) - 9*t(u). Suppose z(p) = 0. What is p?
-2, 2
Find t such that -4*t**2 + 3 + t**3 - t + t**2 + 2*t**3 - 2*t = 0.
-1, 1
Let m(f) = -4*f - 94. Let x be m(-24). What is c in -2/5*c + 2/5*c**4 + 6/5*c**x + 0 - 6/5*c**3 = 0?
0, 1
Let p(d) be the third derivative of d**9/20160 - d**7/1680 - d**5/20 - 4*d**2. Let o(w) be the third derivative of p(w). Find a, given that o(a) = 0.
-1, 0, 1
Suppose q - 64 = -60. Let x(z) be the second derivative of -1/30*z**3 - 1/50*z**5 + 0 - 3*z + 0*z**2 + 1/20*z**q. Let x(i) = 0. Calculate i.
0, 1/2, 1
Let p(w) be the third derivative of w**8/756 + 2*w**7/105 + w**6/9 + 46*w**5/135 + 11*w**4/18 + 2*w**3/3 - 7*w**2. Factor p(f).
4*(f + 1)**3*(f + 3)**2/9
Let v(k) be the third derivative of k**7/42 + k**6/6 + k**5/3 - 4*k**2. Let v(a) = 0. What is a?
-2, 0
Let b(d) be the first derivative of -2*d**5/55 - d**4/22 + 2*d**3/33 + d**2/11 - 7. Suppose b(t) = 0. Calculate t.
-1, 0, 1
Let g(n) be the third derivative of -8*n**8/231 + 144*n**7/385 - 73*n**6/55 + 101*n**5/66 - 19*n**4/22 + 3*n**3/11 - 10*n**2. Factor g(m).
-2*(m - 3)**2*(4*m - 1)**3/11
Let p(s) be the third derivative of s**6/120 - s**5/30 - 7*s**4/24 - 2*s**3/3 + 8*s**2. Let p(l) = 0. Calculate l.
-1, 4
Let p = 3533 - 17796/5. Let q = p - -148/5. Solve -m**5 + 0 - q*m**4 - 11/5*m**2 - 21/5*m**3 - 2/5*m = 0 for m.
-1, -2/5, 0
Let o = 25 - 23. Let v(b) be the first derivative of -3*b**o + 4*b + 0*b**3 + 1/2*b**4 - 2. Factor v(g).
2*(g - 1)**2*(g + 2)
Suppose 2*r + 12 = 3*x, x - r - 2 = 2. Suppose -2*t + 6 = t - 4*m, x*m + 8 = 4*t. Factor -4/9*n + 2/9 + 2/9*n**t.
2*(n - 1)**2/9
Let p(k) = -1. Let q(d) = -3*d**2 + 3*d - 2. Let b(j) = 2*p(j) - q(j). Factor b(s).
3*s*(s - 1)
Let x = -499/21 - -73/3. Solve 24/7*y**4 - 6/7*y**3 - x*y**2 - 2*y**5 + 0*y + 0 = 0 for y.
-2/7, 0, 1
Let g(r) be the second derivative of 2*r + 1/60*r**6 - r**2 + 1/45*r**5 + 0 - 2/9*r**3 - 1/12*r**4. Let u(a) be the first derivative of g(a). Factor u(n).
2*(n - 1)*(n + 1)*(3*n + 2)/3
Suppose c + 3*g - 3 = -c, -5*c - g - 12 = 0. Let p(a) = -2*a - 3. Let h be p(c). Factor n + h*n**2 + n + 0*n**2 - 2*n**2.
n*(n + 2)
Let r(z) = z**3 - 12*z**2 + 12*z - 11. Let p be r(11). Solve p*o + 0*o**2 + 0 - 4/3*o**4 - 4/3*o**3 - 1/3*o**5 = 0.
-2, 0
Let z(t) = -10*t**2 - 5*t - 1. Let q(l) = -l**2 - 1. Suppose 0 = -i - 0 - 3. Let x(w) = i*q(w) + z(w). Suppose x(p) = 0. What is p?
-1, 2/7
Let v(l) be the second derivative of 0*l**2 - 1/10*l**5 + 0 - 2/3*l**3 + 1/2*l**4 + l. Find g such that v(g) = 0.
0, 1, 2
Let q(p) = -p**3 - p**2 + 6. Let l(s) = -s**3 - s**2 + 1. Let m(b) = 6*l(b) - q(b). Factor m(x).
-5*x**2*(x + 1)
Let v(y) be the third derivative of -1/105*y**7 + 1/30*y**5 - 1/24*y**4 + 0*y + 1/120*y**6 + 0*y**3 - 4*y**2 + 0. Suppose v(g) = 0. Calculate g.
-1, 0, 1/2, 1
Let r(i) be the third derivative of -1/15*i**5 - 2*i**3 + 0 + 0*i - 2/3*i**4 + i**2. Factor r(f).
-4*(f + 1)*(f + 3)
Let d(k) be the second derivative of -k**7/2520 + k**6/540 - k**3/6 - k. Let o(j) be the second derivative of d(j). Find x, given that o(x) = 0.
0, 2
Let w(g) be the third derivative of -g**5/30 - g**4/6 - g**3/3 + 5*g**2. Suppose w(b) = 0. What is b?
-1
Let c(l) be the third derivative of l**8/30240 - l**6/1080 + l**5/20 + 2*l**2. Let f(v) be the third derivative of c(v). Factor f(j).
2*(j - 1)*(j + 1)/3
What is a in 8/7*a - 2/7*a**3 + 6/7*a**2 + 0 = 0?
-1, 0, 4
Let k(s) be the third derivative of s**6/80 - s**5/20 - s**4/4 + 2*s**3 - 33*s**2. Determine h so that k(h) = 0.
-2, 2
Let g(f) be the second derivative of 2*f**5/105 + f**4/28 - f**3/21 - f**2/2 - 3*f. Let x(b) be the first derivative of g(b). Factor x(i).
2*(i + 1)*(4*i - 1)/7
Let g(x) be the second derivative of -x**4/6 + 5*x**3/3 + 6*x**2 - 15*x. Factor g(i).
-2*(i - 6)*(i + 1)
Let z(j) be the third derivative of -j**7/12600 - j**6/450 - 2*j**5/75 - j**4/24 - 3*j**2. Let m(r) be the second derivative of z(r). Let m(a) = 0. Calculate a.
-4
Let c(y) be the first derivative of -5*y**4/16 + 5*y**2/8 + 3. Find g, given that c(g) = 0.
-1, 0, 1
Let c(k) be the first derivative of k**5/120 - k**4/48 - k**3/6 + 3*k**2/2 + 3. Let d(p) be the second derivative of c(p). Factor d(u).
(u - 2)*(u + 1)/2
Let m = -52/11 - -304/55. Let b = 266/15 + -52/3. Determine w, given that 2/5*w**4 - 4/5*w - b + 0*w**2 + m*w**3 = 0.
-1, 1
Let k = 22/3 + -7. What is y in k*y**3 - 2/3*y**2 + 2/3 - 1/3*y = 0?
-1, 1, 2
Suppose 11*w = 10*w. Let c be (0 + w)/(1 + -3). Factor 2/3*o**5 + 0 + c*o**3 - 2/3*o - 4/3*o**2 + 4/3*o**4.
2*o*(o - 1)*(o + 1)**3/3
Let l = 16 - 10. Factor 2*m**2 - l*m**2 + 3*m**2 + 1.
-(m - 1)*(m + 1)
Let d(o) be the third derivative of 0*o**5 + 0*o**3 + 1/336*o**8 + 2/105*o**7 + 3*o**2 + 0 + 0*o + 0*o**4 + 1/30*o**6. Factor d(n).
n**3*(n + 2)**2
Determine k so that 0 - 3/4*k**3 + 9/2*k + 3/4*k**2 = 0.
-2, 0, 3
Let a = 162 + -3887/24. Let v(b) be the first derivative of -2 - a*b**6 - 1/8*b**2 + 0*b**3 + 0*b + 0*b**5 + 1/8*b**4. Factor v(z).
-z*(z - 1)**2*(z + 1)**2/4
Let d(a) be the first derivative of a**6/420 + a**5/210 - a**4/84 - a**3/21 + 3*a**2/2 - 1. Let h(s) be the second derivative of d(s). Factor h(y).
2*(y - 1)*(y + 1)**2/7
Let y(h) be the third derivative of -h**8/448 + h**6/160 + 24*h**2. Let y(g) = 0. Calculate g.
-1, 0, 1
Let a(r) be the third derivative of -r**6/30 - r**5/15 - r**4/24 + r**2. Let c(g) = -11*g**3 - 11*g**2 - 2*g. Let y(i) = -8*a(i) + 3*c(i). Factor y(b).
-b*(b - 1)*(b + 2)
Suppose -20*y - 26*y**3 + 8 - 28*y**3 + 4*y**2 + 62*y**3 = 0. What is y?
-2, 1/2, 1
Let u(y) = y**3 - 10*y**2 - 4*y + 4. Let z(m) = 10*m**3 - 110*m**2 - 45*m + 45. Let t(x) = 45*u(x) - 4*z(x). Solve t(h) = 0.
0, 2
Let c(n) be the first derivative of -7*n**6/2 - 54*n**5/5 - 327*n**4/28 - 36*n**3/7 - 6*n**2/7 + 6. Factor c(i).
-3*i*(i + 1)**2*(7*i + 2)**2/7
Let p be (1/1 + 1)*1. Let d be (-8)/10*5/(-2). Factor 3*q**d + 0*q - 6*q**3 + 2*q - 7*q**p.
-2*q*(q + 1)*(3*q - 1)
Suppose -4*i - 2*u + 4 = 0, -7*i - 4*u = -4*i + 2. Let h be (i/(-3))/(3/(-6)). Factor 0*b + 0*b**2 + h*b**3 + 0 - 10/3*b**4.
-2*b**3*(5*b - 2)/3
Let m(u) = u**2 - 4*u + 4. Let x be m(3). Let h = x + 1. Let 2*p**h - 9*p + 2 + 3*p + 2 = 0. What is p?
1, 2
Let q be (7 - 7)*(3 - 30/9). Let h(k) be the second derivative of 0*k**3 + 1/5*k**5 + q + 0*k**2 + 3*k + 0*k**4 + 1/15*k**6. Determine i so that h(i) = 0.
-2, 0
Factor 2 - 2 + 3*t**5 - 2*t**3 + 2*t**2 - 2*t**4 - t**5.
2*t**2*(t - 1)**2*(t + 1)
Let t be 40/(-18) - (-10)/45. Let f be 1 + t + -1 + 2. Factor -6/5*a**2 + 6/5*a**3 + f - 2/5*a**4 + 2/5*a.
-2*a*(a - 1)**3/5
Let r(i) = i**3 - 8*i**2 + 8*i - 7. Let d be r(7). Let v = 2 - d. Factor 3*j**v - 2*j - 3*j**2 + 2*j**2.
2*j*(j - 1)
Suppose 3*o - 56 - 46 = 0. Determine s so that -3*s**3 + 4*s**3 - o*s**2 + 36*s**2 + s = 0.
-1, 0
Let q = 23 - 46. Let h = 27 + q. Solve 1/2*l + 15/2*l**3 - 13/2*l**h + 2*l**5 + 0 - 7/2*l**2 = 0 for l.
0, 1/4, 1
Let n = -25/27 - -77/54. Determine t so that 9/4*t + n + t**2 = 0.
-2, -1/4
Let n(p) be the second derivative of p**5/4 - 25*p**4/12 + 10*p**3/3 - 7*p. Factor n(k).
5*k*(k - 4)*(k - 1)
Let h(i) = 10*i**3 - i**2 + i - 1. Let n be h(1). Let b = n - 6. Factor 2*z**5 + z**4 - 3*z**5 + 0*z**3 + 0*z**b.
-z**4*(z - 1)
Suppose -x - m + 8 = 3*m, -11 = -3*x + m. Let 13 + x*b + 0*b**2 - 2*b**2 - 15 = 0. Calculate b.
1
Let q(p) be the first derivative of 2*p**4/7 - 2*p**3/21 + 5. Let q(j) = 0. What is j?
0, 1/4
Suppose -3 = 12*r - 27. Let d(t) be the second derivative of 0*t**2 + 0*t**3 + 0 + 1/42*t**4 + r*t + 1/105*t**6 - 1/35*t**5. Factor d(w).
2*w**2*(w - 1)**2/7
Let v(d) be the second derivative of 0*d**2 - 1/2*d**3 + 1/5*d**6 + 1/14*d**7 + 3*d + 0*d**5 - 1/2*d**4 + 0. Factor v(p).
3*p*(p - 1)*(p + 1)**3
Let o = 7/36 - -1/18. Let t = 47 - 187/4. Factor 1/2*j**2 + 0*j**3 - t*j + o*j**5 - 1/2*j**4 + 0.
j*(j - 1)**3*(j + 1)/4
Let g(w) be the first derivative of 1/8*w**2 - 7/8*w**4 - 1/4*w - 1 + 1/2*w**3 + 11/20*w**5 - 1/8*w**6. Solve g(a) = 0 for a.
-1/3, 1
Let b(u) = u**2 + 2*u + 2. Let d be b(0). Suppose -4*a = -i - 3, -4*a + 4*i = -d*a + 16. Factor 2/5*g**5 + 4/5*g**4 - 4/5*g**a - 2/5*g + 0 + 0*g**3.
2*g*(g - 1)*(g + 1)**3/5
Let l(b) be the first derivative of -b**4 - 4*b**3/3 + 2*b**2 + 4*b - 1. Suppose l(u) = 0. Calculate u