 0. Calculate n.
1
Let z(u) be the first derivative of -u**4/2 - 2*u**3 - 2*u**2 + 5. What is i in z(i) = 0?
-2, -1, 0
Suppose 0*k - 8 = -3*w - 4*k, w - 3*k = -6. Solve 0 + w*o + 1/3*o**2 - 2/3*o**3 + 1/3*o**4 = 0 for o.
0, 1
Let c(u) be the first derivative of 5*u**6/6 + 14*u**5 + 245*u**4/4 - 26. Suppose c(j) = 0. What is j?
-7, 0
Let z = 4/473 + 1403/1892. Solve 3/2*g**3 - 3/4*g**5 + z*g**4 + 3/4 - 3/4*g - 3/2*g**2 = 0.
-1, 1
Let z be (5 - 3)*(-1)/(-7). Factor z*t**2 + 4/7*t + 2/7.
2*(t + 1)**2/7
Determine b, given that b**4 - 37*b**2 + 8 + 14*b**2 + b**3 - 4*b + 17*b**2 = 0.
-2, 1, 2
Let f(t) be the third derivative of t**7/70 + 3*t**6/40 + t**5/20 - 3*t**4/8 - t**3 - t**2. Factor f(p).
3*(p - 1)*(p + 1)**2*(p + 2)
Let d(u) be the first derivative of u**7/1470 - u**5/420 - u**2/2 - 4. Let y(w) be the second derivative of d(w). Factor y(k).
k**2*(k - 1)*(k + 1)/7
Suppose 4*w - 17 = 39. Suppose 2*k = 4*h - w, -4*h + 5 + 18 = -5*k. Factor 2*z + z**3 - h*z - z.
z*(z - 1)*(z + 1)
Factor -2*h + 1/2*h**4 + 3/2*h**2 - 2 + 2*h**3.
(h - 1)*(h + 1)*(h + 2)**2/2
Let u = -143/7 + 21. Let m = u + -5/21. Determine h so that 0*h**3 - m*h**4 + 0*h + 0 + 1/3*h**2 = 0.
-1, 0, 1
Suppose -4*t + t + 24 = 0. Suppose 0*y = h - 3*y - 9, h + 4*y = -12. Determine g so that 9/2*g**2 + h + 12*g**3 + t*g**4 + 1/2*g = 0.
-1, -1/4, 0
Solve 0 + 2657*d**2 - 1 - 2656*d**2 = 0.
-1, 1
Let p(i) = -i**3 + 7*i**2 + 7*i + 10. Let u be p(8). Let d(x) be the first derivative of -x**3 - 1 - 21/10*x**u - 6/5*x. Factor d(s).
-3*(s + 1)*(5*s + 2)/5
Let r = 5/119 - -199/119. Suppose -2/7*d**2 - r*d - 18/7 = 0. What is d?
-3
Factor -3/5*x - 6/5*x**3 + 3*x**2 - 6/5.
-3*(x - 2)*(x - 1)*(2*x + 1)/5
Factor -59*g**5 - 4*g**4 + 32*g**5 - 2*g**2 + 5*g**3 + 28*g**5.
g**2*(g - 2)*(g - 1)**2
Let k(r) be the first derivative of 0*r**2 + 4/33*r**3 + 2 + 1/22*r**4 + 0*r. Factor k(a).
2*a**2*(a + 2)/11
Suppose -3 = -3*q + 2*q. Find p such that 0*p**q - 3 + 0*p**2 - p**3 + p**2 + p + 2 = 0.
-1, 1
Factor 2*s**5 + 17*s**3 + 24*s**3 - 31*s**3 - 8*s**4 - 4*s**2.
2*s**2*(s - 2)*(s - 1)**2
Suppose -3*v = 4*p - 23, 0*p + v - 1 = 2*p. Factor -8*d**2 - d**3 - p*d - 6*d + 5*d**3 + 2*d**3.
2*d*(d - 2)*(3*d + 2)
Factor -4*w**3 + 4*w**4 + 0*w + 5*w - 5 - 2*w**2 + 3 - 3*w**5 + 2*w**5.
-(w - 2)*(w - 1)**3*(w + 1)
Let l(t) be the second derivative of -3*t + 0*t**3 + 1/20*t**5 + 0*t**2 + 1/12*t**4 + 0. Find c, given that l(c) = 0.
-1, 0
Let w(s) be the third derivative of s**5/300 - s**4/60 + s**3/30 - 6*s**2. Factor w(r).
(r - 1)**2/5
Let r(n) be the first derivative of n**6/90 + n**5/15 + n**4/6 + 3*n**3 + 3. Let z(w) be the third derivative of r(w). Factor z(v).
4*(v + 1)**2
Let h = 8 - 6. Suppose -h = -f + 1. What is z in -2*z**2 + 9*z**4 + 0*z**2 + 7*z**5 + 3*z**3 + f*z**4 = 0?
-1, 0, 2/7
Let h(k) be the third derivative of -7*k**6/80 + k**5/8 + k**4/8 - 4*k**2. What is x in h(x) = 0?
-2/7, 0, 1
Suppose 21*u - 22*u = -5. Let p(g) be the third derivative of 1/672*g**8 - 1/420*g**7 + 0*g**4 + 0 - g**2 + 0*g**3 + 1/120*g**u - 1/240*g**6 + 0*g. Factor p(m).
m**2*(m - 1)**2*(m + 1)/2
Let f(j) be the second derivative of -13*j**6/45 + 11*j**5/30 + j**4/9 - 24*j. Determine t, given that f(t) = 0.
-2/13, 0, 1
Let y(j) be the third derivative of -j**8/1008 + j**7/630 + j**6/360 - j**5/180 - 11*j**2. Determine q so that y(q) = 0.
-1, 0, 1
Let b(z) be the second derivative of 2*z + 0 - 1/39*z**3 + 1/78*z**4 - 2/13*z**2. Factor b(c).
2*(c - 2)*(c + 1)/13
Let s(f) = -f**2 - 5*f - 1. Let y be s(-4). Factor 2*p**2 - 3 + 3*p - p**y + 3 - 4*p.
-p*(p - 1)**2
Let p(k) = k**2 - 6*k + 2. Let c be p(4). Let q be (-17)/c + 3/(-2). Determine o, given that -2/3*o**5 - 2/3 - 2/3*o - 2/3*o**4 + 4/3*o**2 + q*o**3 = 0.
-1, 1
Let x(k) be the third derivative of k**8/10080 + k**7/2520 - k**6/180 + k**5/20 - 2*k**2. Let z(v) be the third derivative of x(v). Factor z(o).
2*(o - 1)*(o + 2)
Suppose r + 20 = 7*u - 2*u, 0 = u - 3*r - 18. Let q(d) be the third derivative of 1/36*d**4 + 0 + 1/180*d**6 + 0*d**u + 1/45*d**5 + d**2 + 0*d. Factor q(z).
2*z*(z + 1)**2/3
Factor -2/3*s + 2/3*s**4 + 2/3*s**3 - 2*s**2 + 4/3.
2*(s - 1)**2*(s + 1)*(s + 2)/3
Factor 4/5*s**4 - 1/5 + s - 3/5*s**2 - s**3.
(s - 1)**2*(s + 1)*(4*s - 1)/5
Suppose 2*o = 1 + 5. Let t(g) be the second derivative of -2*g - 1/100*g**5 + 0 + 0*g**2 + 0*g**o + 0*g**4. Factor t(h).
-h**3/5
Suppose 0*y - 3*y + 3 = 0. Let j = 1 - y. Solve -1/4*h**2 + 1/4*h**5 + 1/4*h**4 + 0*h + j - 1/4*h**3 = 0 for h.
-1, 0, 1
Determine y, given that -y**4 - 8*y**4 + 3*y**4 - 3*y**5 = 0.
-2, 0
Let w be -1 - -10 - (-1 + 3). Suppose -3*k = -y - w, 2*y - k = 5 + 1. Find t such that 1 - y + 2 + t**2 + 0 + t = 0.
-2, 1
Suppose -4*a = 5*z - 18, -2*z + 2 = 2*a - 3*z. Suppose -a + 8 = 2*j. Let -20*y**j + 0*y**5 + 20*y**2 + 6*y**4 - 2*y**5 + 2 + 4*y**4 - 10*y = 0. Calculate y.
1
Let i = -280/13 + 853/39. Factor 0 + u**2 - i*u**3 + 0*u.
-u**2*(u - 3)/3
Let f(t) be the first derivative of t**6/180 + t**5/60 - t**4/6 + 2*t**3/3 + 3. Let h(c) be the third derivative of f(c). Solve h(m) = 0 for m.
-2, 1
Let t = 28/43 - 1637/2580. Let n(x) be the second derivative of 2*x + t*x**6 + 1/12*x**3 + 0*x**2 - 1/40*x**5 - 1/24*x**4 + 0. Factor n(c).
c*(c - 1)**2*(c + 1)/2
Let u = -17/2 - -9. Let 2*d - 2 - u*d**2 = 0. What is d?
2
Let w(l) be the second derivative of -5*l**4/12 + 5*l**3/6 - 47*l. Factor w(b).
-5*b*(b - 1)
Suppose 5*q - 9 = -9. What is a in q - 2/5*a**2 + 2/5*a = 0?
0, 1
Let k(p) be the third derivative of -13*p**8/336 + 9*p**7/35 - 43*p**6/60 + 16*p**5/15 - 7*p**4/8 + p**3/3 - 13*p**2. Find c, given that k(c) = 0.
2/13, 1
Let o(u) = 2*u - 2. Let p be o(5). Suppose -p*b**2 + 8*b + 2*b**3 - 3*b + 3*b = 0. Calculate b.
0, 2
Let r(q) = 3*q**2 + 3. Let b(k) = k**2 + k - 1. Let l(c) = 6*b(c) - r(c). Let l(m) = 0. What is m?
-3, 1
Let l = -86 + 345/4. Solve -l*r**4 + 1/2*r**3 - 1/4*r**2 + 0*r + 0 = 0 for r.
0, 1
Let q be (1/((-4)/12))/(-1). Let w(x) be the first derivative of -1/5*x**2 + 0*x + 2/25*x**5 + 2/5*x**q - 3 - 3/10*x**4. Let w(j) = 0. Calculate j.
0, 1
Let j(s) be the second derivative of 2/3*s**3 - 1/6*s**4 - s**2 - 6*s + 0. Factor j(d).
-2*(d - 1)**2
Suppose -5*u = 3*z - 248 - 302, -5*u + 900 = 5*z. Determine t so that 16*t + 574*t**4 - 187*t**5 - 88*t**2 - 128*t**5 - 12*t**3 - z*t**5 = 0.
-2/5, 0, 2/7, 1
Let i(x) = 6*x**3 - 6*x**2 - 6*x + 22. Let n(q) = -2*q**3 + 2*q**2 + 2*q - 7. Let z(w) = -5*i(w) - 16*n(w). Determine s so that z(s) = 0.
-1, 1
Let y(c) be the first derivative of 0*c + 0*c**2 + 2/15*c**3 + 1. Factor y(x).
2*x**2/5
Let d(h) = 3*h**4 + 12*h**3 + 11*h**2 + 3*h - 1. Let j(n) = -n**4 - n**3 + n - 1. Let i(f) = d(f) - j(f). Find y, given that i(y) = 0.
-2, -1, -1/4, 0
Let k(l) be the first derivative of -l**4/4 + l**3 - 3*l**2/2 + l - 1. Determine g, given that k(g) = 0.
1
Factor -k**2 + 4*k**3 - 3*k**3 + k**2 + 3*k**2 + 1 + 3*k.
(k + 1)**3
Let y(j) be the second derivative of 2*j + 1/54*j**4 + 0 - 1/27*j**3 + 0*j**2. Determine o so that y(o) = 0.
0, 1
Suppose 9 = 3*g, 33 - 1 = 4*x + 4*g. Suppose -x*y + 6 = -2*y. Factor -3/2*v**2 + 2 - y*v.
-(v + 2)*(3*v - 2)/2
Find g such that 2 + 8*g**2 - 3 - 20*g**2 - g**3 + 4*g**4 - 5*g + 3 = 0.
-1, 1/4, 2
Let i(s) = s**2 + 5*s + 6. Let n be i(-4). Let a = n + 0. Solve -2/3*v - 1/3*v**a + 0 = 0.
-2, 0
Let n(g) be the first derivative of g**3/3 - 5*g**2/2 + 22. Suppose n(s) = 0. What is s?
0, 5
Factor -2/5 - 2/5*p**2 + 4/3*p.
-2*(p - 3)*(3*p - 1)/15
Let b(q) be the third derivative of -q**8/2856 + 2*q**7/1785 + q**6/340 - 2*q**5/255 - q**4/51 - 8*q**2 + 1. Solve b(k) = 0 for k.
-1, 0, 2
Let s(o) be the first derivative of -o**4/28 + o**3/21 + 3. Factor s(d).
-d**2*(d - 1)/7
Let j = 1937/9 - 215. Solve -2/9*o**2 + 4/9*o - j = 0.
1
Let q(s) be the second derivative of 1/6*s**4 - 5*s - 2*s**2 + 0 - 1/3*s**3. Solve q(c) = 0 for c.
-1, 2
Let o = -227/4 - -57. Find s such that 1/4 - o*s**2 - 1/4*s + 1/4*s**3 = 0.
-1, 1
Let a be (-25 + 34)*(-6)/(-27). What is k in 2/5*k**4 - 2/5*k**5 + 4/5*k + 0 - 2*k**a + 6/5*k**3 = 0?
-2, 0, 1
Let j(c) = 4*c**2 - 4. Let x be j(3). Factor 47*w**2 - 14*w**2 + 8 + w**2 - x*w - 10*w**3.
-2*(w - 2)*(w - 1)*(5*w - 2)
Let j(n) = -2*n**2 + 3*n. Let a(q) = 14*q**2 - 22*q. Let b(r) = -6*a(r) - 44*j(r). Determine t so that b(t) = 0.
0
Let j(g)