. Let r(h) = 0. What is h?
-1, -2/3, -1/4
Let t(s) be the first derivative of -s**5/100 + s**4/60 + s**3/30 - s**2/10 - 5*s + 2. Let k(w) be the first derivative of t(w). Factor k(p).
-(p - 1)**2*(p + 1)/5
Let t = -13 - -15. Suppose 2*r = -5*j + 21, 3*r - 14 + t = -j. Factor 0*m + 1/4*m**4 + 0*m**j + 1/4 - 1/2*m**2.
(m - 1)**2*(m + 1)**2/4
Factor k**2 - k**3 + 1/3*k**4 - 1/3*k + 0.
k*(k - 1)**3/3
Let o(g) = -g**3 + 8*g**2 + 2*g - 5. Let c be o(8). Factor -9*y + c + 49*y - y**2 + 45*y**2 + 16*y**3 + 1.
4*(y + 1)**2*(4*y + 3)
Let n(q) = -3*q**4 - 18*q**3 - 43*q**2 - 36*q - 8. Let j(w) = -12*w**4 - 72*w**3 - 171*w**2 - 144*w - 33. Let i(d) = 4*j(d) - 15*n(d). Factor i(a).
-3*(a + 1)**2*(a + 2)**2
Suppose -4*u + 8*u = -3*m + 29, -2*u = -4*m - 20. Let l be -1 + u/3 + -1. Factor 0*n + 4/3*n**2 + 0*n**3 - 2/3 - l*n**4.
-2*(n - 1)**2*(n + 1)**2/3
Let r(u) be the second derivative of u**6/10 + 3*u**5/4 + 3*u**4/2 - 2*u**3 - 12*u**2 + 7*u. Factor r(x).
3*(x - 1)*(x + 2)**3
Find n such that n**2 + 2*n + 12 - 3*n**2 - 10 - 2*n**3 = 0.
-1, 1
Let g(l) be the third derivative of l**5/120 + l**4/48 - l**3/6 - 15*l**2. Determine j so that g(j) = 0.
-2, 1
Let s(y) be the first derivative of -6*y + 16*y**3 + 27/4*y**4 + 15/2*y**2 - 2. Factor s(n).
3*(n + 1)**2*(9*n - 2)
Let k(v) be the first derivative of 1 + 1/3*v**2 + 2/9*v**3 - 4/3*v. What is i in k(i) = 0?
-2, 1
Let y(s) be the third derivative of -s**6/720 - s**5/360 - 2*s**2. Factor y(f).
-f**2*(f + 1)/6
Let f(v) be the third derivative of -v**9/3780 - v**8/1680 - v**4/4 - v**2. Let x(j) be the second derivative of f(j). What is i in x(i) = 0?
-1, 0
Factor -3*k**5 + k**5 + 3*k**3 + 2*k**2 + k**5.
-k**2*(k - 2)*(k + 1)**2
Let k(a) = -a**2 - a. Let f(w) = 4*w**4 + w**3 - w**2 + 2*w. Let n(d) = 2*f(d) + 6*k(d). What is l in n(l) = 0?
-1, -1/4, 0, 1
Factor -2/11*q**5 - 2/11*q**2 + 0*q + 0 + 2/11*q**3 + 2/11*q**4.
-2*q**2*(q - 1)**2*(q + 1)/11
Let n(q) be the third derivative of 0 + 0*q**3 + 0*q + 1/70*q**6 - q**2 - 2/105*q**5 + 1/1176*q**8 + 1/84*q**4 - 4/735*q**7. Find g such that n(g) = 0.
0, 1
Let c(z) = z**2 + z - 1. Let d(f) = -2*f**3 - 6*f**2 + 4. Let y(t) = 4*c(t) + d(t). Factor y(k).
-2*k*(k - 1)*(k + 2)
Find m, given that 13*m + 60*m**4 + 35*m**5 - 20*m - 70*m**2 + 10 - 8*m - 10*m**3 - 10*m**3 = 0.
-1, 2/7, 1
Find u, given that -8/13*u**2 - 4/13 + 18/13*u = 0.
1/4, 2
Let h(c) = 2*c**2 - c**2 - c - 3 + 1 + 3. Let m(z) = -10*z**2 + 12*z - 11. Let k(u) = 18*h(u) + 2*m(u). Solve k(x) = 0.
1, 2
Suppose 4*b = o + 2*b + 4, -17 = 2*o + 5*b. Let a be (8/o)/(4/(-6)). Factor -f**a + 3*f**4 - f**2 - f**4.
2*f**2*(f - 1)*(f + 1)
Let d be 1/3 - 6/18. Let g be (-3)/4*(-4 + d). Factor -8/7*i**2 + 0*i - 30/7*i**4 + 0 - 32/7*i**g.
-2*i**2*(3*i + 2)*(5*i + 2)/7
Let f(g) be the second derivative of -g**4/18 + g**2/3 + 2*g. Factor f(x).
-2*(x - 1)*(x + 1)/3
Let h(g) be the first derivative of g**7/168 + g**6/30 + g**5/16 + g**4/24 - g + 4. Let r(s) be the first derivative of h(s). Let r(p) = 0. What is p?
-2, -1, 0
Let r(y) = 2*y**2 + 2*y. Let g(i) = -2*i**2 - i. Suppose 0 = d + 1 + 1. Let u(v) = d*g(v) - 3*r(v). Find o such that u(o) = 0.
-2, 0
Determine k so that -4 + 50*k**3 - 46*k - 24*k**4 - 5 + 1 + 14*k + 14*k**2 = 0.
-2/3, -1/4, 1, 2
Let h be -2*(-1)/4 - -1. Factor h*u**2 - 3*u + 3/2.
3*(u - 1)**2/2
Determine a so that -3*a**5 + 2*a**4 + 8*a**5 + 7*a**5 - 2*a**5 = 0.
-1/5, 0
Let o(a) be the third derivative of -3*a**7/70 - a**6/10 + a**5/20 + a**4/4 - 8*a**2. Let o(t) = 0. Calculate t.
-1, 0, 2/3
Suppose 0*b**2 + 0*b + 0 + 0*b**3 - 1/2*b**5 + 1/6*b**4 = 0. What is b?
0, 1/3
Let h(u) = -2*u**5 - 2*u**4 + u**3 + 3*u**2 + 3. Let z(s) = -s**5 - s**4 + s**3 + s**2 + 1. Suppose -3*m - 2*m = -5. Let c(l) = m*h(l) - 3*z(l). Factor c(i).
i**3*(i - 1)*(i + 2)
Let f(z) = 2*z + 2. Let p be -2 + 3/(-6)*2. Let m(g) = g**2 - 3*g - 3. Let w(l) = p*f(l) - 2*m(l). Factor w(x).
-2*x**2
Let j(a) = -a**3 - 5*a**2 - 3*a + 3. Let s be j(-4). Let o be (s + 0 - -2)*9. Factor 5*v**4 + v**4 + v**2 - o*v**2 - 4*v**3 + 2 + 4*v**5.
2*(v - 1)*(v + 1)**3*(2*v - 1)
Let j(s) be the second derivative of s**9/15120 - s**8/3360 + s**7/2520 - s**4/6 + s. Let h(x) be the third derivative of j(x). Find b, given that h(b) = 0.
0, 1
Let f be ((-2)/(-10) - 4/20)/(-2). Let a(c) be the first derivative of -1/20*c**5 + f*c**2 - 3 + 0*c**4 + 1/12*c**3 + 0*c. What is s in a(s) = 0?
-1, 0, 1
Let r = -39 + 46. Let a(o) be the second derivative of 0*o**5 + 1/168*o**r + 4*o + 0*o**3 + 0 - 1/120*o**6 + 0*o**4 + 0*o**2. Suppose a(z) = 0. Calculate z.
0, 1
Let o be 9/4 - 4/16. Factor -2*i + 20*i**4 - 6*i**2 - 34*i**4 + o*i**3 + 20*i**4.
2*i*(i - 1)*(i + 1)*(3*i + 1)
Factor -7*g**3 + 15*g**2 + 2*g**3 - 12*g**2 + 42*g**2 - 125 - 75*g.
-5*(g - 5)**2*(g + 1)
Let 0*z**3 - 4/5*z**5 - 4/5*z**4 + 0*z**2 + 0*z + 0 = 0. Calculate z.
-1, 0
Let p = -31 - -34. Suppose 3*w = -2*u + 12, 0 = -w + p*w - 3*u + 5. Determine x, given that 4/5*x**w + 0 + 2/5*x**5 + 0*x**3 - 2/5*x - 4/5*x**4 = 0.
-1, 0, 1
Solve 0*d**2 + 4/5 + 8/5*d**3 - 4/5*d**4 - 8/5*d = 0 for d.
-1, 1
Let t(s) be the first derivative of 0*s**4 - 2 + 1/5*s**5 + 0*s**2 - 1/6*s**6 + 0*s + 0*s**3. Factor t(v).
-v**4*(v - 1)
Let f(m) be the second derivative of -m**4/132 + m**3/33 - 20*m. Factor f(s).
-s*(s - 2)/11
Let l be (2 - 4 - -2)/(-1). Let d = 11 - 8. Suppose -1/2*t**d + l*t - t**2 + 0 = 0. What is t?
-2, 0
Solve -1/4*b**3 + 9/4*b**2 - 25/4 - 15/4*b = 0 for b.
-1, 5
Suppose -2*l - o + 6*o = -6, 2*l - 4*o - 6 = 0. Factor 2/7*w**2 - 2/7*w**l + 0*w + 0.
-2*w**2*(w - 1)/7
Let z(t) be the second derivative of -1/126*t**7 + 0 - 2/15*t**5 - 1/9*t**4 - 1/18*t**6 + 0*t**3 + 0*t**2 + t. Solve z(u) = 0 for u.
-2, -1, 0
Let y be (8/10)/((-6)/(-45)). Let z be ((-10)/(-20))/(1/y). Factor 1/4 - 1/4*b + 1/4*b**z - 1/4*b**2.
(b - 1)**2*(b + 1)/4
Let p(o) be the second derivative of o**7/21 + o**6/15 - o**5/10 - o**4/6 + 33*o. Factor p(s).
2*s**2*(s - 1)*(s + 1)**2
Factor 2/3*j - 1/3*j**4 + 0 - 5/3*j**2 + 4/3*j**3.
-j*(j - 2)*(j - 1)**2/3
Let k = 32 - 23. Let b be (4/k)/((-6)/(-27)). Factor -1/4*d + 3/4*d**b + 0.
d*(3*d - 1)/4
Let m(n) be the first derivative of n**2/2 + 6*n - 2. Let a be m(-6). Factor w + 8*w**3 + w**4 + a*w**4 + 5*w**2 + 5*w**4 - 2*w**4.
w*(w + 1)*(2*w + 1)**2
Let x(w) be the first derivative of w**5/10 - w**3/3 + w/2 + 5. Suppose x(k) = 0. Calculate k.
-1, 1
Let a be ((-22)/8)/((-2)/16). Let u = -64/3 + a. Factor 2/9*q**3 + 2/3*q**2 + u*q + 2/9.
2*(q + 1)**3/9
Let p be (64/(-256))/((-1)/9). Factor p*g**3 + 7/4*g**2 + 5/4*g**4 + 0 + 1/4*g**5 + 1/2*g.
g*(g + 1)**3*(g + 2)/4
Factor 0*j**4 + 0*j**2 + 0 + 1/3*j**5 + 1/3*j - 2/3*j**3.
j*(j - 1)**2*(j + 1)**2/3
Let y be (0 - -1)/((-2)/(-4)). Let w(z) = -z**2 + 4*z. Let k be w(y). Factor 0 - 2*n**k - 2*n**3 + 2*n**5 + 0 + 3*n**2 - n**2.
2*n**2*(n - 1)**2*(n + 1)
Let r(t) = 3*t**3 + 20*t**2 - 7*t + 2. Let c be r(-7). Find q, given that 0 + 3/4*q**c - 1/2*q = 0.
0, 2/3
Let r = 51 + -51. Let 11/3*p**2 + r - 14/3*p**3 - 2/3*p = 0. What is p?
0, 2/7, 1/2
Let o(v) be the third derivative of 0 + 1/168*v**8 + 1/15*v**5 + 0*v + 0*v**4 - 1/60*v**6 - 2/105*v**7 + 0*v**3 - 2*v**2. Factor o(r).
2*r**2*(r - 2)*(r - 1)*(r + 1)
Let v(c) = c**3 - 7*c**2 - 5*c + 6. Let a be v(8). Let n be 2 + 0 + (-48)/a. Factor n - 1/5*h - 1/5*h**2.
-(h - 1)*(h + 2)/5
Let c(x) = 3*x**5 - 6*x**3 + 3*x - 4. Let b(l) = 4*l**5 - 7*l**3 - l**2 + 3*l - 5. Let u(j) = 4*b(j) - 6*c(j). Solve u(g) = 0.
-2, -1, 1
Suppose -9 = -3*a + 5*d, -3*d = 2*d. Suppose 0 + 3/4*j**2 + 0*j**a + 1/2*j - 1/4*j**4 = 0. Calculate j.
-1, 0, 2
Let y(n) be the second derivative of n**7/630 + n**6/180 + n**5/180 - 9*n**2/2 + n. Let d(p) be the first derivative of y(p). Factor d(s).
s**2*(s + 1)**2/3
Factor 4/3*q - 1/3*q**2 - 1.
-(q - 3)*(q - 1)/3
What is d in -1 + 1/2*d**2 - 3/2*d + 3/2*d**3 + 1/2*d**4 = 0?
-2, -1, 1
Let n = 99 + -97. Let j(w) be the first derivative of -w - 1 + 1/2*w**4 + 1/3*w**3 - w**n. Determine d, given that j(d) = 0.
-1, -1/2, 1
Let i(j) be the first derivative of -j**6/120 + j**5/30 - j**4/24 - j**2 + 2. Let g(l) be the second derivative of i(l). Let g(b) = 0. What is b?
0, 1
Let f(n) = -n**3 - n**2 - n - 4. Let c be f(0). Let o be (-19)/c - (-6)/24. Factor 0*m**2 - 2/7*m**4 + 0*m + 0*m**3 + 0 + 2/7*m**o.
2*m**4*