3
Let x(s) be the first derivative of -2*s**4/5 + 2*s**3/3 - s**2/5 + 22. Let x(b) = 0. What is b?
0, 1/4, 1
Factor -8 - 4*n**3 + 16*n + 1 + 2 - 11 + 4*n**2.
-4*(n - 2)*(n - 1)*(n + 2)
Factor -5*w**4 - 2*w - 5 - 3*w + 143*w**2 - 133*w**2 - 5*w**5 + 10*w**3.
-5*(w - 1)**2*(w + 1)**3
Let u(b) be the second derivative of 1/4*b**4 + 1/60*b**6 - 3*b + 1/10*b**5 + 0 + 1/3*b**3 - 2*b**2. Let w(v) be the first derivative of u(v). Factor w(d).
2*(d + 1)**3
Let y(o) = -2*o - 18. Let f be y(-9). Let v(x) be the first derivative of 0*x - 3/10*x**5 - 9/16*x**4 - 1 - 1/4*x**3 + f*x**2. Factor v(b).
-3*b**2*(b + 1)*(2*b + 1)/4
Let b = -20 + 22. Suppose 3*d = b*o, 2 = -2*d + 6. What is k in -4/7 + 8/7*k**o + 32/7*k**4 - 22/7*k + 2*k**5 - 4*k**2 = 0?
-1, -2/7, 1
Let p be -3 - 22/(-13) - -1. Let j = p + 21/26. Factor -2*v**4 - j*v**2 + 5/2*v**3 + 0 + 0*v.
-v**2*(v - 1)*(4*v - 1)/2
Let c(b) be the third derivative of b**5/210 - 6*b**2. Let c(u) = 0. Calculate u.
0
Let w(o) be the third derivative of 0*o**3 + 0*o**4 + 0 + 1/90*o**5 - 1/90*o**6 + 1/315*o**7 + 0*o + o**2. What is r in w(r) = 0?
0, 1
Let h(v) be the third derivative of -2*v**2 + 0 + 0*v - 1/240*v**6 + 1/48*v**4 + 1/12*v**3 - 1/120*v**5. Factor h(z).
-(z - 1)*(z + 1)**2/2
Let f(j) = -j - 4. Let u be f(-5). Let q be (-1 + u)/(1/(-1)). What is c in -2/7*c**4 - 2/7*c**3 + 2/7*c**5 + 0 + q*c + 2/7*c**2 = 0?
-1, 0, 1
Determine r, given that 0*r**3 - r**3 + 2*r**5 + 2*r**2 - r**3 - 2*r**4 = 0.
-1, 0, 1
Determine f so that -3/2*f**2 + 18*f + 39/2 = 0.
-1, 13
Let m(h) = 10*h**2 + 2*h - 2. Let w(y) = -y**2 + y + 1. Let x(c) = -m(c) - 6*w(c). Factor x(v).
-4*(v + 1)**2
Let v(q) be the second derivative of -q**7/6300 + q**6/900 - q**5/300 + q**4/6 - 5*q. Let p(j) be the third derivative of v(j). Let p(s) = 0. What is s?
1
Let t be (-12)/18*(-6306)/(-28). Let q = 151 + t. What is a in -2/7*a**2 - 4/7 + q*a = 0?
1, 2
Let j(a) be the second derivative of -4*a**7/105 - 3*a**6/25 + 7*a**5/25 + 2*a**4/5 - 2*a**3/3 - 3*a**2/5 + 37*a. Determine y, given that j(y) = 0.
-3, -1, -1/4, 1
Let a(q) be the first derivative of -q**8/560 + q**6/60 - q**4/8 - 7*q**3/3 - 1. Let z(p) be the third derivative of a(p). Let z(o) = 0. What is o?
-1, 1
Let w(v) be the second derivative of -v**5/6 - 17*v**4/18 - 2*v**3/3 - 32*v. Factor w(m).
-2*m*(m + 3)*(5*m + 2)/3
Let a(p) be the first derivative of -p**9/3024 + p**7/280 - p**6/180 - 2*p**3/3 + 7. Let u(k) be the third derivative of a(k). Factor u(j).
-j**2*(j - 1)**2*(j + 2)
Let u(d) be the second derivative of d**5/5 + d**4 - 8*d**2 - 3*d. Find i such that u(i) = 0.
-2, 1
Let o be -3 + 3/1 + 2. Factor -5 + o + g**3 + 1 - 3*g.
(g - 2)*(g + 1)**2
Let g be (((-90)/(-189))/((-16)/(-28)))/5. Factor -1/6*k + g*k**2 + 0.
k*(k - 1)/6
Suppose 2*x = 7*x. Let c(q) be the second derivative of 1/48*q**4 + x*q**2 - q + 0 + 0*q**3. Solve c(w) = 0 for w.
0
Let m(c) be the second derivative of 1/75*c**6 + 0*c**2 - 1/30*c**4 + 0 + 6*c + 1/15*c**3 - 1/50*c**5. Factor m(w).
2*w*(w - 1)**2*(w + 1)/5
Let a(i) be the first derivative of -2*i**3/33 + 10*i**2/11 - 50*i/11 + 6. Factor a(u).
-2*(u - 5)**2/11
Let m = 1207/9 + -134. Let x(a) be the first derivative of 1/3*a + 1 + 1/3*a**2 + m*a**3. Suppose x(g) = 0. What is g?
-1
Let t(u) be the first derivative of -u**3/3 - 2*u**2 + u - 3. Let d be t(-3). Factor 0*n**2 - 2/3*n**3 - 2/9*n**d + 8/9*n + 0.
-2*n*(n - 1)*(n + 2)**2/9
Suppose -4*q + 3 = -5. Factor -4*t - q*t**2 - 2*t**3 + 3*t**2 + 5*t**2.
-2*t*(t - 2)*(t - 1)
Let v = -155 - -1089/7. Suppose 2/7*a**2 + 2/7*a - v = 0. Calculate a.
-2, 1
Solve -5*s - 5 + 5*s**3 + 7*s**3 - 7*s**3 + 7*s**2 - 2*s**2 = 0 for s.
-1, 1
Suppose -2 = -c - 0*c. Let v be 3/(-21)*-4 + 2/(-28). Determine j, given that -1/2*j**3 - v*j + 7/4*j**4 - c*j**2 + j**5 + 1/4 = 0.
-1, 1/4, 1
Let q(b) be the third derivative of b**9/4725 - b**7/1050 - b**6/900 + 5*b**4/24 - 4*b**2. Let p(m) be the second derivative of q(m). Solve p(r) = 0.
-1/2, 0, 1
Suppose 2*a - 7 + 3 = 0. Let b = 3/62 - -239/186. Factor b*g - 2/3 - 2/3*g**a.
-2*(g - 1)**2/3
Let f(u) = 10*u**5 - 10*u**4 - 12*u**3 + 10*u**2 + 2*u + 18. Let a(c) = -c**5 + c**3 - 1. Let q(j) = 36*a(j) + 2*f(j). Suppose q(y) = 0. Calculate y.
-1, -1/4, 0, 1
Find m, given that 0*m + 16/5*m**2 + 0 - 4*m**4 + 32/5*m**3 = 0.
-2/5, 0, 2
Let b(h) = -h**3 - h**2 - h + 4. Let p be b(0). Let l(f) be the second derivative of 0*f**3 + 0*f**2 - 1/90*f**6 + 0 + 0*f**5 + 1/36*f**p + 2*f. Factor l(v).
-v**2*(v - 1)*(v + 1)/3
Suppose 1 = -u - 0*u. Let o be 2 - u/((-12)/8). Factor 0*x**2 - o + 2/3*x**3 - 2*x.
2*(x - 2)*(x + 1)**2/3
Let n = -826 - -842. Suppose 0 + 23/4*o**2 + n*o**5 - 21*o**3 + 20*o**4 - 1/2*o = 0. What is o?
-2, 0, 1/4
Let u(o) = o**2 + 10*o + 21. Let h be u(-7). Suppose -5*p = 2*s - 16, 2*p - 5*s + 17 = 3*p. What is d in h*d - 1/4*d**p + 1/4 = 0?
-1, 1
Let z = -241/2 - -769/6. Let y = 25/3 - z. Determine l so that 0 - y*l - 2*l**3 - 2*l**2 - 2/3*l**4 = 0.
-1, 0
Let f(o) be the first derivative of o**6/3 - 14*o**5/5 + 8*o**4 - 8*o**3 + 7. Factor f(a).
2*a**2*(a - 3)*(a - 2)**2
Let c(l) be the first derivative of l**9/4032 - l**8/1120 + l**7/1120 - 4*l**3/3 - 1. Let x(y) be the third derivative of c(y). Solve x(b) = 0.
0, 1
Suppose 0*s = 3*s + 2*h - 16, 3*h = -s + 17. Factor -c**s + 3 - 4 + 2*c**2.
(c - 1)*(c + 1)
Let x(k) be the first derivative of -5*k**4 + 9*k**3 + 12*k**2 + 4*k + 2. Factor x(m).
-(m - 2)*(4*m + 1)*(5*m + 2)
Let g(f) be the second derivative of -f**4/36 - f**3/18 - 3*f. Factor g(t).
-t*(t + 1)/3
Let b(j) = -j - 4. Let h be b(-4). Let l = -263/5 - -53. Determine q so that -2/5*q**5 + 6/5*q**3 + l*q**2 + h - 2/5*q**4 - 4/5*q = 0.
-2, -1, 0, 1
What is p in 3*p**3 + 0 + 9/5*p**4 - 6/5*p**2 + 0*p = 0?
-2, 0, 1/3
Let o be (3/6*0)/(-1). Let l(w) be the second derivative of 0*w**2 - 4/15*w**6 + o*w**3 - 1/10*w**5 + w + 1/12*w**4 + 0. Factor l(g).
-g**2*(2*g + 1)*(4*g - 1)
Let m = 1 + 2. Let t(j) = 1. Let b(c) = 1 - 2*c**2 + 0 + 2 + 2. Let l(f) = m*t(f) - b(f). Suppose l(z) = 0. What is z?
-1, 1
Let z(y) = y**5 - y**4 - y**3 + y**2 + y - 1. Let p(c) = 7*c**5 - 5*c**4 - 11*c**3 + 9*c**2 + 9*c - 9. Let k(h) = 2*p(h) - 18*z(h). What is g in k(g) = 0?
0, 1
Let f(n) = n**3 - 9*n**2 + 6. Let z be f(9). Let o = -4 + z. Factor -2/3*c**4 + 1/3*c**3 + 0 + 0*c + 0*c**o + 1/3*c**5.
c**3*(c - 1)**2/3
Let h(x) be the third derivative of 0*x - 3*x**2 + 1/6*x**3 + 0 - 1/30*x**5 - 1/24*x**4. Suppose h(b) = 0. What is b?
-1, 1/2
Let h**3 + 4*h**3 - 5*h**3 - 2*h**3 - 2*h**4 = 0. What is h?
-1, 0
Suppose -4*h = -5*p + 3 + 17, 4*h + 20 = -3*p. Let v(z) be the first derivative of p*z**4 + 0*z + 0*z**2 + 0*z**3 - 2/5*z**5 + 1. Factor v(s).
-2*s**4
Suppose -2*d = d - 12. Let u(m) be the second derivative of 0*m**3 + 0 + m + 1/40*m**5 + 1/24*m**d + 0*m**2. Solve u(q) = 0 for q.
-1, 0
Let a(k) be the third derivative of k**5/20 - k**4/4 - 3*k**3/2 - 25*k**2. Determine f, given that a(f) = 0.
-1, 3
Let y(u) be the first derivative of 0*u**4 - 2/9*u**3 - 1/6*u**2 + 1 + 2/15*u**5 + 1/18*u**6 + 0*u. Factor y(n).
n*(n - 1)*(n + 1)**3/3
What is v in v - 2*v + v**2 + 3*v + v - 4 = 0?
-4, 1
Let o(m) be the first derivative of -m**5/70 + m**4/14 - m**3/7 + m**2/7 - 2*m - 3. Let x(b) be the first derivative of o(b). Factor x(w).
-2*(w - 1)**3/7
Let l(p) be the second derivative of p**5/10 - p**4/3 + p**3/3 - 5*p. Factor l(s).
2*s*(s - 1)**2
Let t(b) = 5*b**2 + 2*b - b**3 - 4*b**2 + 0*b**2 - 2. Let r(a) = -a - 1. Let p be r(0). Let s(x) = x**3 - x**2. Let q(g) = p*s(g) + t(g). Factor q(c).
-2*(c - 1)**2*(c + 1)
Let k be -1*(-5)/(5/6). Let d(q) be the third derivative of 0*q**k + 1/168*q**8 + 3*q**2 + 0 + 0*q**5 + 0*q**4 - 1/105*q**7 + 0*q**3 + 0*q. Factor d(r).
2*r**4*(r - 1)
Solve -4*o + 3*o**2 + 6 - 21 + 6 - 2*o = 0.
-1, 3
Let d(b) = b**3 - 14*b**2 + 8*b + 2. Let v(a) = -2*a**3 + 13*a**2 - 7*a - 2. Let q(j) = -2*d(j) - 3*v(j). Factor q(p).
(p - 2)*(p - 1)*(4*p + 1)
Suppose 14 = 5*k - 1. Let d(a) be the first derivative of 2/3*a**k - 2 + 2*a**2 + 0*a. Suppose d(q) = 0. What is q?
-2, 0
Let u be -5*(-3 + 26/10). Factor 26*o - u*o**2 + 2 - 26*o.
-2*(o - 1)*(o + 1)
Let f(i) be the third derivative of i**5/12 + 5*i**4/8 + 10*i**2. Factor f(d).
5*d*(d + 3)
Let t(z) be the first derivative of -2/5*z**5 + 3 - 4/3*z**3 + 