7
Let j(n) be the first derivative of -n**6/120 - n**5/20 - n**4/8 - n**3/3 - 5. Let z(q) be the third derivative of j(q). Factor z(m).
-3*(m + 1)**2
Let y(d) be the third derivative of 0 + 0*d**3 + 0*d**4 + 1/780*d**6 - 8*d**2 + 1/1365*d**7 - 1/390*d**5 - 1/2184*d**8 + 0*d. What is r in y(r) = 0?
-1, 0, 1
Let v(n) be the second derivative of n**7/84 + n**6/20 + n**5/40 - n**4/8 - n**3/6 - 11*n. Factor v(o).
o*(o - 1)*(o + 1)**2*(o + 2)/2
Let o(x) = -3*x**2 - 15*x - 16. Let j(y) = -21*y**2 - 105*y - 114. Let p(t) = 2*j(t) - 15*o(t). Factor p(k).
3*(k + 1)*(k + 4)
Let w(i) be the second derivative of -i**8/3360 + i**7/420 - i**6/180 + i**4/4 + 2*i. Let u(k) be the third derivative of w(k). Suppose u(l) = 0. Calculate l.
0, 1, 2
Suppose m - 4 = -0*m - 4*c, 0 = -5*m + c - 1. Let j(r) be the second derivative of m*r**2 + r - 1/30*r**6 + 0*r**4 + 0 + 1/20*r**5 + 0*r**3. Factor j(l).
-l**3*(l - 1)
Let h = 21 - 13. Suppose h*g = 3*g. Suppose -2/5*d - 2/5*d**2 + g = 0. What is d?
-1, 0
Let n(j) be the first derivative of -j**4 - 23*j**3/9 - 13*j**2/6 - 2*j/3 - 7. Factor n(l).
-(l + 1)*(3*l + 2)*(4*l + 1)/3
Suppose 2 = 2*h - 2. Solve 3 + h*i**2 + 0*i**2 + i**2 + 6*i = 0 for i.
-1
Let s(f) be the second derivative of -1/14*f**4 - 1/7*f**2 + 0 + 1/70*f**5 + f + 1/7*f**3. Factor s(a).
2*(a - 1)**3/7
Let d**4 - 4*d**5 - 2*d**3 + 10*d**3 - d**2 - 4*d**3 = 0. Calculate d.
-1, 0, 1/4, 1
Let l(d) be the second derivative of d**7/1260 - 7*d**6/720 + d**5/40 + d**4/12 + 2*d. Let z(n) be the third derivative of l(n). Find k, given that z(k) = 0.
1/2, 3
Let a(x) be the second derivative of -3/4*x**2 + 1/4*x**3 + 7*x - 3/40*x**5 + 1/8*x**4 + 0. Factor a(n).
-3*(n - 1)**2*(n + 1)/2
Let d(k) = k + 18. Let x be d(-13). Find f such that 0 - 1/3*f**x - 1/3*f**2 - f**3 + 0*f - f**4 = 0.
-1, 0
Let u(y) be the second derivative of -y**6/70 + 9*y**5/140 - 2*y**3/7 + 19*y. Factor u(v).
-3*v*(v - 2)**2*(v + 1)/7
Let r(h) = 4*h**2 - 1. Let c be r(1). Suppose -c*u = 2*u. Find f such that 5*f**2 - 5*f**4 - 4*f**5 - f + u*f**5 + 2*f + 3*f**3 = 0.
-1, -1/4, 0, 1
Let s(d) be the first derivative of 2*d**3/21 + 3*d**2/7 - 8*d/7 + 6. Factor s(j).
2*(j - 1)*(j + 4)/7
Let f(w) be the first derivative of 2 + 2/27*w**3 + 2/9*w - 2/9*w**2. Solve f(s) = 0 for s.
1
Let x = 7 + -5. Find k such that 2/3*k**x + 2/9 - 2/9*k**3 - 2/3*k = 0.
1
Find x, given that -2/5*x**2 + 2/5*x**4 - 2/5*x + 2/5*x**3 + 0 = 0.
-1, 0, 1
Suppose -5*u = -130 + 40. Factor -12*t + 2*t**2 + u + 0*t + 0*t.
2*(t - 3)**2
Let g = -1/4 - 0. Let k = g + 19/12. Find n such that 4/3*n**3 + 0*n - k*n**5 - 1/3*n**4 + 0 + 1/3*n**2 = 0.
-1, -1/4, 0, 1
Let h be 7/14 + -2*1/4. Factor h + 4/9*j**2 + 0*j**3 - 4/9*j**4 - 2/9*j + 2/9*j**5.
2*j*(j - 1)**3*(j + 1)/9
Let t(y) = -4 - 2*y - 7 + 3 + y. Let d be t(-10). Suppose 4/9*p**d - 10/9*p**4 + 0 + 2/3*p**3 + 0*p = 0. What is p?
-2/5, 0, 1
Let c(k) be the first derivative of 6/5*k**5 - 1 + 1/2*k**6 + 0*k - 2*k**3 - 3/2*k**2 + 0*k**4. Factor c(y).
3*y*(y - 1)*(y + 1)**3
Let z(r) be the first derivative of -1/3*r**3 - 9*r + 8 - 3*r**2. Determine t so that z(t) = 0.
-3
Suppose -2*b + 1 = -3. Factor s + 2*s**3 - b*s - s.
2*s*(s - 1)*(s + 1)
Let r(h) = -h**2 + 45*h + 95. Let n(j) = 4*j**2 - 224*j - 476. Let g(d) = 5*n(d) + 24*r(d). Factor g(y).
-4*(y + 5)**2
Let a(h) = -5*h**3 - 11*h**2 - 6*h + 8. Let s(j) = -3*j**3 - 7*j**2 - 4*j + 5. Let i(g) = -5*a(g) + 8*s(g). Suppose i(l) = 0. Calculate l.
-1, 0, 2
Let q(y) be the third derivative of 0*y**4 + 1/1260*y**7 + 1/36*y**3 + 0*y - 3*y**2 + 0*y**6 + 0 - 1/180*y**5. Determine d so that q(d) = 0.
-1, 1
Let p(y) be the first derivative of -1 - 1/2*y**2 + 1/3*y**3 + 0*y. Find v such that p(v) = 0.
0, 1
Let i = 76 - 220/3. Determine d, given that 4*d**3 + i*d**4 + 2/3*d**5 + 0 + 8/3*d**2 + 2/3*d = 0.
-1, 0
Let q(u) = u**2 - u - 1. Let d(y) = -10*y - 10. Let r(w) = d(w) - 2*q(w). Find a, given that r(a) = 0.
-2
Suppose -2*d + 1 = -3. Let m be (4/(-3))/(2/(-12)). Factor -66/5*a**d - 8/5 + m*a + 36/5*a**3.
2*(2*a - 1)*(3*a - 2)**2/5
Factor -28/17*n**2 + 0*n + 10/17*n**4 + 0 - 66/17*n**3.
2*n**2*(n - 7)*(5*n + 2)/17
Let b(c) = -c**2 + 7*c - 7. Let s be b(4). Find m such that m**3 + 4*m + 22*m**3 + 53*m**3 - 33*m**4 + s*m**4 + 8 - 60*m**2 = 0.
-2/7, 1
Let 0*v + 1/3*v**3 + 0*v**2 + 0 + 1/3*v**4 = 0. What is v?
-1, 0
Let b(u) = u**3 - 9*u**2 - u - 6. Let l be b(11). Factor -l*o**3 + 12 + 6*o + 234*o**3 - 30*o + 3*o**2.
3*(o - 1)*(o + 2)*(3*o - 2)
Factor 2/11*m**2 - 10/11 + 8/11*m.
2*(m - 1)*(m + 5)/11
Find q such that 52/7*q**3 - 68/7*q**2 - 10/7 + 2/7*q**5 + 6*q - 18/7*q**4 = 0.
1, 5
Factor 55 - u - 11*u - 60 - 5*u**2 + 2*u.
-5*(u + 1)**2
Let l(x) be the second derivative of -x**7/280 + x**6/120 + 5*x**3/6 + x. Let z(f) be the second derivative of l(f). Find w, given that z(w) = 0.
0, 1
Suppose 3*z - 4*s + 14 = 0, 5*z + 6 = 3*s + 1. Let m(w) be the second derivative of 3*w - 2*w**3 + 3*w**4 + 0 + 0*w**z - 27/20*w**5 + 1/5*w**6. Factor m(v).
3*v*(v - 2)**2*(2*v - 1)
Let a(k) = -3*k**4 + 13*k**3 - 10*k**2. Let v(b) = b**4 - 4*b**3 + 3*b**2. Let u(w) = 6*a(w) + 21*v(w). Factor u(x).
3*x**2*(x - 1)**2
Let i(x) be the first derivative of x**5/5 + x**4/6 - x**3/3 - x**2/3 + 5. What is j in i(j) = 0?
-1, -2/3, 0, 1
Let h(w) be the second derivative of w**6/30 - w**4/6 + w**2/2 + 25*w. Factor h(k).
(k - 1)**2*(k + 1)**2
Let n(i) be the third derivative of -i**5/24 - i**4/4 - i**3/3 - 13*i**2. Solve n(o) = 0.
-2, -2/5
Let v(b) be the second derivative of b**6/5 + 2*b**5/5 - b**4/6 - 2*b**3/3 - 62*b. Factor v(f).
2*f*(f + 1)**2*(3*f - 2)
Let v(i) = 9*i**5 + i**4 - 9*i**3 - 5*i**2 - 4*i - 4. Let b(m) = 26*m**5 + 4*m**4 - 26*m**3 - 15*m**2 - 11*m - 11. Let w(a) = 4*b(a) - 11*v(a). Factor w(x).
5*x**2*(x - 1)*(x + 1)**2
Let i(o) = -o**2 - 3*o + 20. Let m be i(-6). Let n(k) be the first derivative of 0*k**m + 3/8*k**4 - 3/10*k**5 + 0*k + 2 + 1/12*k**6 - 1/6*k**3. Factor n(r).
r**2*(r - 1)**3/2
Let k(z) be the third derivative of -z**6/540 - z**5/45 - z**4/9 - 8*z**3/27 - 11*z**2. Factor k(j).
-2*(j + 2)**3/9
Let n(w) be the third derivative of -3*w**6/25 + w**5/5 + 23*w**4/240 + w**3/60 - 9*w**2 - 1. Factor n(a).
-(a - 1)*(12*a + 1)**2/10
Let v be 11/((-44)/(-8))*1/8. Let q(p) be the first derivative of 2 + v*p**4 + 0*p**2 + 0*p + 0*p**3 - 1/5*p**5. Suppose q(u) = 0. What is u?
0, 1
Let b(h) be the first derivative of h**9/6048 - h**8/3360 - h**7/560 + h**6/144 - h**5/120 - h**3/3 - 1. Let g(k) be the third derivative of b(k). Factor g(p).
p*(p - 1)**3*(p + 2)/2
Let n(b) be the second derivative of b**4/12 - b**3/3 - 22*b. Determine m, given that n(m) = 0.
0, 2
Factor 39*g**2 - 12*g**2 + 75*g + 18 - 15*g**2.
3*(g + 6)*(4*g + 1)
Suppose -4*a**4 - 6*a - 2*a**5 - a**2 + a**3 + 14*a + 17*a**2 + 5*a**3 = 0. What is a?
-2, -1, 0, 2
Let a(p) be the second derivative of -8*p**6/5 - 17*p**5/5 - p**4 + 4*p**3/3 + 20*p. Solve a(u) = 0.
-1, -2/3, 0, 1/4
Let r(m) be the third derivative of -m**8/1512 - 4*m**7/945 - m**6/108 - m**5/135 - 3*m**2. Factor r(f).
-2*f**2*(f + 1)**2*(f + 2)/9
Let f = 1134 - 7934/7. Factor -f*i - 4/7*i**2 + 8/7.
-4*(i - 1)*(i + 2)/7
Let v(x) be the first derivative of -3*x**5/20 - 9*x**4/8 - 9*x**3/4 - 3*x**2/2 + 1. Factor v(q).
-3*q*(q + 1)**2*(q + 4)/4
Let b = 3/19 - -67/57. Factor -4/3*z**2 - 2/3 + 2*z**4 - 2/3*z**5 - b*z**3 + 2*z.
-2*(z - 1)**4*(z + 1)/3
Let u(a) be the second derivative of -3*a - 3/20*a**5 + 1/4*a**3 + 0 + 1/4*a**4 - 1/20*a**6 + 1/28*a**7 - 3/4*a**2. Determine o, given that u(o) = 0.
-1, 1
Let o = 280543/15 + -18712. Let h = 28/3 + o. Factor -1/5*t**3 + 1/5*t**2 - 1/5*t**4 + 0 + h*t.
-t*(t - 1)*(t + 1)**2/5
Let o be (2/(-21))/((-1)/3). Let d be (12/42)/(-1 + 2). Let -2/7*m**3 - d*m**2 + o*m**4 + 0 + 2/7*m**5 + 0*m = 0. What is m?
-1, 0, 1
Let x(m) be the third derivative of 1/150*m**5 + 0*m**3 - 1/525*m**7 + 0 + 0*m + m**2 - 1/240*m**8 + 7/600*m**6 + 0*m**4. Find h such that x(h) = 0.
-1, -2/7, 0, 1
Let a(m) be the first derivative of m**7/21 + m**6/6 + m**5/5 + m**4/12 + m - 1. Let s(x) be the first derivative of a(x). Let s(y) = 0. Calculate y.
-1, -1/2, 0
Let c(i) be the third derivative of 1/2*i**4 - 2/15*i**5 - 2/3*i**3 - 8*i**2 + 0*i + 0. Factor c(l).
-4*(l - 1)*(2*l - 1)
Let k(i) = -6*i**3 - 96*i**2 - 1092*i - 3993. Let r(m