3
Let i(y) be the first derivative of -2/3*y**3 - 17 + 4*y**2 - 6*y. What is p in i(p) = 0?
1, 3
Let f = -15239/2 + 7622. Factor 1/4*j**2 - 11/4 + f*j.
(j - 1)*(j + 11)/4
Let m(v) be the second derivative of v**6/450 + v**5/300 - v**4/20 - 5*v**3/6 + 7*v. Let n(w) be the second derivative of m(w). Let n(s) = 0. Calculate s.
-3/2, 1
Let r(m) = 2*m**3 - 37*m**2 + 4*m - 427. Let b be r(19). Suppose -b*v**2 + 0*v - 2/5*v**4 + 4*v**3 + 0 = 0. Calculate v.
0, 5
Let d(c) be the third derivative of c**7/630 - c**6/30 + 5*c**4/12 - 11*c**2. Let a(t) be the second derivative of d(t). Factor a(v).
4*v*(v - 6)
Suppose 5*o - 2*o - 18 = 0. Solve s + 3*s**3 + 3*s**2 - 5 + s**4 + o - 1 = 0 for s.
-1, 0
Suppose 5*n + 3 = 3*k, 0 = k - 3 + 2. Suppose -128*u + 123*u = n. Factor u + 0*h - 1/2*h**3 - h**2.
-h**2*(h + 2)/2
Factor 48/5*i - 18/5*i**2 + 0 - 3/5*i**3.
-3*i*(i - 2)*(i + 8)/5
Let n = -15/17 + 164/51. Let -2/3*t + t**5 + 0 + 7/3*t**4 - n*t**2 - 1/3*t**3 = 0. What is t?
-2, -1, -1/3, 0, 1
Let t(r) be the second derivative of 1/3*r**4 + 2*r**2 + 0 + 6*r - 4/3*r**3. Factor t(i).
4*(i - 1)**2
Suppose -44*n**3 + 126*n**2 + 107*n**2 + 72 - 177*n**2 + 156*n - 16*n**4 = 0. What is n?
-3, -1, -3/4, 2
Let -8/7*m**3 - 4/7*m + 10/7*m**2 + 0 + 2/7*m**4 = 0. Calculate m.
0, 1, 2
What is i in 80*i + 6*i**2 + 9*i**2 + 25*i**2 - 75*i**3 - 45*i**4 = 0?
-4/3, 0, 1
Let a(q) be the third derivative of -1/36*q**4 + 0 - 1/54*q**5 + 1/3*q**3 - 1/540*q**6 + 0*q - 52*q**2. Find s, given that a(s) = 0.
-3, 1
Suppose -137*o - 2 = 2 - 4. Factor o - 1/2*g**2 - 3/2*g.
-g*(g + 3)/2
Let n(v) be the third derivative of v**7/6300 + v**6/1800 - 3*v**4/8 + 5*v**2. Let s(p) be the second derivative of n(p). Factor s(d).
2*d*(d + 1)/5
Suppose 9 = 5*r - 16. Let w(l) be the third derivative of 4*l**2 + 0 + 3/8*l**4 - 1/20*l**r - l**3 + 0*l. Solve w(d) = 0 for d.
1, 2
Let z(m) be the second derivative of 0 + 43*m - 1/3*m**4 - 16*m**3 - 288*m**2. Factor z(j).
-4*(j + 12)**2
Let y = -927 - -928. Let q be 5 + -1 - (-1 - (-18)/4). Factor y - 3/2*p**2 - q*p**3 + 1/2*p + 1/2*p**4.
(p - 2)*(p - 1)*(p + 1)**2/2
Let m(d) be the second derivative of d**7/10080 - d**6/960 + d**5/240 - 11*d**4/12 - 9*d. Let v(s) be the third derivative of m(s). Suppose v(u) = 0. What is u?
1, 2
Let k(i) be the first derivative of i**6/60 + i**5/10 + i**4/4 + i**3/3 - 4*i**2 + 1. Let m(g) be the second derivative of k(g). Suppose m(q) = 0. Calculate q.
-1
Factor a**2 + 8*a**2 - 4*a**4 + 2*a**3 - 5*a**2 - 4*a**3 + 2*a**5.
2*a**2*(a - 2)*(a - 1)*(a + 1)
Suppose 42*h - 37*h = 0. Let x(z) be the second derivative of h*z**2 + 1/10*z**5 + 1/84*z**7 + 0*z**3 + 0*z**4 + 0 + 1/15*z**6 - 2*z. Factor x(a).
a**3*(a + 2)**2/2
Let o(x) be the third derivative of -5*x**8/1344 - 3*x**7/56 - 11*x**6/96 + 29*x**5/48 + 25*x**4/8 + 35*x**3/6 + 51*x**2 + 4*x. Suppose o(j) = 0. Calculate j.
-7, -2, -1, 2
Suppose -l = -6*l. Let i(b) = -b**3 + 11*b**2 + 168*b - 1186. Let n be i(6). Factor l*x + 2/3*x**5 + 2/3*x**3 + 0*x**n + 4/3*x**4 + 0.
2*x**3*(x + 1)**2/3
Let u(h) be the second derivative of h**7/84 - h**6/15 + h**5/10 + h**4/12 - 5*h**3/12 + h**2/2 - h + 17. What is b in u(b) = 0?
-1, 1, 2
Let x(g) be the second derivative of -g**8/1176 + g**6/210 - g**4/84 + 9*g**2/2 + 9*g. Let k(h) be the first derivative of x(h). Factor k(r).
-2*r*(r - 1)**2*(r + 1)**2/7
Let x(v) be the first derivative of -4*v**3/3 - 424*v**2 - 44944*v + 40. Determine p, given that x(p) = 0.
-106
Let h(q) = -q**3 - 9*q**2 + 9*q. Let m be h(-10). Factor -4*i**4 - 7 - 1 + 9*i**4 - m*i**2 + 13.
5*(i - 1)**2*(i + 1)**2
Let m(q) be the first derivative of q**5/5 + 3*q**4/2 + 8*q**3/3 - 3*q**2 - 9*q + 171. Factor m(d).
(d - 1)*(d + 1)*(d + 3)**2
Let 55*p - 6734*p**2 + 23*p + 3*p**3 + 48 + 13501*p**2 - 6734*p**2 = 0. Calculate p.
-8, -2, -1
Suppose -u + 2*w = 0, -u - 2*w - 15 = -7*w. Let j = 14 - u. Suppose -1 + 6*d**2 + d - 2 - j*d = 0. Calculate d.
-1/2, 1
Let c(l) = -l**3 - l**2 - l - 1. Let b(h) = -2*h**3 + 152*h**2 - 7804*h + 132650. Let i(t) = 5*b(t) - 5*c(t). Factor i(j).
-5*(j - 51)**3
Let n be (-1)/4 + 136/32. Solve x**5 + 13 - 2*x**n - 13 + x**3 = 0 for x.
0, 1
Let m(j) be the first derivative of -j**5/5 + 178. Let m(z) = 0. What is z?
0
Let w be ((-9)/36)/(2/12)*-2. Factor 0*o**3 + o + 2*o**w + o - 4*o**2.
2*o*(o - 1)**2
Suppose 2*f - 14 = 32. Let a = -14 + f. Factor 0*b**2 + a*b**2 - 4*b**4 + 2 + 5*b**4 + 7*b + 5*b**3.
(b + 1)**3*(b + 2)
What is w in -171/4*w**4 + 0 - 6*w + 93/2*w**3 + 35/4*w**5 + 11*w**2 = 0?
-2/5, 0, 2/7, 2, 3
Let r(y) = y**2 - 7*y + 28. Let g be r(8). Let k be ((-10)/6 - -1)*g/(-48). Factor -5/4*i**2 + 0 - i**3 - k*i - 1/4*i**4.
-i*(i + 1)**2*(i + 2)/4
Let w = 3128 - 12509/4. Solve 0 - 27/8*o**5 + 0*o**2 - 33/8*o**4 + 0*o - w*o**3 = 0.
-1, -2/9, 0
Let z(o) be the third derivative of o**7/1050 - o**6/300 - o**5/75 + o**4/60 + o**3/10 - 5*o**2 - 6. Factor z(t).
(t - 3)*(t - 1)*(t + 1)**2/5
Solve 0 + 1/4*s**2 + 12*s = 0.
-48, 0
Let n(t) be the first derivative of t**4/4 - 28*t**3/3 + 29*t**2/2 - 54*t - 70. Let m be n(27). Factor m - 4/3*l**4 + 2/3*l**3 + 2/3*l**5 + 0*l**2 + 0*l.
2*l**3*(l - 1)**2/3
Let x(z) = -z**2 + 12*z - 10. Let c be x(11). Let y be c/(12/10 + -1). Let -2*j**2 - 3*j + 0*j - 6 - y*j = 0. Calculate j.
-3, -1
Let s = 51 - 47. Let k be -2 + (-3)/(-9)*7. Factor 0 + k*y**s - 1/3*y**2 + 0*y**3 + 0*y.
y**2*(y - 1)*(y + 1)/3
Let g(f) = 2*f**4 - 14*f**2 - 6*f. Let b(x) = -5*x**4 + 43*x**2 + 17*x. Let v(m) = -2*b(m) - 7*g(m). Factor v(i).
-4*i*(i - 2)*(i + 1)**2
Let u(w) = -16*w - 3. Suppose 0 = -k - 0*k + t - 1, 0 = -k - 4*t - 1. Let v be u(k). Factor -v - s**5 + 13 - s**4.
-s**4*(s + 1)
Let o(k) be the third derivative of -k**5/15 + 2*k**4/3 + 14*k**3 + 56*k**2. Factor o(h).
-4*(h - 7)*(h + 3)
Let a(z) be the first derivative of 9*z**4/4 - 22*z**3 - 51*z**2/2 + 24*z + 148. Solve a(w) = 0.
-1, 1/3, 8
Let f be (-8)/(128/100) + 7. Let q(m) be the first derivative of 0*m + f*m**4 + m**2 - 5 + 5/3*m**3. Factor q(h).
h*(h + 1)*(3*h + 2)
Let n(z) be the second derivative of 0 - 6655/2*z**2 - 23*z - 55/4*z**4 + 1/4*z**5 + 605/2*z**3. Factor n(m).
5*(m - 11)**3
Let o = 5/18 + -1/2. Let k = 5/9 + o. Factor 1/3*t + 0 + 2/3*t**2 + k*t**3.
t*(t + 1)**2/3
Suppose 75*c + 39*c - 65*c = -94*c. Find h, given that c + 2/5*h**2 + 3/5*h**3 + 0*h**4 + 0*h - 1/5*h**5 = 0.
-1, 0, 2
Let b(q) = 50*q**2 + 4*q + 5. Let k be b(-2). Determine c, given that -197 + 2*c**2 - 2*c + k = 0.
0, 1
Determine h, given that 3/4*h**3 - 45*h**2 + 0 + 675*h = 0.
0, 30
Let b(n) = -2*n**2. Let k(l) = -l. Let f(c) = -b(c) - 4*k(c). Factor f(d).
2*d*(d + 2)
Let n(o) be the third derivative of 1/420*o**7 + 1/20*o**5 + 1/12*o**4 + 1/12*o**3 + 19*o**2 + 1/60*o**6 + 0 + 0*o. Suppose n(p) = 0. Calculate p.
-1
Suppose -p + 38 = 3*p - 2*z, 0 = 2*p + 2*z - 28. Suppose -p - 1 = -3*k. Let -4*t**2 + k*t**2 + 2*t + 0*t + 2*t**2 = 0. Calculate t.
-1, 0
Let k(f) = -f**3 + 15*f**2 + 16*f - 4. Let r be k(16). Let w = r - -7. Determine m, given that 2*m + 7*m - 9*m**w - 2 - 4 - m**2 + 7*m**2 = 0.
-1, 2/3, 1
Let y(l) be the second derivative of l**6/6 + l**5 + 500*l. Let y(b) = 0. What is b?
-4, 0
Find h such that -18*h**2 - 18*h**2 + 35*h**2 + 24 - 9 + 39 + 15*h = 0.
-3, 18
Let d(y) = -14*y**4 + 20*y**3 + 30*y**2 - 10*y + 2. Let w(c) = -14*c**4 + 20*c**3 + 34*c**2 - 9*c + 3. Let f(m) = -6*d(m) + 4*w(m). Factor f(t).
4*t*(t - 2)*(t + 1)*(7*t - 3)
Determine w so that -51*w**3 + 64*w - 280*w**2 - 44*w**4 - 324*w**2 + 3297 - 3225 - 340*w - 249*w**3 = 0.
-3, -1, 2/11
Let q = 3889/6720 + -7/960. Factor 26/7*v**2 + 0 + 18/7*v**4 + 40/7*v**3 + q*v.
2*v*(v + 1)**2*(9*v + 2)/7
Find n, given that 1182*n**2 - 2*n**3 + 8493890 + 9597555 - 2800699 - 257047*n + 24193*n = 0.
197
Let j(g) be the second derivative of 5*g**3/6 + 21*g**2 - 33*g + 1. Let h be j(-8). Determine n so that -2/3 + 1/3*n + 1/3*n**h = 0.
-2, 1
Let c(b) be the first derivative of b**4 + 40*b**3/3 + 24*b**2 - 288*b + 41. Determine h, given that c(h) = 0.
-6, 2
Let c(a) be the third derivative of a**7/280 - 19*a**6/240 - a**5/4 + 7*a**4/12 - 183*a**2. Factor c(d).
d*(d - 14)*(d + 2)*(3*d - 2)/4
Let m be 1916/8143*(-17)/(-6). Factor 1/3 + 1/3*l**2 + m*l.
(l + 1)**2/3
Let g(a) be the third derivative of -1/8*a**6 + 2*a**2 + 7/60*a**5 + 0*a - 2/15*a**3