- 9*h. Factor y(i).
(i - 1)**2*(i + 3)/4
Let o(x) be the third derivative of -x**5/30 + 25*x**4/6 - 625*x**3/3 + 287*x**2. Find l, given that o(l) = 0.
25
Let g(f) be the third derivative of 15*f**2 + 0 + 0*f**3 + 1/180*f**6 - 1/30*f**5 + 0*f + 1/18*f**4. Suppose g(x) = 0. What is x?
0, 1, 2
Let o(f) be the first derivative of 3*f**3/5 + 16*f**2/5 + 28*f/5 + 363. Factor o(c).
(c + 2)*(9*c + 14)/5
Let s(k) = -11*k**4 + 19*k**3 - 7*k**2 - 13*k. Let a(x) = 32*x**4 - 58*x**3 + 19*x**2 + 41*x. Let u(p) = 6*a(p) + 17*s(p). Determine n, given that u(n) = 0.
-1, 0, 1, 5
Let i(j) be the second derivative of -3/20*j**5 + 2*j**4 - 10*j**3 + 0 + 24*j**2 - 16*j. Factor i(a).
-3*(a - 4)*(a - 2)**2
Let t(a) = -a**3 + 7*a**2 - 9*a + 4. Let f be t(5). Determine r, given that 277*r**2 - 2*r**3 - 265*r**2 - r**3 - f*r = 0.
0, 1, 3
Let p(r) be the second derivative of -r**7/14 - 11*r**6/120 + 2*r**5/15 + r**4/6 - 13*r**2/2 - 8*r. Let a(d) be the first derivative of p(d). Factor a(i).
-i*(i + 1)*(3*i - 2)*(5*i + 2)
Let c = -265 + 528. Let p = -263 + c. Factor p - 2/5*i**2 - 2/5*i.
-2*i*(i + 1)/5
Let a(h) be the second derivative of h**4/16 - 77*h**3/4 + 17787*h**2/8 - h + 99. Factor a(s).
3*(s - 77)**2/4
Factor 1/5*i**2 + 7/5*i + 12/5.
(i + 3)*(i + 4)/5
Let q(n) be the first derivative of n**4/48 + 2*n**3/3 + 8*n**2 + 4*n + 1. Let j(r) be the first derivative of q(r). Factor j(h).
(h + 8)**2/4
Let x(h) = h + 12. Let b be x(-9). Suppose -4*c + 3*c = 0, 2*u - 6 = 5*c. What is t in 4*t - b*t - 1 - u*t - t**2 = 0?
-1
Let f be (-1*(-2 + 3))/(7409/(-279) - -26). Factor 0 - 3*o**3 + f*o**2 + 6/5*o.
-3*o*(o - 1)*(5*o + 2)/5
Factor -17*c**2 - 12*c - 9*c**2 + 0 + 27*c**2 - 13.
(c - 13)*(c + 1)
Let x be -2*3/1*(-18)/54. Let u(p) be the first derivative of 6*p - 10 - 3/2*p**x - p**3. What is w in u(w) = 0?
-2, 1
Let f(g) = 2*g**2 - g + 2. Let u(w) = -9*w**2 - 13*w - 4. Let n(z) = -2*f(z) - u(z). What is c in n(c) = 0?
-3, 0
Let x(o) be the second derivative of o**4/4 - 15*o**3/2 - 24*o**2 + 3*o - 4. Suppose x(b) = 0. What is b?
-1, 16
Let p = -43 + 45. Let b be -1*(0 - 2) + 0. Factor i**3 + 5*i + 2 + 10*i**b - 3*i**p - 3*i**2.
(i + 1)**2*(i + 2)
Let b be (215/(-172))/((-4)/((-144)/(-15))). Let p be (-1 + 3)*(-6)/(-36). Factor -2/3*m**2 + 0 + p*m**b - m.
m*(m - 3)*(m + 1)/3
Let g(x) = 41*x - 19. Let r(q) = 19*q - 9. Let j(c) = -6*g(c) + 13*r(c). Let b be j(5). Determine a so that 4*a - a**3 + 0 + 2*a**b - 1/2*a**4 = 0.
-2, 0, 2
Let t(i) = -i**3 + i**2 - 1. Let k be 15/(-2)*224/70. Let l(n) = -73*n**3 + 145*n**2 - 88*n + 24. Let d(h) = k*t(h) - 3*l(h). Find y such that d(y) = 0.
4/9, 1
Suppose 3*f + 4*s = 4, 0 = 3*f + 43*s - 38*s - 5. Factor 0 + 0*b**2 + f*b + 2/3*b**3 + 2/21*b**4.
2*b**3*(b + 7)/21
Let h(p) be the second derivative of 1/8*p**4 - p - 1/20*p**5 + 1/56*p**7 + 1/24*p**3 + 0 - 1/4*p**2 - 1/30*p**6. Solve h(y) = 0.
-1, -2/3, 1
Factor -4*o**5 - 1247*o**2 - 28*o**4 + 1247*o**2 - 24*o**3.
-4*o**3*(o + 1)*(o + 6)
Let j(u) be the second derivative of -u**4/96 - 29*u**3/24 - 841*u**2/16 + 6*u + 2. Factor j(h).
-(h + 29)**2/8
Let c(u) = -6*u**3 - 15*u**2 - 24*u - 15. Suppose -16 = -5*n - 6. Let t = -5 + n. Let q(i) = i**3 + 1. Let p(r) = t*q(r) - c(r). Find y, given that p(y) = 0.
-2, -1
Let y(p) be the first derivative of -p**7/420 + p**6/180 + p**5/30 - 7*p**3 - 31. Let v(k) be the third derivative of y(k). Determine a, given that v(a) = 0.
-1, 0, 2
Let x(y) be the second derivative of -13*y + 5*y**2 - 5/12*y**4 + 0 - 5/6*y**3. Factor x(p).
-5*(p - 1)*(p + 2)
Let t(r) be the third derivative of r**7/70 + r**6/10 + r**5/4 + r**4/4 - 2*r**2 + 64*r. Let t(q) = 0. What is q?
-2, -1, 0
Let u(f) = f. Let r be u(2). Factor -v**5 - 2*v - 6*v**3 + 50 + 4*v**r + 4*v**4 + v - 50.
-v*(v - 1)**4
Let f = 1814419/35 - 51857. Let m = 118/7 + f. Factor -m*k**4 + 0 + 0*k**3 + 2/5*k**2 + 0*k.
-2*k**2*(k - 1)*(k + 1)/5
Let x = -235311/5 - -47070. Find h such that 12/5 + 3/5*h**4 - 36/5*h + x*h**2 - 18/5*h**3 = 0.
1, 2
Let v(a) = a**2 + 5*a + 9. Let f be v(-6). Let n be 63/15 + (-8)/(-10). Determine b, given that 285*b**n + 135*b**4 - 181*b**3 + 12*b + 4*b**3 + f*b**5 = 0.
-1, -1/4, 0, 2/5
Let o = -1339/51 + 452/17. Factor 0 + 1/3*j + 1/3*j**2 - 1/3*j**3 - o*j**4.
-j*(j - 1)*(j + 1)**2/3
Factor -32 + 20*s**2 - 158*s + 106*s - 104*s.
4*(s - 8)*(5*s + 1)
Let a(u) be the first derivative of 4*u**3/3 + 36*u**2 + 128*u - 64. Factor a(b).
4*(b + 2)*(b + 16)
Let u be 4*1 + 1435/(-420). Let n(a) be the first derivative of -3/2*a**2 - a - 6 + u*a**3. Factor n(d).
(d - 2)*(7*d + 2)/4
Factor -26 + 8*r**2 + 7 + 2 + 2 + 7 - r**3 + r.
-(r - 8)*(r - 1)*(r + 1)
Suppose -5*c + 21 - 51 = 0. Let a(g) = 9*g**2 + 7*g - 2. Let k(r) = -5*r**2 - 4*r + 1. Let x(z) = c*a(z) - 11*k(z). Let x(i) = 0. Calculate i.
-1
Factor 1/7*o**3 + 5/7*o**2 + 0 - 1/7*o**4 + 3/7*o.
-o*(o - 3)*(o + 1)**2/7
Solve -18*t**3 + 3*t**5 + 3618*t - 3618*t + 15*t**4 = 0 for t.
-6, 0, 1
Suppose 175*o - 126*o = 0. Let s(a) be the second derivative of 4/5*a**2 - 2/3*a**3 - 6*a + o + 2/15*a**4. Determine p so that s(p) = 0.
1/2, 2
Let d(c) be the second derivative of 0*c**2 + 3*c + 2/9*c**4 - 1/25*c**6 - 4/45*c**3 - 7/150*c**5 + 0. Let d(x) = 0. Calculate x.
-2, 0, 2/9, 1
Let q be -4 + -1 - ((-22287)/(-68))/(-57). Find k such that 0*k - 9/8*k**5 + 0 + q*k**4 - 1/8*k**3 + 0*k**2 = 0.
0, 1/3
Let l(a) be the second derivative of 5*a**4/12 + 25*a**3 + 1125*a**2/2 + 3*a - 108. Factor l(r).
5*(r + 15)**2
Let i(k) be the second derivative of -3*k + 0 + 1/18*k**4 - 2/45*k**5 + 0*k**3 + 1/2*k**2. Let a(u) be the first derivative of i(u). What is p in a(p) = 0?
0, 1/2
Suppose -2197/5 - 39/5*q**2 - 1/5*q**3 - 507/5*q = 0. Calculate q.
-13
Let y(j) be the second derivative of -j**5/420 + j**4/28 - 5*j**3/42 + 27*j**2/2 - j. Let o(d) be the first derivative of y(d). Solve o(w) = 0.
1, 5
Let o be 4 + -2 + (2 - -1). Let -2*q**5 - 8*q**2 + q**4 + 0*q**o + 5*q**4 = 0. Calculate q.
-1, 0, 2
Suppose -4*d = -3*j - 9*d - 176, 3*d - 225 = 4*j. Let s = j + 115/2. Let s*k**4 + 3/2*k**3 + 0 + 1/2*k + 3/2*k**2 = 0. Calculate k.
-1, 0
Determine s, given that -15/2*s + 9*s**3 + 6*s**4 - 3/2*s**5 - 6*s**2 + 0 = 0.
-1, 0, 1, 5
Suppose 2*n + 4 = 2*z + 12, -3*z - 4 = n. Let m be n/6*(2 + 1). Factor 3 - q**3 + m + q**2 - 4.
-q**2*(q - 1)
Let y(o) be the first derivative of 8 + 16*o**2 + 3*o - 3*o - 81*o**5 + 48*o**3 - 250*o**6 - 179*o**5 - 30*o**4. Determine g so that y(g) = 0.
-2/5, 0, 1/3
Let c be (-3*(-10)/135)/(48/108). Factor c*i**2 - 1 + 1/2*i.
(i - 1)*(i + 2)/2
Let x(t) = -t**2 - 10*t + 4. Let r be x(-10). Suppose z**4 + 102*z**3 - 105*z**3 - 4*z**r = 0. What is z?
-1, 0
Let k(v) be the second derivative of -v**8/30240 + v**7/2835 + 5*v**4/2 - 5*v. Let x(n) be the third derivative of k(n). What is s in x(s) = 0?
0, 4
Let s be (-1 - (-4 - -6)) + 7. Find z such that -2*z**2 - 12*z**3 + z**5 - 12*z**s - 3*z**5 - 2*z**2 - 2*z**5 = 0.
-1, 0
Suppose 4*g = -l + 14, -62*g + 61*g + 1 = -l. Suppose 12/7*p + 20/7*p**l + 0 - 8/7*p**5 - 4/7*p**3 - 20/7*p**4 = 0. Calculate p.
-3/2, -1, 0, 1
Suppose 10 = 4*v - 18. Suppose 4*p = v*p. Factor 0*l**2 - 2/7*l**3 + 0*l + 2/7*l**4 + p.
2*l**3*(l - 1)/7
Let l(f) be the second derivative of -f**10/7560 + f**9/3780 + f**8/840 + 5*f**4/3 - 21*f. Let k(h) be the third derivative of l(h). Factor k(n).
-4*n**3*(n - 2)*(n + 1)
Let y(h) be the first derivative of -5*h**4/4 - 5*h**3/3 + 5*h**2 + 58. Factor y(q).
-5*q*(q - 1)*(q + 2)
Let r(y) be the third derivative of -y**5/48 - 67*y**4/96 - 13*y**3/12 - 86*y**2. Factor r(j).
-(j + 13)*(5*j + 2)/4
Factor 45 + 10 + 3*n + 0*n - 23 + n**2 + 30*n.
(n + 1)*(n + 32)
Suppose -8 = -4*v + 3*f, 0*v + 10 = 5*v - 3*f. Determine h, given that 1 + 3 - 4*h**2 + 0*h**v + 0 = 0.
-1, 1
Let a(d) be the third derivative of -d**5/360 + 19*d**4/144 - 4*d**3/3 + 177*d**2 - 2*d. Factor a(s).
-(s - 16)*(s - 3)/6
Let w(g) be the second derivative of -g**4/6 + 8*g**3/3 - 7*g**2 + 13*g + 5. Factor w(v).
-2*(v - 7)*(v - 1)
Factor 3*d**3 - 2*d**4 + 100*d + 142*d**2 - 4*d**3 - 232*d**2 + 25*d**3.
-2*d*(d - 5)**2*(d - 2)
Let t(b) be the second derivative of -b**5/100 - b**4/12 + b**3/30 + b**2/2 - 224*b - 1. Solve t(c) = 0 for c.
-5, -1, 1
Suppose -5*r = 0, -2*t + 3*r + 5 + 1 = 0. Find m such that -36*m - 3*m**4 + 24*m**2 + 14 + 3*