7 - 4/7*u**2 - 5/7*u - 5/7*u**5 + 2/7*u**h = 0.
-1, 2/5, 1
Let q = -6/667 - -40711/2668. Let z = q - 293/20. Suppose 3/5*y**2 + z + 6/5*y = 0. Calculate y.
-1
Let g(t) = 2*t**3 + t**2. Let c be g(1). Let p(f) = f + 6. Let a be p(-4). Let o**2 + c*o + 3*o**2 - 2*o - a*o = 0. What is o?
0, 1/4
Factor -7/4*g**3 - 1/4*g**5 + 0 + 0*g + 5/4*g**4 + 3/4*g**2.
-g**2*(g - 3)*(g - 1)**2/4
Let a(n) be the second derivative of -n**6/40 + n**5/20 - 11*n**2/2 + 13*n. Let v(x) be the first derivative of a(x). Suppose v(p) = 0. Calculate p.
0, 1
Let u be (3/3 + -3)*-2. Factor 6*x**u + 32*x**2 + 0*x**4 - 2*x**4 + 448*x + 208*x**2 + 256 + 52*x**3.
4*(x + 1)*(x + 4)**3
Let y(j) = j**2 - j. Let r(d) = 6*d**2 + d. Let w(f) = -r(f) + 5*y(f). Find k such that w(k) = 0.
-6, 0
Let a(n) = n**2 + 44*n - 2880. Let l be a(36). Factor 1/8*f**5 - 9/4*f**4 + 0 - 27*f**2 + 27/2*f**3 + l*f.
f**2*(f - 6)**3/8
Suppose -5*p = -t - 10, -2*t - 3*t = 4*p - 8. Determine i, given that -6 + 3 + 0*i**2 + 11*i**2 + i**p + 9*i = 0.
-1, 1/4
Let a - 1/7*a**2 - 12/7 = 0. Calculate a.
3, 4
Let o = 266/85 - 52/17. Let y = 57/85 - o. Factor -2/5 - 1/5*w**2 + y*w.
-(w - 2)*(w - 1)/5
Let x = -7965 - -7968. Find a such that 0*a**2 + 0*a + 4/5*a**4 + 0*a**x + 0 = 0.
0
Let n(g) be the second derivative of g**6/180 - g**4/24 - g**3/18 + 117*g. Factor n(s).
s*(s - 2)*(s + 1)**2/6
Factor 456*h - 936*h - 5 + h**4 - 12*h**2 + 466*h - 2*h**3.
(h - 5)*(h + 1)**3
Let m = -47 + 73. Let k(a) = 2*a**2 + 6*a - 5. Let i(r) = -3*r**2 + 2*r**2 + 25*r + 10*r**2 - 29 + 8. Let n(g) = m*k(g) - 6*i(g). Factor n(z).
-2*(z - 2)*(z - 1)
Let i(a) be the second derivative of 169/6*a**4 + 4*a**2 + 0 + 11*a - 52/3*a**3. Factor i(u).
2*(13*u - 2)**2
Factor 0 + 156*g**4 + 60*g**5 + 234/5*g**2 + 687/5*g**3 + 27/5*g.
3*g*(g + 1)**2*(10*g + 3)**2/5
Let a(z) be the third derivative of 0*z**5 + 1/192*z**4 - 1/960*z**6 + 0 - 40*z**2 + 0*z**3 + 0*z. Factor a(v).
-v*(v - 1)*(v + 1)/8
Let f(u) be the first derivative of -5*u**6/6 - 6*u**5 + 20*u**4 - 10*u**3/3 - 75*u**2/2 + 40*u - 353. Let f(q) = 0. What is q?
-8, -1, 1
Solve 3*z**5 + 11*z**2 - 18*z**3 + 24*z - 77*z**4 + z**2 + 152*z**4 + 0*z**2 - 78*z**4 = 0.
-2, -1, 0, 2
Suppose -4*m + 3*l + 15 = 0, 11 = 5*m - 0*l + 4*l. Factor -2*o**2 + 3*o + 3*o**4 - 3*o**m - 5*o**2 + 4*o**2.
3*o*(o - 1)**2*(o + 1)
Factor 616*t + 88/3*t**3 + 2/3*t**4 + 294 + 1052/3*t**2.
2*(t + 1)**2*(t + 21)**2/3
Let n(q) be the first derivative of q**4/2 + 30*q**3 + 675*q**2 + 6750*q + 47. Solve n(z) = 0 for z.
-15
Let s be 8/(-28) - 112/(-49). Suppose 4*o - 4*i + 16 = 0, -4*o - 8 = -3*o - 2*i. Let o + 1/3*d**s - 1/3*d = 0. Calculate d.
0, 1
Let a(x) be the first derivative of x**6/3 - 2*x**5 + 7*x**4/2 - 2*x**3 + 13. Let a(n) = 0. What is n?
0, 1, 3
Let q(c) be the first derivative of -8*c**6/3 - 36*c**5/5 + 2*c**4 + 12*c**3 + 4*c**2 - 21. Let q(n) = 0. Calculate n.
-2, -1, -1/4, 0, 1
Suppose 0 = -5*w + 2*v + 29, -29 = -w - w - 5*v. Suppose w*o + 12*o = 95. Find h, given that 2/3*h**4 + 0*h**3 - 1/3*h - 2/3*h**2 + 0 + 1/3*h**o = 0.
-1, 0, 1
Let l be (-3)/(9/12) - (-32)/4. Let s(f) be the second derivative of 0 - 7/20*f**5 + 0*f**2 + 0*f**3 + 2*f + 2/15*f**6 - 1/6*f**l. Factor s(x).
x**2*(x - 2)*(4*x + 1)
Let u(w) be the third derivative of -w**5/90 + 5*w**4/36 - 81*w**2. Solve u(n) = 0 for n.
0, 5
Let u(j) = j**3 - 30*j**2 + 33*j - 114. Let p be u(29). Solve 1125/4*m**5 + 1425/4*m**4 + 5/4 - 75/2*m**p + 85/2*m**3 - 15/4*m = 0 for m.
-1, -1/3, 1/5
Let h be 0*14/56*(-1)/3. Let v(k) be the second derivative of -1/12*k**4 + 0*k**2 - 4*k - 1/3*k**3 + h. Solve v(f) = 0 for f.
-2, 0
Factor 4/3*f**3 - 4/3*f**2 - 20/3*f - 4.
4*(f - 3)*(f + 1)**2/3
Let h(w) = w + 21. Let g be h(-16). Factor -5*z**4 - 11 + g*z**2 - 3 + 14.
-5*z**2*(z - 1)*(z + 1)
Find n, given that 0 + 0*n - 1/12*n**4 - 13/6*n**3 - 4*n**2 = 0.
-24, -2, 0
Let x(c) be the first derivative of 4*c - 6 - 1/9*c**3 + 1/2*c**2 - 1/36*c**4. Let s(o) be the first derivative of x(o). Let s(j) = 0. Calculate j.
-3, 1
Let m(f) be the second derivative of -f**5/50 + 29*f**4/30 - 224*f**3/15 + 196*f**2/5 + 144*f. Factor m(y).
-2*(y - 14)**2*(y - 1)/5
Let z be (-1)/(-6)*(-6 + 555). Let f = -91 + z. Find k such that 0 + 1/2*k**3 - f*k + 1/2*k**2 - 1/2*k**4 = 0.
-1, 0, 1
Let z(b) be the second derivative of -1/40*b**5 + 3*b + 3/16*b**4 + 0 + 1/2*b**2 - 1/2*b**3. Let q(k) be the first derivative of z(k). Solve q(v) = 0.
1, 2
Let z(m) be the third derivative of m**5/60 - 7*m**4/8 + 24*m**2 + 5*m. Factor z(a).
a*(a - 21)
Suppose 0*k + 4*k = -5*g - 13, -26 = -2*k + 4*g. Suppose 3*u = 7*u - 12. Solve -p**4 + 0*p**3 + p**k + 0*p**u = 0.
0, 1
Factor -3/5*b**3 - 93/5*b**2 + 768/5 - 672/5*b.
-3*(b - 1)*(b + 16)**2/5
Find o such that -1/2*o**4 + 3/2*o**3 + 0 - o**2 + 0*o = 0.
0, 1, 2
Let n(w) be the third derivative of w**6/900 + w**5/90 + w**4/45 - 17*w**2. Factor n(c).
2*c*(c + 1)*(c + 4)/15
Let q be 10 + (-38)/4 - (-2)/(-4). Let j(b) be the second derivative of q - 4*b**2 + 1/2*b**4 - b - 1/10*b**5 + 0*b**3. Let j(v) = 0. What is v?
-1, 2
Let p be 7/(-14) - (-1)/2. Let x = p + 8. Factor -7*z**2 + 9*z**2 + x*z**2 - 4*z + 4*z**2.
2*z*(7*z - 2)
Let l(k) be the second derivative of k**4/28 + 23*k**3/7 + 1587*k**2/14 - 249*k. Factor l(s).
3*(s + 23)**2/7
Let q(l) be the first derivative of 9/7*l**2 - 32/21*l**3 + l**4 + 1/21*l**6 + 22 - 4/7*l - 12/35*l**5. Determine i so that q(i) = 0.
1, 2
Let w(a) be the third derivative of a**8/336 + a**7/42 + a**6/60 - 7*a**5/30 - a**4/8 + 3*a**3/2 - a**2 + 5. Factor w(o).
(o - 1)**2*(o + 1)*(o + 3)**2
Let v(c) be the first derivative of 4/5*c**5 + 0*c + 32/3*c**3 - 8*c**2 - 5*c**4 - 1. Find y such that v(y) = 0.
0, 1, 2
Let o(c) = -c**2 - 10*c + 2*c + 1 + 3*c + 6*c. Let m(g) = -2*g**4 + 10*g**2 + 18*g + 8. Let y(x) = 2*m(x) - 4*o(x). Factor y(b).
-4*(b - 3)*(b + 1)**3
Let a be 4/1 - 2076/168. Let p = 17/2 + a. Let 1/7 + 1/7*q**3 - 1/7*q - p*q**2 = 0. What is q?
-1, 1
Let d = 5 + 11. Let -4*g**2 - 32 - 14*g**2 - 30*g**2 - 2*g**4 - 64*g - d*g**3 = 0. What is g?
-2
Let d(s) be the second derivative of 2/3*s**4 - 2*s**3 - 27*s + 0*s**2 + 0 + 1/5*s**5. Factor d(h).
4*h*(h - 1)*(h + 3)
Let s(x) be the second derivative of x**5/140 - x**4/7 + 8*x**3/7 - 14*x**2 - 34*x. Let v(j) be the first derivative of s(j). Factor v(i).
3*(i - 4)**2/7
Let d(s) be the third derivative of s**5/60 + 11*s**4/24 + 211*s**2. Factor d(f).
f*(f + 11)
Let m = 9/715 - -5639/6435. Determine x so that -2/9*x**3 + 0 - m*x - 4/3*x**2 + 1/3*x**4 + 1/9*x**5 = 0.
-2, -1, 0, 2
Let f = -9089 - -9091. Factor -3/5*d**3 + 0 + 3*d**f - 12/5*d.
-3*d*(d - 4)*(d - 1)/5
Let c be (1 - 1) + 2 + 0. Suppose -17 = -5*w + 2*k, -3*w - 12 = -8*w - 3*k. Factor -7*j**2 - 15*j + w + 0*j**2 + 19*j**c.
3*(j - 1)*(4*j - 1)
Let i(h) = -12*h - 236. Let o be i(-20). Let k(x) be the second derivative of -1/6*x**o + 0*x**2 + 1/3*x**3 + 0 + 11*x. Factor k(s).
-2*s*(s - 1)
Let m(c) = c**2 + c + 2. Let g be m(-1). Factor 157*s + 1 - 153*s + g*s**2 - 4*s**3 - 2*s**4 - 1.
-2*s*(s - 1)*(s + 1)*(s + 2)
Let s(i) be the third derivative of i**5/210 + 5*i**4/21 - 163*i**2. Determine g, given that s(g) = 0.
-20, 0
Solve -32/9*l + 10/3 + 2/9*l**2 = 0.
1, 15
Let w(i) be the first derivative of -3*i**4/22 + 218*i**3/11 + 663*i**2/11 + 666*i/11 - 294. Determine r, given that w(r) = 0.
-1, 111
Let n(f) be the first derivative of f**6/27 + f**5/9 - f**4/12 - 8*f**3/27 + 2*f**2/9 - 74. Find d such that n(d) = 0.
-2, 0, 1/2, 1
Let o(a) be the third derivative of a**5/270 - 47*a**4/108 + 62*a**2 - 5. Factor o(k).
2*k*(k - 47)/9
Let h(b) = -5*b - 2. Let t be 2 + 6*2/(-4). Let r be h(t). Factor -34*c - 6*c**4 + r*c**5 + 34*c.
3*c**4*(c - 2)
Let k(c) be the third derivative of 0*c**3 + 0*c**4 - 1/3*c**5 + 26*c**2 + 2/9*c**6 + 0*c + 0 - 1/18*c**7 + 5/1008*c**8. Solve k(o) = 0.
0, 2, 3
Let f(w) be the third derivative of w**7/1575 + w**6/900 - w**5/50 - w**4/20 + 30*w**2 - 1. Factor f(x).
2*x*(x - 3)*(x + 1)*(x + 3)/15
Let m(k) = k**3 - 15*k**2 + 7*k - 4. Let p be m(13). Let o = p + 255. Let 8*a**o + 2/7*a**3 + 0*a - 4/7*a**2 + 0 = 0. Calculate a.
-2/7, 0, 1/4
Let h(p) be the first derivative of -p**5/660 - 7*p**4/264 + 4*p**3/33 - 16*p**2 + 45. Let i(t) be the second derivative of h(t). Factor i(o).
-(o - 1)*(o + 8)/11
Suppose 32/13*