e 1 = w, -z + 6 - 3 = v*w. Determine m, given that 2/3*m**2 + z*m + 0 + 1/3*m**3 = 0.
-2, 0
Suppose 71*p = 85*p - 28. Factor -2/15*c**p + 0 - 2/15*c + 2/15*c**3 + 2/15*c**4.
2*c*(c - 1)*(c + 1)**2/15
Let w(v) be the first derivative of v**5/130 - 7*v**4/156 + 2*v**3/39 + 13*v**2/2 + 12. Let d(i) be the second derivative of w(i). Solve d(s) = 0.
1/3, 2
Factor -10 - 5*w**3 + 20*w - 15/2*w**2 + 5/2*w**4.
5*(w - 2)*(w - 1)**2*(w + 2)/2
Factor 51*f - 8562 + 8688 + f**2 + 2*f**2.
3*(f + 3)*(f + 14)
Let v(d) = d**2 + d + 4. Let p be v(0). Let z(o) = -o + 23. Let n be z(7). Suppose 2*a**2 + 3 - 12*a**3 - 12*a + 0*a**2 + 3*a**p + n*a**2 = 0. Calculate a.
1
Let r = -281 + 281. Let l(d) be the first derivative of r*d**3 + 2/15*d**5 + 3 + 0*d + 0*d**2 - 1/6*d**4. Factor l(v).
2*v**3*(v - 1)/3
Factor 0 + 0*w + 18/7*w**5 + 4/7*w**3 + 0*w**2 + 22/7*w**4.
2*w**3*(w + 1)*(9*w + 2)/7
Let r(p) be the first derivative of 0*p**3 - 1/20*p**5 - 3*p - 2 + 0*p**4 + 0*p**2. Let q(b) be the first derivative of r(b). Find h, given that q(h) = 0.
0
Let s(z) = 18*z**3 + 3*z**2 + 9*z. Let p(r) = 4*r**3 - r**3 + 4*r + 6*r**3 - 4*r**2 + 5*r**2. Let d be (2/2 - 2) + 10. Let n(h) = d*p(h) - 4*s(h). Factor n(c).
3*c**2*(3*c - 1)
Suppose -6380 = 1196*n - 1486*n. Determine x, given that -5/2*x**4 - 6*x**2 + 0*x + n*x**3 - 7/2*x**5 + 0 = 0.
-3, 0, 2/7, 2
Let m(j) be the third derivative of j**5/330 + 7*j**4/132 - 6*j**3/11 + 6*j**2 - 5. Suppose m(s) = 0. What is s?
-9, 2
Suppose 0 = -6*v - 0*v + 54. Let c be 5/(-1 + 24/v). Factor -1/3*r**2 + 1/3*r**c + 0*r + 0.
r**2*(r - 1)/3
Factor -1817*r**2 - 128*r + 5732*r**2 - 2630 - 1290 + 5*r**4 - 64*r - 88*r + 280*r**3.
5*(r - 1)*(r + 1)*(r + 28)**2
Let y = -248 - -257. Let d be (y - (-11 + 17))*(-2)/(-48). Find j, given that 1/8*j**3 - d*j - 3/8*j**2 + 3/8 = 0.
-1, 1, 3
Let p = -118 + 120. Let z(i) be the first derivative of -1/4*i**4 + 1/2*i**2 + p + 1/3*i**3 + 0*i - 1/5*i**5. Find n such that z(n) = 0.
-1, 0, 1
Let v(x) be the third derivative of x**8/112 + 3*x**7/35 + 13*x**6/40 + 3*x**5/5 + x**4/2 + 7*x**2 - 6. Suppose v(y) = 0. What is y?
-2, -1, 0
Let d(m) be the third derivative of 1/8*m**4 + 0 + 19*m**2 + 1/10*m**5 + 0*m - 1/40*m**6 - m**3. Factor d(o).
-3*(o - 2)*(o - 1)*(o + 1)
Let q(h) be the first derivative of h**4/20 - 8*h**3/15 + 6*h**2/5 + 96. Factor q(v).
v*(v - 6)*(v - 2)/5
Let x(z) = -20*z**3 - 304*z**2 + 5172*z + 11556. Let m(r) = 14*r**3 + 302*r**2 - 5171*r - 11555. Let f(k) = -4*m(k) - 3*x(k). Factor f(v).
4*(v - 38)**2*(v + 2)
Let w(b) = 3*b**2 + 64*b + 396 + 0*b**2 + 2*b**2 - 145. Let o(p) = -10*p**2 - 129*p - 501. Let x(j) = 6*o(j) + 11*w(j). Factor x(r).
-5*(r + 7)**2
Suppose 0 = 14*x - 7*x - 742. Let 12*g + 60 + 5*g**2 - x + 50 = 0. What is g?
-2, -2/5
Let q(i) be the first derivative of -i**5/240 - i**4/48 + 43*i**2/2 + 4. Let z(j) be the second derivative of q(j). Determine g so that z(g) = 0.
-2, 0
Let o(u) be the first derivative of -u**7/84 + u**6/30 - u**5/40 + u - 12. Let s(m) be the first derivative of o(m). Factor s(p).
-p**3*(p - 1)**2/2
Factor 2/7*w**4 - 222/7*w**2 + 226/7*w - 76/7 + 10*w**3.
2*(w - 1)**3*(w + 38)/7
Suppose 3*p - 12 = 0, 3*l + 3*p = -l + 36. Factor 5*a**4 + 2*a**4 - 5*a**4 - 8*a + l*a**3.
2*a*(a - 1)*(a + 2)**2
Let k(r) be the third derivative of r**8/2240 - r**7/210 - r**4/3 + 3*r**2. Let o(d) be the second derivative of k(d). Solve o(h) = 0 for h.
0, 4
Suppose 42 = 3*p + 3*d, 31*p - 34*p = -2*d - 27. Let w(t) be the first derivative of 0*t**2 + 4/3*t**3 + 0*t + p - t**4. Suppose w(c) = 0. What is c?
0, 1
Suppose 189*r - 6*r - 366 = 0. Find g such that -16/5*g + 16/5 + 4*g**3 + 4/5*g**4 - 4/5*g**5 - 4*g**r = 0.
-2, -1, 1, 2
Let o(x) = -x**2 - 22*x + 98. Let w be 5*(2 + (-32)/10). Let i(k) = 6*k**2 + 111*k - 489. Let l(z) = w*i(z) - 33*o(z). What is d in l(d) = 0?
10
Let x(m) be the second derivative of -165*m**5/8 + 245*m**4/8 - 16*m**3 + 3*m**2 - 2*m + 19. Factor x(d).
-3*(5*d - 2)**2*(11*d - 1)/2
Let x be (-54)/(-21) + 8/(-14). Suppose -x*p + p + 3 = 0. Factor -7*k**3 + 8*k**3 + k**2 + k**2 + k**p.
2*k**2*(k + 1)
Let r = -229/14 + 118/7. Find t, given that 1/2*t + 1/2*t**2 - r - 1/2*t**3 = 0.
-1, 1
Suppose 0*b + 0 - 8*b**2 + 8/3*b**3 + 2/3*b**4 = 0. What is b?
-6, 0, 2
Let f(x) be the second derivative of -x**7/252 - 31*x**6/90 - 299*x**5/40 + 248*x**4/9 - 256*x**3/9 + 119*x - 1. Factor f(g).
-g*(g - 1)**2*(g + 32)**2/6
Let t(r) be the second derivative of 0*r**3 + 1/6*r**4 - 1/120*r**6 - 5*r - 2*r**2 + 0 + 0*r**5. Find s such that t(s) = 0.
-2, 2
Let -14 - 5*f - 11*f + 639*f**2 - 637*f**2 + 4*f = 0. What is f?
-1, 7
Factor 0 - 2/3*p**3 + 0*p - 4/3*p**2.
-2*p**2*(p + 2)/3
Let r be (-5 - 440/(-96))/(100/(-40)). Factor -1/3 + 1/2*q - r*q**2.
-(q - 2)*(q - 1)/6
Suppose 3*q - 4 = -u + 10, 0 = 5*u + q - 14. Solve 2 + 17*m**2 - 5 - 5*m**u + 9*m = 0.
-1, 1/4
Let a(u) be the third derivative of -u**9/15120 - u**8/6720 + u**7/252 - u**6/90 - 13*u**4/12 - 43*u**2. Let g(v) be the second derivative of a(v). Factor g(n).
-n*(n - 2)*(n - 1)*(n + 4)
Let o(r) = -r**2 + r + 1. Let b(c) = -8*c**2 + 41*c - 28. Let m(v) = -b(v) + 5*o(v). Factor m(f).
3*(f - 11)*(f - 1)
Let i(k) be the second derivative of -2*k**7/21 - 22*k**6/15 - 27*k**5/5 - 25*k**4/3 - 16*k**3/3 - 637*k + 1. Determine m so that i(m) = 0.
-8, -1, 0
Let c be -3*(-2 + 1 + (-6)/(-18)). Factor 4/5*x - 2/5 - 2/5*x**c.
-2*(x - 1)**2/5
Suppose 4*g = 4*w - 44, 5 = w - 23*g + 28*g. Let o(u) be the second derivative of 0 + 0*u**3 - 1/3*u**2 + w*u + 1/18*u**4. Solve o(l) = 0 for l.
-1, 1
Let l = -140 + 134. Let h be (2/l)/(3*14/(-189)). Factor -3/2*w**2 - h - 3*w.
-3*(w + 1)**2/2
Solve -3/2*t**2 + 0 - 21/8*t**3 + 9/2*t - 3/8*t**4 = 0 for t.
-6, -2, 0, 1
Let c = 245 + -4899/20. Let p(v) be the first derivative of -7 + 0*v**2 - 1/16*v**4 + 0*v - c*v**5 + 0*v**3. Factor p(w).
-w**3*(w + 1)/4
Suppose 13*o = 8*o - 30, o = -2*g - 2. Let 24/7*i + 150/7*i**4 + 144/7*i**g + 270/7*i**3 + 0 = 0. What is i?
-1, -2/5, 0
Let f(p) be the first derivative of -13*p**5 - 35/3*p**3 - 10/3*p**6 + 0*p - 5/2*p**2 - 75/4*p**4 + 6. Find z, given that f(z) = 0.
-1, -1/4, 0
Let g(n) be the second derivative of -2/5*n**2 + 1/30*n**3 + 0 + 13/120*n**4 - 46*n + 3/200*n**5. Factor g(i).
(i + 1)*(i + 4)*(3*i - 2)/10
Factor -1/6*g**2 - 20 + 31/3*g.
-(g - 60)*(g - 2)/6
Solve -29/4*h + 1/4*h**2 + 7 = 0 for h.
1, 28
Let x = -1173 + 3419/3. Let y = 36 + x. Factor 0 + 8/3*m**2 - 4*m**3 + y*m**4 - 2/3*m - 2/3*m**5.
-2*m*(m - 1)**4/3
Suppose 18 = 7*b + 60. Let v be (-433)/b + 1/(-6). Factor -v + 49 - 2*p**2 - 3*p**2 - 40*p - 57.
-5*(p + 4)**2
Suppose 5*r = -3*v - 14, -4*r = -7*r + 4*v + 9. Let k(h) = -h**2 - h - 1. Let i(t) = 12*t + 11. Let y(m) = r*k(m) + i(m). Factor y(c).
(c + 1)*(c + 12)
Suppose -1 = -g, 143*j - 146*j + 3*g = -3. Factor 1/4*o + 1/2 - 3/4*o**j.
-(o - 1)*(3*o + 2)/4
Let i = 9513 + -9511. Find m such that 0 + 1/2*m**i - m = 0.
0, 2
Suppose 7*p + 25 = 5*s + 3*p, -s = -3*p - 5. Let 21*b**3 + 155 + 105*b**2 + 228*b + 111*b**2 - s + 357*b = 0. What is b?
-5, -2/7
Let 18*s**4 - s**4 + 455*s**2 + 5 + 6*s**3 + 3*s**5 - 477*s**2 - 9*s = 0. What is s?
-5, -1, 1/3, 1
Let o(w) be the third derivative of 4*w**7/105 + 7*w**6/10 + 8*w**5/15 - 7*w**4/2 - 20*w**3/3 - 2*w**2 + 112. Let o(t) = 0. What is t?
-10, -1, -1/2, 1
Let n = 5/1319 + 2613/6595. Find o such that 2*o + n*o**2 + 8/5 = 0.
-4, -1
Let r(i) be the first derivative of i**7/1050 - i**5/150 + 2*i**3/3 + 9. Let l(p) be the third derivative of r(p). Factor l(m).
4*m*(m - 1)*(m + 1)/5
Let o(i) be the third derivative of -i**8/6720 - i**7/2520 + i**6/720 + i**5/120 - i**4/8 + 28*i**2. Let l(p) be the second derivative of o(p). Factor l(h).
-(h - 1)*(h + 1)**2
Let z(u) be the third derivative of 3*u**7/35 + 31*u**6/60 + u**5 + 2*u**4/3 + 30*u**2 - u. Suppose z(v) = 0. What is v?
-2, -1, -4/9, 0
Let f(s) = 3*s**2 + 48*s + 90. Let y(x) = -x**2 - x + 1. Let o(k) = -f(k) - 6*y(k). What is t in o(t) = 0?
-2, 16
Let l(k) = -k + 19. Let x be l(14). Suppose -x*t + 4*c = -36, 2*t - 3*c + 7*c + 8 = 0. Find i, given that i**3 + 2*i**2 - t*i**3 + 22*i**4 - 24*i**4 = 0.
-2, 0, 1/2
Factor -1/4*w**2 + 0 + 75/2*w.
-w*(w - 150)/4
Let a(u) = -11*u**2 - 120*u - 102. Let i(f) = -9*f**2 - 117*f - 102. Let x(h) = -6*a(h) + 7*i(h). Suppose x