(b) = 0.
-6, 5
Suppose -4423 + 4423 + 4*z**3 - 16*z**2 = 0. Calculate z.
0, 4
Factor -2/3*w - 2/9*w**2 - 4/9.
-2*(w + 1)*(w + 2)/9
Factor 0*v + 2/9*v**4 - 32/9*v**3 + 56/9*v**2 + 0.
2*v**2*(v - 14)*(v - 2)/9
Let r be 8/2 + (1 - 3). Suppose 5*m - 20 = -r*n + m, n - 7 = -m. Find b such that -b - 15*b + 12*b**3 + 4*b**3 + n*b**4 - 16 + 12*b**2 = 0.
-2, -1, 1
Let t = -73 + 73. Suppose 15*k = 16*k - 3. Factor 1/4*n**5 + t*n + n**4 + 0 + 5/4*n**k + 1/2*n**2.
n**2*(n + 1)**2*(n + 2)/4
Let q(t) = 5*t**5 + 11*t**4 + 6*t**3 - 4*t**2 - 9*t - 1. Let g(c) = c**5 + c**4 + c**2 + 1. Let a be 175/(-75) - (-1)/3. Let v(m) = a*g(m) + q(m). Factor v(j).
3*(j - 1)*(j + 1)**4
Let s be (-210)/18 - 84/(-7). Solve -2/3 + 2/3*q**2 + 0*q**4 - q - s*q**5 + 4/3*q**3 = 0 for q.
-1, 1, 2
Suppose 2*j + 26 = 5*c - 35, -5*j - 202 = 4*c. Let o be (j/(-15))/(15/90). Suppose -o*p**2 - 12*p**3 + 16/5 + 0*p = 0. What is p?
-1, -2/3, 2/5
Let a(u) be the second derivative of -u**6/30 + 3*u**5/20 + u**4/6 - 2*u**3 + 4*u**2 - 97*u. Factor a(q).
-(q - 2)**2*(q - 1)*(q + 2)
Let n(l) = 2*l + 9. Let f be n(5). Suppose 2*g = 3*x + f - 8, 3*x - 2 = g. Solve 3*i**2 - i**2 + 15*i**3 - g*i**3 = 0 for i.
-1, 0
Suppose -7*g + 2*g + 60 = 0. Suppose -15*d + 24 = -g*d. Factor 4*p - 7*p**2 - 5*p + d*p**2.
p*(p - 1)
Let f be ((-3)/1)/(-3)*19/(152/16). What is p in 0 - 15/4*p + 3/4*p**f = 0?
0, 5
Suppose -3*u - 2 = 4*o, 18*u = 19*u - 5*o - 12. Factor 1/4*v + 3/2 - 1/4*v**u.
-(v - 3)*(v + 2)/4
Let q(o) = 7*o + 59. Let c be q(-8). Let s(x) be the second derivative of x + c*x**2 + 3/2*x**3 + 0 + 1/4*x**4. Let s(k) = 0. What is k?
-2, -1
Solve -2/11*l**4 - 50/11*l + 2/11*l**3 + 26/11*l**2 + 24/11 = 0.
-4, 1, 3
Factor 526*t**2 + 1375*t**3 + 34320*t - 685*t**3 - 34848 - 688*t**3.
2*(t - 1)*(t + 132)**2
Let g(k) be the first derivative of 0*k**2 + 5 + 2/9*k**3 + 0*k. Find v such that g(v) = 0.
0
Let l be (-1*(-9 + -1))/2. Let n(s) be the second derivative of -s - 1/60*s**l + 0 + 1/6*s**4 - 2/3*s**3 + 4/3*s**2. Factor n(d).
-(d - 2)**3/3
Let r(f) be the second derivative of f**7/1260 - f**6/135 - f**5/60 + 3*f**4/2 - 10*f. Let c(j) be the third derivative of r(j). Factor c(v).
2*(v - 3)*(3*v + 1)/3
Let y(j) be the second derivative of j**6/15 - j**5/10 - 4*j**4/3 + 4*j**3 + 7*j - 3. Factor y(k).
2*k*(k - 2)**2*(k + 3)
Let o(a) be the second derivative of -a**6/600 + a**5/25 - 2*a**4/5 + 32*a**3/15 + 7*a**2/2 + 33*a. Let t(q) be the first derivative of o(q). Factor t(i).
-(i - 4)**3/5
Let l(q) be the third derivative of 2*q**5/15 - 181*q**4/12 + 15*q**3 - 3*q**2 - 12*q. Factor l(p).
2*(p - 45)*(4*p - 1)
Let t(q) be the first derivative of -2*q**3/15 - 72*q**2 - 12960*q - 394. Factor t(z).
-2*(z + 180)**2/5
Let g(a) be the second derivative of 0*a**3 + 0*a**5 + 0 + 1/9*a**2 + 21*a - 1/27*a**4 + 1/135*a**6. Factor g(t).
2*(t - 1)**2*(t + 1)**2/9
Suppose -3*c = -7*c. Suppose -4*t + c*t = -g - 9, 0 = -4*g - 3*t + 21. Factor 3*f**2 - 3*f**5 - 14*f**3 - f**4 + 17*f**g - 2*f**4.
-3*f**2*(f - 1)*(f + 1)**2
Let q be ((-4)/4)/(1/(-3)). Let a = q + 4. Factor -a*k**2 - 1 + k**2 + k**3 - 7 - 2*k**3 - 12*k.
-(k + 2)**3
Let o(c) be the third derivative of c**8/98 + 11*c**7/735 - c**6/420 + 28*c**2 + 8*c. Solve o(m) = 0.
-1, 0, 1/12
Factor -1/4*p**3 + 4*p**2 + 7/2 - 29/4*p.
-(p - 14)*(p - 1)**2/4
Let u(t) = -4*t**2 - 4*t + 2*t - 8*t**3 + 11*t**3. Let d be u(2). Factor -6/11*g**3 + 0*g + 10/11*g**d - 4/11*g**2 + 0.
2*g**2*(g - 1)*(5*g + 2)/11
Suppose -8 - 8 = -8*j. Factor 500 + 145*k**j - 280*k**2 + 140*k**2 + 36*k + 64*k.
5*(k + 10)**2
Let h(w) be the third derivative of w**6/480 + w**5/24 + w**4/3 + 4*w**3/3 + 2*w**2 - 1. Factor h(o).
(o + 2)*(o + 4)**2/4
Let r = 316 + -313. Let p(d) be the first derivative of -9/5*d**5 + 7 - 3/4*d**4 + 3*d**r + 3/2*d**2 + 0*d. Factor p(x).
-3*x*(x - 1)*(x + 1)*(3*x + 1)
Let f(o) be the second derivative of o**6/80 + 9*o**5/32 + 21*o**4/8 + 13*o**3 + 36*o**2 - 5*o - 16. Factor f(u).
3*(u + 3)*(u + 4)**3/8
Let m = 52 - 36. Let t be 7 - 12/(m/4). Determine j, given that 2*j**t + 2*j**2 - 3*j**5 - 8*j**4 - j**5 = 0.
-1, 0, 1/2
Let t(g) be the first derivative of 0*g**4 + 0*g**3 - 1/360*g**6 - 12 + 0*g**5 + 0*g + 7*g**2. Let c(u) be the second derivative of t(u). Factor c(v).
-v**3/3
Let i(f) = 2*f**3 + 5*f**2 - 4*f - 3. Let k be i(3). Let j = -84 + k. Determine z so that j - 4/11*z**3 + 2/11*z**2 + 2/11*z**4 + 0*z = 0.
0, 1
Suppose r - 1 = -h, 4 + 6 = r - 2*h. Suppose 5*m - m = 5*n - 16, r = 4*n - m. Suppose 0*o + 3/5*o**2 + n + 3/5*o**3 = 0. What is o?
-1, 0
Suppose -2368/7*l**4 - 944/7*l - 96/7 - 64*l**5 - 3176/7*l**2 - 4308/7*l**3 = 0. What is l?
-2, -3/4, -2/7, -1/4
Let k = -510 - -513. Let y(o) be the second derivative of 0 + 0*o**2 - 1/5*o**k - 4*o + 1/20*o**4. Let y(t) = 0. What is t?
0, 2
Let x(u) be the first derivative of u**3 + 3*u**2/2 - 199. Let x(h) = 0. Calculate h.
-1, 0
Suppose -35*j = -10*j. Let p(q) be the third derivative of q**2 + 0*q**5 + 0*q + 0*q**4 + 0*q**3 - 1/360*q**6 + j. Factor p(w).
-w**3/3
Suppose -5*s - 50 = -5*b, 3*s = -s - 4*b - 72. Let r be s/30 - 2*(-4)/12. Let -1/5*y + r*y**4 - 1/5*y**2 + 1/5*y**3 + 0 = 0. What is y?
-1, 0, 1
Let v(x) be the third derivative of 0*x**4 - 10*x**2 - 1/525*x**7 + 3 + 1/150*x**5 + 0*x**6 + 0*x + 0*x**3. Factor v(i).
-2*i**2*(i - 1)*(i + 1)/5
Let x(j) = j**3 + 3*j**2 - j - 4. Let g be x(-2). Suppose 10 - 8 + 3*o - g*o**3 + o**3 = 0. What is o?
-1, 2
Suppose 4*s = -2*l + 5*s + 128, 64 = l - 5*s. Factor -l*q**3 - 182*q**2 - 8 - 23*q**2 - 68*q + 45*q**2.
-4*(q + 2)*(4*q + 1)**2
Suppose 8*q = 5 + 11. Suppose 2*h - 3*f + 5 = 0, 5*h - 11 - q = -f. Factor 13/2*s**h + 1 + 11/2*s + 2*s**3.
(s + 1)*(s + 2)*(4*s + 1)/2
Let v(l) = 7*l**2 + 5*l - 13. Suppose 0 = -13*p - p + 70. Let t(r) = 6*r**2 + 4*r - 14. Let c(f) = p*t(f) - 4*v(f). Suppose c(x) = 0. What is x?
-3, 3
Suppose 46 = 11*x + 2. Let -32*d**3 - 10*d**2 + 20*d - x - 2*d**2 - 15*d**3 + 11*d**3 = 0. What is d?
-1, 1/3
Let c(m) = 0*m - 2*m - 37 + 39 + 4*m**2. Let p(d) = 5*d**2 - 2*d + 3. Let g(n) = 3*c(n) - 2*p(n). Factor g(a).
2*a*(a - 1)
Let i(g) be the third derivative of 841*g**5/570 - 29*g**4/114 + g**3/57 + 2*g**2 + 47. Suppose i(j) = 0. Calculate j.
1/29
Let f be (-7)/(-6)*(-24)/(-84). Solve 1/6 + 1/3*s - 1/6*s**4 + 0*s**2 - f*s**3 = 0 for s.
-1, 1
Let s(t) be the third derivative of 0*t**7 + 0*t + 0 + 0*t**3 + 1/30*t**6 + 0*t**4 + 0*t**5 + 6*t**2 - 1/84*t**8. Factor s(x).
-4*x**3*(x - 1)*(x + 1)
Let k be (-42)/(-357) - 162/(-357). Let r be ((-2)/4)/((-14)/4). What is w in k*w + r*w**2 + 3/7 = 0?
-3, -1
Let k(t) = -t**3 - 10*t**2 + 25*t + 22. Let g(u) = 2*u**3 + 10*u**2 - 25*u - 24. Let p(c) = -4*g(c) - 3*k(c). Factor p(r).
-5*(r - 2)*(r + 1)*(r + 3)
Let d(m) be the first derivative of -m**3 - 9*m**2/2 - 6*m - 44. Factor d(i).
-3*(i + 1)*(i + 2)
Let u(g) = 155*g**2 + 605*g. Let j(d) = -25*d**2 - 101*d. Let x(k) = 25*j(k) + 4*u(k). Solve x(p) = 0.
-21, 0
Factor 475*g + 529*g + 4*g**2 + 188*g + 88804.
4*(g + 149)**2
Let a(f) = -f**2 - 14*f - 18. Suppose -4*y + 21 - 57 = 0. Let j be a(y). Factor -13 + 3*t - 15 + j - 3*t**2 + t**3.
(t - 1)**3
Let c(j) = j - 2*j**2 + 1 - 2*j + j**2. Let q(z) = -10*z**2 + 50*z + 6. Let p(a) = 6*c(a) + q(a). Solve p(k) = 0.
-1/4, 3
Let q(c) be the third derivative of -c**7/42 + 3*c**6/8 - 29*c**5/12 + 65*c**4/8 - 15*c**3 - 4*c**2 + 9. Determine m, given that q(m) = 0.
1, 2, 3
Let w = 5 - -4. Factor w*q**2 + 3 - 2*q - 15*q**2 + 2*q + 3*q**4.
3*(q - 1)**2*(q + 1)**2
Let b(t) be the first derivative of -6/7*t + 4/7*t**2 - 2/21*t**3 - 8. What is i in b(i) = 0?
1, 3
Let j(y) be the first derivative of 4*y**3 + 6*y + 4 + 3/4*y**4 + 15/2*y**2. Suppose j(d) = 0. What is d?
-2, -1
Let a(j) be the first derivative of j**6/42 - 4*j**5/35 + 5*j**4/28 - 2*j**3/21 + 141. Factor a(h).
h**2*(h - 2)*(h - 1)**2/7
Let s(a) be the first derivative of -3*a**5/5 + 3*a**4/4 + a**3 - 3*a**2/2 + 83. Determine j, given that s(j) = 0.
-1, 0, 1
Let p(t) be the first derivative of -35*t**4/4 - 641*t**3/3 + 226*t**2 - 76*t + 583. Determine d so that p(d) = 0.
-19, 2/7, 2/5
Let d be 4 - (1 - -1) - (40/(-7))/(-5). Factor 6/7*m**4 + d*m - 6/7*m**2 + 0 - 6/7*m**3.
6*m*(m - 1)**2*(m + 1)/7
Factor -2*j**2 - j**2 + 3*j**2 - 4*j**2 - 176*j + 6*j**2 + 3872.
2*(j - 44)**2
Suppose 3*t - 