 0
Suppose 1514*f = -5*h + 1515*f + 18, 3*h + f = -2. Factor 3*t**h - 4 - 2*t + 5/2*t**3 + 1/2*t**4.
(t - 1)*(t + 2)**3/2
Let u be (-4)/(-18) - 24/108. Suppose 3*j = u, -3*k = 4*j - 0*j - 9. Find z such that -3*z**2 + k*z**2 + z - 2*z**2 - 3*z = 0.
-1, 0
Suppose -s - 24 = -5*l - 4, -3 = 4*l + 3*s. Let m = 2619/13 + -201. Solve m*v + 6/13*v**2 + 2/13*v**l + 2/13 = 0.
-1
Let g = 13732 - 96112/7. Factor 8/7*q + g*q**2 + 0.
4*q*(3*q + 2)/7
Let x(c) = -7*c**4 - 4*c**3 - 2*c**2 + 11*c + 5. Let j(f) = 8*f**4 + 3*f**3 + f**2 - 12*f - 6. Let i(t) = -5*j(t) - 6*x(t). Factor i(d).
d*(d + 2)*(d + 3)*(2*d - 1)
Let x(p) be the second derivative of p**6/1260 + p**5/105 + p**4/21 + 7*p**3 - p - 15. Let g(n) be the second derivative of x(n). Factor g(j).
2*(j + 2)**2/7
Let x(r) = 11*r + 56. Let g(z) = 17*z + 85. Let d(n) = -5*g(n) + 8*x(n). Let l be d(-6). Factor 0 + 0*t**2 + 0*t - 1/4*t**l + 0*t**3 + 0*t**4.
-t**5/4
Suppose 12 = l - 3*m, -2*m - 11 = -5*l + 10. Solve 0 + 18/5*u - 12/5*u**2 + 2/5*u**l = 0.
0, 3
Let s(g) be the first derivative of g**6/1620 + g**5/135 + g**4/27 + 4*g**3 + g**2 + 41. Let d(r) be the third derivative of s(r). Let d(c) = 0. What is c?
-2
Let b(g) = -2*g - 8. Let p be b(-8). Suppose 10*j - 6 = p*j. Factor 3*y**3 - 2*y**2 + j*y - y**5 - 3*y.
-y**2*(y - 1)**2*(y + 2)
Let u(i) = 2*i**2 - 75*i - 1643. Let p be u(53). Factor p + 1/4*j - j**2.
-j*(4*j - 1)/4
Suppose 2*r + 5*k = r + 22, 2*r + k - 8 = 0. Solve -2/5*n**4 + 0*n + 2/5*n**5 + 2/5*n**r - 2/5*n**3 + 0 = 0 for n.
-1, 0, 1
Suppose -4*c + 13 = -p - 2, p - 20 = -3*c. Let z(w) be the first derivative of -1 + 0*w**2 + 1/15*w**p + 0*w + 0*w**4 + 0*w**3. Factor z(f).
f**4/3
Factor -8*r**2 + 6*r**2 + 18*r + 1241 - 1277.
-2*(r - 6)*(r - 3)
Factor 64/9*v + 8/3 + 34/9*v**2 + 4/9*v**3.
2*(v + 2)*(v + 6)*(2*v + 1)/9
Let x(i) = 12*i**4 + 75*i**3 + 240*i**2 + 171*i. Let u(p) = 3*p**4 + 19*p**3 + 60*p**2 + 43*p. Let g(r) = 21*u(r) - 5*x(r). Factor g(n).
3*n*(n + 2)**2*(n + 4)
Let w(j) be the third derivative of 23*j**5/60 - 5*j**4/4 + 19*j**3/6 - 37*j**2. Let p(o) = 4*o**2 - 5*o + 3. Let y(g) = 34*p(g) - 6*w(g). Factor y(d).
-2*(d - 3)*(d - 2)
Let y(i) be the third derivative of -i**6/1200 + i**5/150 + i**4/3 + 16*i**3/5 + 679*i**2. Find t such that y(t) = 0.
-4, 12
Factor -242*k + 263 + 787 + 811*k - 2*k**2 - 3*k**2 + 476*k.
-5*(k - 210)*(k + 1)
Let m(l) = 2*l**2 - 14*l + 8. Let a be m(6). Let p be 140/30 + a/6. Let -2*k**2 + 8*k**3 - k**p - 4*k**3 + k**4 - 2*k**4 = 0. What is k?
0, 1
Let w(o) = 32*o + 96. Let s be w(-3). Let n(c) be the first derivative of s*c - 1/20*c**5 + 0*c**2 + 0*c**3 - 1/12*c**6 + 1/16*c**4 - 13. Factor n(r).
-r**3*(r + 1)*(2*r - 1)/4
Let f(s) = 64*s**3 - 150*s**2 - 102*s - 2. Let p(x) = -x**2 + x - 1. Let v = 19 + -18. Let y(o) = v*f(o) + 10*p(o). Find c such that y(c) = 0.
-1/4, 3
Suppose -33*u + 39*u = 0. Let o(d) be the second derivative of 1/50*d**5 - 3*d + u + 0*d**2 + 4/15*d**3 + 2/15*d**4. Find f such that o(f) = 0.
-2, 0
Let f = -811 + 813. Let i(y) be the first derivative of -3/13*y**f - 7 - 2/39*y**3 + 8/13*y. Factor i(c).
-2*(c - 1)*(c + 4)/13
Let j(a) = -265*a**4 + 3710*a**3 + 1370*a**2 + 55*a. Let s(z) = -19*z**4 + 265*z**3 + 98*z**2 + 4*z. Let v(i) = -4*j(i) + 55*s(i). Find f, given that v(f) = 0.
-1/3, 0, 18
Let y(a) be the first derivative of -a**6/360 + a**4/6 - 14*a**3/3 - 5. Let z(r) be the third derivative of y(r). Suppose z(j) = 0. Calculate j.
-2, 2
Let v be (-4)/(-18) + (5/2 - (-180)/648). Factor 0 - y**4 + 2/5*y**2 + 3/5*y**v + 0*y.
-y**2*(y - 1)*(5*y + 2)/5
Factor -10/7 - f - 1/7*f**2.
-(f + 2)*(f + 5)/7
Let a(t) be the second derivative of -t**6/150 - 222*t**5/25 - 24642*t**4/5 - 7294032*t**3/5 - 1214456328*t**2/5 + 383*t. Find z such that a(z) = 0.
-222
Suppose 5*n + 65 = 10*n. Let i = -11 + n. Find a such that -a**3 + 3*a**i + 2*a**2 - 7*a**2 = 0.
-2, 0
Let u(w) be the third derivative of 5/84*w**4 + 0 + 31*w**2 + 0*w - 1/210*w**5 - 2/7*w**3. Determine t so that u(t) = 0.
2, 3
Let v(z) = z**4 - 45*z**3 - 105*z**2 + 405*z - 284. Let n(u) = u**4 - 15*u**3 - 35*u**2 + 135*u - 94. Let m(r) = -7*n(r) + 2*v(r). Let m(s) = 0. What is s?
-3, 1, 2, 3
Let b(y) be the third derivative of -2*y**7/735 + 4*y**5/35 - 8*y**4/21 + 178*y**2. Suppose b(o) = 0. What is o?
-4, 0, 2
Suppose 1 = -29*y + 26*y + j, -5 = -3*y - 5*j. Let u be (-2)/3*3/(-7). Factor -1/7*o**5 + 0*o - 1/7*o**3 + y - u*o**4 + 0*o**2.
-o**3*(o + 1)**2/7
Let r = 2633 - 34213/13. Let -14/13*m**2 + r*m + 2/13*m**3 + 32/13 = 0. Calculate m.
-1, 4
Let k = 2143/1912 - -1/239. Factor 9/8*u**2 + k*u + 3/8 + 3/8*u**3.
3*(u + 1)**3/8
Let y(i) be the third derivative of i**5/80 + 25*i**4/16 + 625*i**3/8 - 2*i**2 - 447. Determine m, given that y(m) = 0.
-25
Let d(g) be the third derivative of -g**7/525 + g**6/60 - g**5/50 - g**4/12 + 4*g**3/15 + 15*g**2. Find v such that d(v) = 0.
-1, 1, 4
Let u(p) = 2*p**3 + 17*p**2 - 9*p - 2. Let h be u(-9). Let m be (h/10)/(4*3/(-12)). Factor -3/5*a + 0*a**4 - m*a**5 - 2/5*a**2 + 4/5*a**3 + 2/5.
-(a - 1)**3*(a + 1)*(a + 2)/5
Let j(x) be the first derivative of -x**4/16 - x**3/12 + x**2/8 + x/4 + 77. Solve j(p) = 0.
-1, 1
Let b(x) = -x**2 + 1. Let z(d) be the second derivative of 3*d**5/20 - 5*d**4/4 + 6*d**2 - 2*d. Suppose 33*r = 36*r - 36. Let m(p) = r*b(p) - z(p). Factor m(o).
-3*o**2*(o - 1)
Let w be 12/(-14) - 1539/(-399). Let r(l) be the second derivative of 0 + 1/54*l**4 + 2/9*l**w - 2*l + l**2. Factor r(g).
2*(g + 3)**2/9
Let n(z) = 70*z + 912. Let c be n(-13). Solve -c*k - 1/6*k**3 - k**2 - 4/3 = 0 for k.
-2
Let w(g) = -26 + 33 - 34 - 5*g - 8. Let h be w(-7). Find b, given that 1/2*b**2 + 0*b + h = 0.
0
Let f(n) = -n**3 - 3*n**2 + 10*n + 3. Let j be 8/(-4) + (0 - (2 + 1)). Let d be f(j). Factor 20/3*u**5 + 12*u**d + 0 + 0*u - 16*u**4 - 8/3*u**2.
4*u**2*(u - 1)**2*(5*u - 2)/3
Factor k**3 + 6*k**5 + k**5 - 12*k**2 + 4*k**4 + 28*k**4 + 12*k**3.
k**2*(k + 1)*(k + 4)*(7*k - 3)
Let g be -3*(14/(-6) - -2). Let f(h) = -h**3 - 9*h**2 - 7*h + 19. Let b be f(-8). Suppose 3 + b*m + g - 2*m + 3*m**2 + 2 = 0. What is m?
-2, -1
Factor -4/13*q**2 - 2/13*q**3 + 0 + 30/13*q.
-2*q*(q - 3)*(q + 5)/13
Suppose 0 = -2*d + 5*d - 21. Suppose -5*w = -17 + d. Determine b, given that 5*b**w - 2*b**3 + 2 - 5*b**2 + 2*b - 2*b**2 = 0.
-1, 1
Let l(b) = -b + 5. Let m be l(2). Suppose 2*q + i = -1 + m, 2*q + 2*i - 4 = 0. Factor -5*k**3 + 4 + q*k**3 + 0*k**3 + 5*k**2 - 8*k + 4*k**3.
-(k - 2)**2*(k - 1)
Factor 3/5*u**3 + 0 - 1/5*u**4 + 0*u + 4/5*u**2.
-u**2*(u - 4)*(u + 1)/5
Let j = -30 - -92/3. Suppose -12*z = -13*z. Factor -8*d**3 + 14/3*d**2 + z - j*d.
-2*d*(3*d - 1)*(4*d - 1)/3
Let c(j) be the second derivative of j**4/84 - 13*j**3/21 - 155*j**2/14 - 941*j. Solve c(h) = 0.
-5, 31
Let r be (8425/180)/5 - (-1 + 5). Let f = r - 46/9. Find m such that 1/4*m + 0 + f*m**2 = 0.
-1, 0
Let d be (1/3)/(13/52*10). Let h(v) be the second derivative of 0 - d*v**3 + 0*v**2 + 4*v - 1/10*v**4. Factor h(o).
-2*o*(3*o + 2)/5
Let k = -43 + 218/5. Find d, given that k*d**3 - 1/5*d**2 + 0 - 3/5*d**4 + 1/5*d**5 + 0*d = 0.
0, 1
Let l = -108 + 112. Let u(n) be the second derivative of -6*n + 0 + 0*n**3 - 1/6*n**4 + l*n**2. Find s, given that u(s) = 0.
-2, 2
Suppose 0 = -28*h + 561 - 505. What is k in 3/4*k + 27*k**4 + 7*k**h + 27/4*k**5 + 45/2*k**3 + 0 = 0?
-3, -1/3, 0
Suppose -36 - 60 = -6*n. Let p be (4/(-72))/((-1)/n). Factor -2/9*z + p*z**4 - 2/9*z**5 + 8/9*z**2 + 0 - 4/3*z**3.
-2*z*(z - 1)**4/9
Let z(k) be the second derivative of -4*k**5/25 - 2*k**4/5 - 2*k**3/5 - k**2/5 - 2*k + 214. Solve z(d) = 0 for d.
-1/2
Factor 3*g**4 - 27*g**3 - 17*g**3 + 3*g**4 - 12*g + 50*g**2.
2*g*(g - 6)*(g - 1)*(3*g - 1)
Suppose 7 = -3*c - 26. Let k(g) = -g**3 - 11*g**2 + 3. Let s be k(c). What is h in -3*h + 4*h - 9*h - 42*h**s + 40*h**2 = 0?
0, 2/7, 2/3
Let g(o) be the third derivative of -13/3*o**4 + 3*o**2 + 0*o - 3 + 338/3*o**3 + 1/15*o**5. Let g(p) = 0. Calculate p.
13
Let x(c) be the second derivative of 3*c**6/25 + c**5/2 + 7*c**4/10 + c**3/5 - 2*c**2/5 + 11*c - 1. Factor x(l).
2*(l + 1)**3*(9*l - 2)/5
Let y(z) be the first derivative of -3*z**4/28 - 13*z**3/21 + 2*z**2 - 12*z/7 + 51. Factor y(c).
-(c - 1)*(c + 6)*(3*c - 2)/7
Let m(g) = -3*g**2 - 4*g - 2. Suppose 48*z - 3 = 47*z. Let v(a) = -a**2 - a - 1. Let f(k) = 