h(m) = 0.
-1, 1, 18
Let v(i) = -i**3 + 13*i**2 + 15*i - 9. Let f be v(14). Suppose -6350 = -5*z + 2*j + j, 0 = f*z + 2*j - 6325. Factor 1258*c - z*c + 7*c**2 - 4*c**2.
3*c*(c - 3)
Let q be (-32)/40*1*5/(-2). Suppose -4*b - 5*z + 14 = -3*z, q*b - z = 5. Factor 1/4*s**4 + 0*s + 0 - 5/4*s**b + s**2.
s**2*(s - 4)*(s - 1)/4
Determine f so that -85/2*f - 83/2*f**2 + f**3 + 0 = 0.
-1, 0, 85/2
Let x(l) = 1663*l + 68186. Let r be x(-41). Let -55/3*c**2 + 20*c**4 + 65/6*c - 5/3 - 15/2*c**5 - 10/3*c**r = 0. Calculate c.
-1, 1/3, 1, 2
Suppose 36 = -5*c + 3*x, 23*c + 9 = -x + 95. Factor 0 - 26/3*a**2 - 22/3*a**c - 4/3*a.
-2*a*(a + 1)*(11*a + 2)/3
Let x(p) be the third derivative of -1/570*p**5 + p - 148*p**2 - 1/228*p**4 + 0 + 2/19*p**3. Factor x(v).
-2*(v - 2)*(v + 3)/19
Let t be (-16 - -14) + 1/(3/18). Factor -29*b**4 - 5*b**3 + 23*b**3 - 15*b**2 + 26*b**t.
-3*b**2*(b - 5)*(b - 1)
Let t(q) be the second derivative of -q**4/3 + 112*q**3/3 - 686*q**2 + 2804*q. Find x, given that t(x) = 0.
7, 49
Let t(z) = 30*z**2 + 714*z - 728. Let q(u) = 128*u**2 + 2857*u - 2913. Let i(x) = -4*q(x) + 18*t(x). Suppose i(v) = 0. Calculate v.
-363/7, 1
Let v = -2 - -1. Let r(a) = a**2 - 1. Let m(g) = 8*g**2 - 12. Let x be ((-48)/10)/((-70)/175). Let i(j) = v*m(j) + x*r(j). What is d in i(d) = 0?
0
Let r(a) be the first derivative of a**4/4 + 7*a**3/3 + 49*a**2/8 - 923. Determine k, given that r(k) = 0.
-7/2, 0
Let n(v) be the third derivative of -v**7/1050 + 17*v**6/600 - 77*v**5/300 + 127*v**4/120 - 11*v**3/5 - 90*v**2 + 13. Determine w, given that n(w) = 0.
1, 2, 3, 11
Let q(k) = -10*k + 18. Suppose i = -v + 10, -5*i = 5*v - 4*i - 46. Let t(m) = m - 66 - 16 - v + m**2 + 48*m. Let n(y) = 11*q(y) + 2*t(y). What is c in n(c) = 0?
2, 4
Let c(y) be the third derivative of y**5/390 + 5*y**4/52 + 44*y**3/39 + 2*y**2 - 280. Factor c(n).
2*(n + 4)*(n + 11)/13
Let j(o) be the third derivative of o**5/15 - 321*o**4 + 618246*o**3 + 30*o**2 + 21*o - 3. Factor j(g).
4*(g - 963)**2
Let t be 6/15 + 32929/85. Let u = t - 387. Find a, given that -u - 2/5*a + 2/5*a**2 = 0.
-1, 2
Suppose 3*w - 4*z - 59 = 185, z = 5. Let x = 88 - w. Determine b, given that -94*b**5 + 3*b**2 - 4*b**3 + 95*b**5 - 3*b**4 + 5*b**3 + x*b**3 - 2*b = 0.
-1, 0, 1, 2
Let z(c) be the third derivative of c**6/810 - c**5/90 - 13*c**3/3 - 60*c**2. Let s(r) be the first derivative of z(r). Find w, given that s(w) = 0.
0, 3
Let p = 78 - 76. Determine v, given that -4*v + 5*v**4 - 6 + 60*v - 56*v**3 - 56 + 10 + 48*v**p - v**4 = 0.
-1, 1, 13
Let w(n) be the second derivative of 17/10*n**3 + 13/5*n**2 - 1/100*n**5 + 2/5*n**4 - 27*n + 0. Find q such that w(q) = 0.
-1, 26
Let c(n) be the first derivative of -n**7/21 + 14*n**6/15 - 61*n**5/10 + 14*n**4 - 12*n**3 - 27*n - 78. Let q(i) be the first derivative of c(i). Factor q(p).
-2*p*(p - 6)**2*(p - 1)**2
Let f(u) = 15*u**2 + 15*u - 25. Suppose 0 = 4*p - p + 78. Let q = p - -1. Let r(w) = 2*w**2 + 2*w - 3. Let h(y) = q*r(y) + 3*f(y). Factor h(i).
-5*i*(i + 1)
Suppose 3*a - 2*x - 2 = 0, -3 = -4*a - 13*x + 16*x. Let u(b) be the first derivative of b**4 + 0*b**2 + 0*b - 2 + 2/5*b**5 + a*b**3. Find n such that u(n) = 0.
-2, 0
Let r(g) be the third derivative of g**7/70 - g**6/2 + 89*g**5/20 - 35*g**4/4 + 1264*g**2 - 2*g - 1. Factor r(b).
3*b*(b - 14)*(b - 5)*(b - 1)
Let t = 174747738 - 392133887341/2244. Let c = -1/204 + t. Find s such that -432/11 + 34/11*s**3 + 216/11*s + 2/11*s**4 + c*s**2 = 0.
-6, 1
Suppose -5*l - 5*l + 2280 = 0. Suppose 11*m + 8 = l. Factor -25*d - m*d**2 - d**3 - 2*d**3 - 2*d**3 - 10.
-5*(d + 1)**2*(d + 2)
Let l(r) = r**2 + 25*r + 144. Let b be l(-16). Let i(q) be the second derivative of 0 + 1/15*q**5 - 3*q + 0*q**4 + b*q**2 - 2/9*q**3. Factor i(w).
4*w*(w - 1)*(w + 1)/3
Let t(r) be the second derivative of -5*r**7/231 + r**6/5 - 3*r**5/55 - 34*r**4/33 - 8*r**3/11 + 614*r. Find z, given that t(z) = 0.
-1, -2/5, 0, 2, 6
Solve -38/5*x + 0 + 2/5*x**4 - 42/5*x**3 + 78/5*x**2 = 0.
0, 1, 19
Let b be (-2)/5 + 44/10. Suppose 2*q - 12 = -b*q. Suppose -8*l**q + l**3 - 10*l**2 + l**3 - 2*l**4 + 20*l**2 - 2*l**5 = 0. What is l?
-1, 0, 1
Let x(c) be the third derivative of c**6/30 + 14*c**5/15 - 37*c**4/2 + 120*c**3 - 3853*c**2. What is m in x(m) = 0?
-20, 3
Let o(s) be the third derivative of -129*s**2 + 0*s**3 + 0*s - 1/780*s**6 + 0 - 1/195*s**5 + 0*s**4 + 1/2184*s**8 + 2/1365*s**7. Solve o(w) = 0.
-2, -1, 0, 1
Let i(c) be the first derivative of 2*c**6/3 + 32*c**5/5 + 20*c**4 + 64*c**3/3 + 1069. Factor i(u).
4*u**2*(u + 2)**2*(u + 4)
Suppose 2*t + 122 = 4*a, 87 = a + 3*a + 5*t. Let h be (14/a)/((-2)/(-20)). Solve -43*i + 2*i**4 + 39*i - i**2 - h*i**2 = 0 for i.
-1, 0, 2
Find w, given that -32/3 + 22/9*w**3 + 8/9*w + 2/9*w**4 + 64/9*w**2 = 0.
-6, -4, -2, 1
Find y such that 0 - 40/7*y - 2/7*y**3 + 24/7*y**2 = 0.
0, 2, 10
Let x(o) = -3*o**3 - 3*o**2 - 20*o - 20. Let m be x(-1). Let a(i) be the third derivative of -1/15*i**5 + 1/6*i**4 + 2*i**2 + 0 + 0*i**3 + m*i. Factor a(k).
-4*k*(k - 1)
Let a(n) = 29*n**2 - 461*n + 931. Let m(p) = 6*p**2 + p - 1. Let b(c) = a(c) - 5*m(c). Factor b(r).
-(r - 2)*(r + 468)
Factor 117/2 + 1/2*b**2 - 49/4*b.
(b - 18)*(2*b - 13)/4
Solve 534*u**2 - 1161*u**2 - 18 - 384*u + 438*u**2 + 6 = 0.
-2, -2/63
Let y be (-78)/(-325)*300/9. Factor 1/2*v**2 - 3*v - y.
(v - 8)*(v + 2)/2
Let l(t) be the third derivative of 7*t**6/24 + 19*t**5/2 - 145*t**4/8 - 85*t**3/3 + 3518*t**2. Factor l(c).
5*(c - 1)*(c + 17)*(7*c + 2)
Let g(n) be the first derivative of -n**4/2 - 53*n**3/4 + 5*n**2/2 + 2014. Factor g(o).
-o*(o + 20)*(8*o - 1)/4
Let y = 4159284/7 + -594183. Factor 8/7 - y*q**2 - 23/7*q.
-(q + 8)*(3*q - 1)/7
Let g = 96 - 90. Let p = g - 3. Factor -12 - 16*c + 16*c**p - 6*c**3 + 8*c**2 + 6*c**3 + 7*c**4 - 3*c**4.
4*(c - 1)*(c + 1)**2*(c + 3)
Suppose g + 2 = z + 6, -8 = -2*g. Suppose 2452*m - 2436*m = z. Find i, given that m + 1/5*i**2 + 9/5*i = 0.
-9, 0
Let v be 28/(-8) + (-927)/90 + 14. Suppose 0*c**2 + 1/5*c**4 + 0 + 0*c + v*c**3 = 0. What is c?
-1, 0
Factor 1163141/2*t + 3485689/6 + 1/6*t**3 + 1245/2*t**2.
(t + 1)*(t + 1867)**2/6
Let h = 283/114 - 69/38. Let o be ((-6)/(-9)*3)/(7 + -1). Factor -h*r + o*r**2 + 0.
r*(r - 2)/3
Determine o so that 574*o - 3362/5 + 474/5*o**2 + 18/5*o**3 = 0.
-41/3, 1
Let j(h) = -6*h**3 - 10*h - 44 - 20*h + 3*h**2 + 5*h**2. Let c(r) = -5*r**3 + 9*r**2 - 31*r - 45. Let n(s) = -5*c(s) + 4*j(s). Solve n(d) = 0 for d.
-1, 7
Let d be ((-10955)/(-315) - 33) + 48/(-27) + 2. Factor -12 + 7*f - 1/2*f**d.
-(f - 12)*(f - 2)/2
Let g = -9945 - -9945. Let z(j) be the third derivative of 0*j + g*j**3 + 4/15*j**5 + 1/30*j**6 - 9*j**2 + 0*j**4 + 0. Determine n, given that z(n) = 0.
-4, 0
Find j, given that -8*j**4 + 21*j**3 + 8*j - 22*j**2 - 23927*j**5 - 23932*j**5 + 47860*j**5 = 0.
0, 1, 2, 4
Let c(u) = 3*u**3 + 9*u**2 - 27*u + 4. Let t be c(-7). Let n = -392 - t. Factor 4/7*d**2 + 16/7*d - 4/7 - 16/7*d**n.
-4*(d - 1)*(d + 1)*(4*d - 1)/7
Suppose 0 = 3*x + 9 - 15. Let d(v) = 4*v**2 - 3*v. Let n be d(-3). Factor -52*c**2 + 93*c**x - c**5 - 4*c + 2*c**4 + 3*c**3 - n*c**2.
-c*(c - 2)**2*(c + 1)**2
Let h(f) = -f**2 - 22*f - 17. Let i be h(-21). Suppose i*z - 20 = -0*z. Factor -48*q + 31 + 1 + 11*q**2 - 4*q**3 - z*q**2 + 18*q**2.
-4*(q - 2)**3
Let l be -2*1015/(-20)*2. Factor -203*x**3 + 4*x**4 - 4*x**2 + l*x**3.
4*x**2*(x - 1)*(x + 1)
Let v(m) be the first derivative of 3*m**5/40 - 219*m**4/16 - m**3/8 + 219*m**2/8 - 129. Let v(z) = 0. What is z?
-1, 0, 1, 146
Determine c so that -10/3*c + 8/3*c**2 - 2/3*c**3 + 4/3 = 0.
1, 2
Let y(d) = 4*d**3 + 21*d**2 - 49*d + 29. Let h(k) = 40 - 15 - 32*k**2 - 69 - 6*k**3 + 74*k. Let a(p) = -5*h(p) - 8*y(p). Factor a(s).
-2*(s - 1)**2*(s + 6)
Let s(j) be the third derivative of 0*j - 2*j**2 + 0*j**3 - 1/210*j**5 - 41 + 0*j**4. Solve s(i) = 0.
0
Let d(h) be the first derivative of h**4/12 - 2*h**3/9 - 32*h**2/3 - 160*h/3 - 3969. Suppose d(k) = 0. Calculate k.
-4, 10
Suppose -6*o - 364 = -16. Let v = -53 - o. Let z(l) = l**2 + l + 2. Let p(d) = 2*d**2 + d + 5. Let m(f) = v*z(f) - 2*p(f). Suppose m(n) = 0. What is n?
-3, 0
Let i(a) = -5*a**2 - 11*a. Let n(l) be the first derivative of 0*l + 2/3*l**3 + 5/2*l**2 + 2. Let h(o) = -3*i(o) - 7*n(o). Determine z so that h(z) = 0.
0, 2
Suppose w = -3*u + 92, -3*u + 2*