 1/135*c**6 - 2/9*c**4 - 1/3*c**2 + 10/27*c**3 - 33*c + 1/15*c**5. Suppose n(z) = 0. What is z?
1, 3
Let i(b) = -b - 53. Let y be i(-53). Let q(x) be the third derivative of -8/5*x**3 + x**4 - 1/4*x**5 - 11*x**2 + 0 + y*x. Suppose q(t) = 0. What is t?
4/5
Suppose -2*z + 3*s - 28 = 0, -3*z - 14 = 4*s + 11. Let h = -6 - z. Solve -30*n**2 + 15*n - n**3 - 3 + 25*n**3 + 6*n**3 - 15*n**4 + 3*n**h = 0.
1
Let o(t) be the third derivative of t**7/315 + t**6/90 - 2*t**5/45 - 2*t**4/9 + 106*t**2 + t. Factor o(r).
2*r*(r - 2)*(r + 2)**2/3
Let r be 1148/21*(-51)/(-2). Let u = -9742/7 + r. Solve -6/7*f**4 + 8/7*f - 22/7*f**3 - u*f**2 + 0 = 0 for f.
-2, 0, 1/3
Let p(a) be the first derivative of -2*a**3/33 + 10*a**2/11 - 42*a/11 + 108. Determine i so that p(i) = 0.
3, 7
Let a = -12 + 4. Let i = -6 - a. What is l in -l**2 + 2*l**2 - 2*l**i = 0?
0
Let t = 401 - 401. Let i(r) be the third derivative of -1/90*r**6 + 0*r**3 - 1/90*r**5 + 0*r + 0 - 1/315*r**7 + t*r**4 - 2*r**2. Determine d so that i(d) = 0.
-1, 0
Find m, given that -222*m - 15/2*m**2 + 90 = 0.
-30, 2/5
Let j(z) be the second derivative of -z**5/10 + 5*z**4/2 - 16*z**3 + 44*z**2 + 3*z + 2. Factor j(k).
-2*(k - 11)*(k - 2)**2
Let m = 87 + -93. Let k be (m/3)/(-3 + -3). Solve 1/3*l**2 + 1/3*l - 1/3 - k*l**3 = 0 for l.
-1, 1
Suppose 4*g + 65 = 9*g. Suppose 11 = 8*k - g. Let 2/7 - 2/7*b**2 - 2/7*b**k + 2/7*b = 0. What is b?
-1, 1
Let c be (-32)/8 - ((-52)/16 - 3). Let r(m) be the first derivative of -5 - c*m**2 + 2/3*m**3 + m. Find i, given that r(i) = 0.
1/4, 2
Factor 97200 - 560*k + 184*k**2 + 1640*k - 181*k**2.
3*(k + 180)**2
Let d be -8 - -2 - (-3 - 0). Let h be (2 + -2)/(d + 4). Factor 3*l**2 + h*l**2 + 0*l - l + 7*l - 3*l**3.
-3*l*(l - 2)*(l + 1)
Let d(o) = 265*o**3 + 21*o**4 - 3*o**4 - 12*o**5 - 117*o**3 - 132*o**3. Let s(y) = 12*y**5 - 19*y**4 - 16*y**3. Let b(v) = -3*d(v) - 2*s(v). Factor b(c).
4*c**3*(c - 2)*(3*c + 2)
Suppose -114*j + 45 = -105*j. Solve -6/5 + 9/5*y**2 - j*y = 0 for y.
-2/9, 3
Let v(r) be the first derivative of -3/4*r**4 - 4 + 1/5*r**5 + 0*r**3 + 0*r + 2*r**2. Factor v(n).
n*(n - 2)**2*(n + 1)
Let a(h) = -4*h**4 - 136*h**3 - 1304*h**2 - 2216*h - 1024. Let o(c) = c**2 + 2*c. Let m(k) = a(k) + 20*o(k). Solve m(w) = 0.
-16, -1
Determine c so that -3*c**4 - 18 - 17*c**2 - 32*c**3 - 4*c**4 - 11*c**3 - 2*c**4 + 87*c = 0.
-3, 2/9, 1
Factor -28*r**3 - 4*r**4 - 389*r**2 + 3*r**4 + 65*r**2 - 8*r**3.
-r**2*(r + 18)**2
Solve 21 + 109*p - 28*p + 33*p**2 - 45*p**2 = 0 for p.
-1/4, 7
Let -35/4*n**2 + 5/4*n**5 + 0 - 15/4*n**3 + 15/2*n + 15/4*n**4 = 0. Calculate n.
-3, -2, 0, 1
Let t(w) be the third derivative of -1/20*w**5 - 1/2*w**4 + 0*w - 6*w**2 + 0 - 3/2*w**3. Factor t(n).
-3*(n + 1)*(n + 3)
Let f(w) = 2*w**2 - 29*w - 25. Let x(y) = y**2 - 28*y - 20. Let r(i) = 4*f(i) - 5*x(i). Factor r(z).
3*z*(z + 8)
Suppose -4*m = -4 + 12. Let s(o) = -2*o**3 - 4*o**2 - 3*o + 21. Let b(j) = j**3 + 4*j**2 + 3*j - 20. Let v(u) = m*s(u) - 3*b(u). Determine t so that v(t) = 0.
-2, 3
Let q(s) be the third derivative of -s**8/16800 - s**7/1260 - s**6/450 + s**4/3 - 15*s**2. Let l(v) be the second derivative of q(v). Let l(p) = 0. Calculate p.
-4, -1, 0
Let o(b) be the first derivative of -b**5/8 + 5*b**4/6 + 5*b**3/12 - 5*b**2 - 21*b + 14. Let p(i) be the first derivative of o(i). Factor p(c).
-5*(c - 4)*(c - 1)*(c + 1)/2
Let l(v) = -v**2 + 4*v - 2. Let b(z) = z**3 + z**2 - z + 2. Let k be b(0). Let c be l(k). Factor -c*g**3 + 3 - 10*g**3 - 4*g**4 - 12*g + 7*g**4 + 18*g**2.
3*(g - 1)**4
Suppose -3*g + 219 = -4*d, 5*d + 2*g + 235 = -2*g. Let o = d + 154/3. Solve -8/3*h**2 + 5/3*h**3 + 4/3*h - o*h**4 + 0 = 0.
0, 1, 2
Suppose 2*m - 4 = h - 4*h, 2*h - 16 = 2*m. Factor -z**2 + z - z**3 - z**4 + 2*z**2 + 4*z**2 - h*z**2.
-z*(z - 1)*(z + 1)**2
Suppose -2*y + 1 = 3*m, 5*y = -2*m - 12 - 2. Factor -12*f**3 + m*f**5 + 13*f - 6 + 9*f**2 - 4*f - 3*f**2.
3*(f - 1)**3*(f + 1)*(f + 2)
Let i be 7 + (20 + -17)/(6/(-8)). Let r(p) be the second derivative of 0 - i*p + 0*p**2 + 1/3*p**3 + 1/12*p**4. Factor r(d).
d*(d + 2)
Let o = -394 - -1972/5. Factor o*j - 4/5 + 2/5*j**2.
2*(j - 1)*(j + 2)/5
Suppose 3*u - a + 4*a + 144 = 0, -a - 154 = 3*u. Let x = u - -100. Determine b so that 24*b**3 + 9*b**4 - b**2 + 23*b + 4*b**2 - x*b - 12 = 0.
-2, -1, -2/3, 1
Factor -90*q**4 + 90*q**4 - q**5 + 2*q**3 - q.
-q*(q - 1)**2*(q + 1)**2
Let l(b) be the third derivative of -b**9/5040 - b**8/2240 + b**7/840 + b**6/240 - 3*b**4/8 - 8*b**2. Let f(j) be the second derivative of l(j). Factor f(s).
-3*s*(s - 1)*(s + 1)**2
Let k(h) be the first derivative of -3*h**4/4 - 10*h**3 - 21*h**2/2 + 54*h + 182. Let k(p) = 0. What is p?
-9, -2, 1
Let u(x) be the second derivative of -x**5/130 + 5*x**4/78 - 4*x**3/39 + 44*x. Determine z so that u(z) = 0.
0, 1, 4
Suppose -2*g + 5*g - 18 = 0. Factor 2*c**2 - c**2 - 12 + 16*c - g*c**2 + c**2.
-4*(c - 3)*(c - 1)
Let b(l) be the second derivative of -l**7/84 - l**6/60 + 9*l**5/40 - 11*l**4/24 + l**3/3 - 79*l. Factor b(s).
-s*(s - 1)**3*(s + 4)/2
Let b(v) be the first derivative of 3*v**4/2 - 62*v**3/3 - 62*v**2 + 48*v - 95. Factor b(l).
2*(l - 12)*(l + 2)*(3*l - 1)
Let d(q) = 8*q + 1. Let m be d(-2). Let i(x) = x + 17. Let f be i(m). Factor -6 + 3*l**2 - 3*l - 2*l**f + 2*l**3 + l**3 + 5*l**2.
3*(l - 1)*(l + 1)*(l + 2)
Let p = 7 + -3. Suppose 8*u**4 + 2*u**2 + 13*u**2 - 21*u**4 - 10*u + 8*u**p = 0. What is u?
-2, 0, 1
Let r(y) = y**2 + 8*y + 22. Let p be r(-4). Solve 4 - p*g**4 + 356*g + 2*g**2 - 9*g**3 - 5*g**3 - 342*g = 0.
-2, -1, -1/3, 1
Let j(b) be the third derivative of b**8/336 + b**7/14 + 71*b**6/120 + 31*b**5/20 - 3*b**4 - 18*b**3 + b**2 + 15. Find q, given that j(q) = 0.
-6, -3, -1, 1
Find x such that 992*x**2 - 71 - 405*x - 159*x - 816*x + 400*x - 16*x**3 + 315 = 0.
1/2, 61
Let q(a) be the first derivative of a**6/4 + 6*a**5/5 + 3*a**4/8 - 7*a**3 - 15*a**2 - 12*a - 369. Solve q(c) = 0 for c.
-2, -1, 2
Let h(d) = -4*d - 53 - 2*d**5 + 49 + d**4 + 3*d**5 + 0*d**5 + 2*d**3. Let s(p) = -p**4 - p**3 + p**2 + p - 1. Let q(m) = -5*h(m) + 20*s(m). Factor q(n).
-5*n*(n - 1)*(n + 2)**3
Suppose -4/5*q**3 + 2/5*q**4 + 0*q - 6/5*q**2 + 0 = 0. What is q?
-1, 0, 3
Let q be (0 + -5)/5 - 1024/234. Let t = -47/9 - q. Factor 0 + t*y + 2/13*y**2.
2*y*(y + 1)/13
Let a be 256/48 + 90/(-27). Suppose 1/2*o**a - 1/2 - 1/2*o + 1/2*o**3 = 0. Calculate o.
-1, 1
Let 288 + 1796*l**2 + 2925*l + 2733*l**3 + 400*l**5 - 573*l + 2640*l**4 + 3543*l**3 + 4500*l**2 = 0. Calculate l.
-2, -3/10
Let r(z) be the second derivative of 0*z**2 - 1/18*z**3 + 0 + 0*z**5 - 5*z + 1/45*z**6 + 1/126*z**7 - 1/18*z**4. Factor r(k).
k*(k - 1)*(k + 1)**3/3
Let r(h) be the second derivative of -h**7/5880 + h**6/2520 - 5*h**3/2 - 36*h. Let c(a) be the second derivative of r(a). Factor c(s).
-s**2*(s - 1)/7
Let c(q) be the first derivative of -54*q**5/5 + 243*q**4/2 - 78*q**3 - 3887*q**2 + 17576*q + 797. Find d such that c(d) = 0.
-4, 13/3
Suppose -5*c = -9 - 1. Let r(u) = u**3 - 2*u**2 + 2*u - 1. Let b be r(c). Solve -3/2*y - 1/2 + 3/2*y**b + 1/2*y**2 = 0.
-1, -1/3, 1
Let y(d) be the first derivative of 22*d**2 + 23 + 20*d + d**4 + 28/3*d**3. Determine a, given that y(a) = 0.
-5, -1
Find z, given that 130*z**2 + z**3 + 4092*z + 1147 - 6111 - 3748 + 0*z**3 = 0.
-66, 2
Suppose 33*n + 445 = -9*n + 529. Factor 196/3 - 56/3*b + 4/3*b**n.
4*(b - 7)**2/3
Factor 66365*i**3 + 388 + 252*i**2 - 130 - 66362*i**3 - 513*i.
3*(i - 1)**2*(i + 86)
What is s in -4/5*s**4 - 56/5*s**3 - 204/5*s**2 - 216/5*s + 0 = 0?
-9, -3, -2, 0
Let f(c) be the first derivative of -c**4/4 + 2*c**3 + 7*c**2/2 + 3*c - 17. Let a be f(7). Solve -7/2*i - 1 - 3/2*i**a - 4*i**2 = 0.
-1, -2/3
Let y(z) be the second derivative of 1/6*z**3 + 1/72*z**4 - 1/60*z**5 - 2*z - 1/360*z**6 + 0 - 9/2*z**2. Let r(b) be the first derivative of y(b). Factor r(m).
-(m - 1)*(m + 1)*(m + 3)/3
Find r, given that -688 - 891*r - r**2 - 1340 + 973*r + 347 = 0.
41
Let b(t) be the second derivative of -t**5/4 - 15*t**4/2 - 55*t**3/2 - 40*t**2 + 5*t + 4. Factor b(i).
-5*(i + 1)**2*(i + 16)
Let o = 152 + -137. Let k be o/(-25) - ((-128)/30 + 1). Factor -k - 32/3*z - 10*z**2.
-2*(3*z + 2)*(5*z + 2)/3
Let o be 7/(-770)*1015/6. Let z = -1/12 - o. Factor 32/11*y**2 + 2/11 + z*y.
2*(4*y + 1)**2/11
Factor -141/7*z - 144/7 + 3/7*z**2.