7*r**b + 2/7*r**5 + 0*r + 0*r**3 + 0*r**2 + 0 = 0. What is r?
-2, 0
Let r = -5 - -10. Suppose r*p - 9 = 1. Factor 4*o**p + 23*o + 3*o**3 - o**3 - 23*o.
2*o**2*(o + 2)
Suppose 3*z - 33 + 27 = -5*m, 4*m - 2*z = 18. Factor 5/4*g**m + 7/4*g + 3/2 - 9/2*g**2.
(g - 3)*(g - 1)*(5*g + 2)/4
Suppose 0 = 451*i - 456*i + 2*s + 33, 4*i - 3*s - 39 = 0. What is y in 0 + 3/10*y + 1/10*y**i + 2/5*y**2 = 0?
-3, -1, 0
Let s(t) be the third derivative of t**8/112 + t**7/70 - t**6/20 - t**5/10 + t**4/8 + t**3/2 + 114*t**2. Find m such that s(m) = 0.
-1, 1
Let v(m) = -52*m - 258. Let h be v(-5). Suppose 0*x + 16/5 - 4/5*x**h = 0. Calculate x.
-2, 2
Let k(j) be the third derivative of -j**7/945 - j**6/270 + 19*j**5/270 - 7*j**4/27 + 4*j**3/9 + 3*j**2 + 20. What is f in k(f) = 0?
-6, 1, 2
Let z(o) = -o**3 - 8*o**2 - 7*o + 9. Let f be z(-7). Let p be ((-8)/(-6))/(42/f). Factor 2/7 - p*j**2 + 1/7*j**3 - 1/7*j.
(j - 2)*(j - 1)*(j + 1)/7
Let z(h) = 2*h + 4. Let d be z(6). Let j be 2/9 - (-8 - (-222)/27). Find k such that -3*k + 4*k**2 + 6 - 10*k**4 + 19*k - d*k**3 + j*k**2 = 0.
-1, -3/5, 1
Suppose -7*r = -4*r - 9. Factor 9 - r*n**2 + n + 2*n + 0*n + 3*n.
-3*(n - 3)*(n + 1)
Let i = -155 + 162. Let r(v) be the third derivative of -1/96*v**4 - 1/1344*v**8 + 1/210*v**i - 3*v**2 - 1/80*v**6 + 0*v + 0*v**3 + 0 + 1/60*v**5. Factor r(p).
-p*(p - 1)**4/4
Suppose 2*p + 6 = -o, -4*o + 5*p - 3*p = -6. Suppose -m - v + o*v + 1 = 0, 5*m + 4*v = 8. Factor 13*g**m + 22*g**4 - 4*g**5 - g**3 - 3*g**3 - 43*g**4.
-4*g**3*(g + 1)**2
Let n(q) be the third derivative of -q**7/12600 + q**6/900 - q**5/200 + 3*q**4/4 + 5*q**2. Let p(r) be the second derivative of n(r). Factor p(f).
-(f - 3)*(f - 1)/5
Let u(v) be the third derivative of -v**5/270 + 31*v**4/108 - 10*v**3/9 + 69*v**2. Let u(d) = 0. Calculate d.
1, 30
Let n be (-22)/(-363)*44/12. Find d such that -n*d**2 + 4/9*d - 2/9*d**3 + 0 = 0.
-2, 0, 1
Let t(d) be the third derivative of d**6/200 - d**5/100 - d**4/40 + d**3/10 + 31*d**2 + 3*d. Factor t(v).
3*(v - 1)**2*(v + 1)/5
Let j(f) be the second derivative of -f**9/3780 + f**8/1680 + 13*f**4/12 - 30*f. Let u(n) be the third derivative of j(n). Factor u(p).
-4*p**3*(p - 1)
Let y(k) be the second derivative of k**8/2240 + k**7/210 - k**6/240 - k**5/10 + 5*k**4/4 - 14*k. Let j(d) be the third derivative of y(d). Factor j(z).
3*(z - 1)*(z + 1)*(z + 4)
Let p(z) be the first derivative of -3 + 1/20*z**5 + 1/24*z**4 + 0*z**2 + 0*z**3 + z. Let s(l) be the first derivative of p(l). Factor s(i).
i**2*(2*i + 1)/2
Determine y, given that 2/11*y**5 + 34/11*y**3 - 14/11*y**4 - 34/11*y**2 + 12/11*y + 0 = 0.
0, 1, 2, 3
Let j(h) be the second derivative of 0*h**3 - 3/4*h**5 + 0*h**2 - 12*h + 5/6*h**4 + 0. Find k, given that j(k) = 0.
0, 2/3
Let l(m) be the third derivative of -m**5/110 + m**4/4 + 26*m**3/11 + 270*m**2. Factor l(a).
-6*(a - 13)*(a + 2)/11
Let z = 335 + -335. Factor -1/3*i**4 + 1/3*i**5 + z + 0*i**3 + 0*i**2 + 0*i.
i**4*(i - 1)/3
Let d(l) be the first derivative of -2*l**3/21 + 10*l**2 - 350*l + 43. Let d(o) = 0. What is o?
35
Let g(o) = -o**4 - 6*o + 1. Let f(x) = -20*x**4 + 50*x**3 - 35*x**2 - 50*x + 25. Let p(v) = f(v) - 5*g(v). Determine u, given that p(u) = 0.
-2/3, 1, 2
Let d = -1/99 - -109/990. Let l(z) be the second derivative of -z + 0 + 1/3*z**3 + 0*z**2 + d*z**5 + 1/3*z**4. Factor l(p).
2*p*(p + 1)**2
Let b = 3 - 2. Let r(c) = 7*c - 44. Let m be r(7). What is h in -h**2 - m + b + 4 + h**3 = 0?
0, 1
Let d(m) be the first derivative of -2*m**4 + 130*m**3/3 - 16*m**2 + 169. Let d(p) = 0. Calculate p.
0, 1/4, 16
Let p(f) be the second derivative of -f**4/3 - 2*f**3 + 8*f**2 + 258*f. Factor p(g).
-4*(g - 1)*(g + 4)
Let o(t) = -6*t**2 + 2*t - 8. Let f(s) = -s**2 - s - 2. Let n(k) = -4*f(k) + o(k). Factor n(p).
-2*p*(p - 3)
Let k(h) be the first derivative of -5*h**3/3 - 20*h**2 - 80*h - 218. Factor k(b).
-5*(b + 4)**2
Suppose -8*l + 28*l**2 - 34*l**4 - 30*l**3 - 32*l + 32*l**2 - 33*l**4 + 72*l**4 = 0. What is l?
0, 2
Let k(x) be the first derivative of -x**4/32 - x**3/2 - 21*x**2/16 - 5*x/4 + 67. Factor k(i).
-(i + 1)**2*(i + 10)/8
Let g be 7/((-28)/(-8)) - 6. Let a be 3 - 5 - 16/g. Factor -k**3 + 3*k**a + 0*k + 2*k**4 - k**5 - 5*k**4 + 2*k.
-k*(k - 1)*(k + 1)**2*(k + 2)
Factor 68*o**3 + 87*o**2 + 51*o**3 - 122*o**3 - 162*o.
-3*o*(o - 27)*(o - 2)
Find g such that 22707/8 + 3/8*g**2 - 261/4*g = 0.
87
Let a(r) be the first derivative of -15*r**4/4 - 13*r**3 + 27*r**2/2 + 27*r + 819. Factor a(p).
-3*(p - 1)*(p + 3)*(5*p + 3)
Let p be 0/8 + (-6)/2 + 7. Find l such that 2/5*l + 4/5*l**p - 2/5*l**5 + 0*l**3 - 4/5*l**2 + 0 = 0.
-1, 0, 1
Let m(u) = -5*u**2 - 2*u - 5. Let y be m(3). Let d = y - -60. Factor -6/5*p**2 - 2/5*p**3 + 2/5*p + 4/5 + 2/5*p**d.
2*(p - 2)*(p - 1)*(p + 1)**2/5
Suppose 8*v - 62 = -22. Factor -4*x**4 + 4*x**2 + 3*x**v - 4*x**3 + 5*x**5 - 4*x**5.
4*x**2*(x - 1)**2*(x + 1)
Let s(o) be the third derivative of o**6/24 - o**5/2 + 55*o**4/24 - 5*o**3 - 265*o**2. Factor s(b).
5*(b - 3)*(b - 2)*(b - 1)
Let l(f) = -161*f + 2900. Let c be l(18). Factor 1/4*t**c - 5/2 - 9/4*t.
(t - 10)*(t + 1)/4
Let p(g) = g**3 + g**2 + g - 75. Let w be p(0). Let z = w + 77. Find n such that 3/2*n**z - 3 + 7/2*n = 0.
-3, 2/3
Let x(w) be the third derivative of 24*w**7/175 + 3*w**6/10 - 11*w**5/15 + 8*w**3/15 + 28*w**2. Find h such that x(h) = 0.
-2, -1/4, 1/3, 2/3
Let b(w) be the first derivative of -w**6/270 + w**5/9 - 25*w**4/18 + 6*w**3 + 19. Let p(a) be the third derivative of b(a). Factor p(s).
-4*(s - 5)**2/3
Determine v so that 15*v + v**2 + 8*v**2 - 5*v - 16*v - 3*v**4 = 0.
-2, 0, 1
Let k(z) be the third derivative of 0*z**3 + 0*z - 1/36*z**4 + 1/120*z**6 + 0 - 12*z**2 - 1/180*z**5. Factor k(y).
y*(y - 1)*(3*y + 2)/3
Let j = 1086141583/2887821 + -2/320869. Let n = j + -375. Factor 2/9*t**3 + 4/9 + 2/3*t**2 - 2/9*t**4 - n*t.
-2*(t - 1)**3*(t + 2)/9
Let p = -10 - -16. Let x(n) = 56*n**4 - 78*n**3 + 56*n**2 + 34. Let u(k) = 5*k**4 - 7*k**3 + 5*k**2 + 3. Let d(b) = p*x(b) - 68*u(b). Factor d(m).
-4*m**2*(m - 1)**2
Solve -5/2*f**3 - 1 + 5/2*f - 21*f**4 + 22*f**2 = 0 for f.
-1, -2/7, 1/6, 1
Let f be (-210592)/(-163530) - 9/(180/8). Let r = f - -2/1817. What is b in -r*b + 8/9 + 2/9*b**2 = 0?
2
Let y(o) be the third derivative of 1/180*o**5 + 19*o**2 + 0*o**4 - 2/9*o**3 + 0*o + 0. Suppose y(s) = 0. Calculate s.
-2, 2
Suppose 22*j = -13*j + 6*j. Let b(k) be the first derivative of 2 + j*k + 0*k**2 - 3/4*k**4 + 3*k**3. Factor b(f).
-3*f**2*(f - 3)
Let j(q) be the second derivative of 21*q - 2/15*q**2 + 1/5*q**3 - 2/45*q**4 + 0. Determine a, given that j(a) = 0.
1/4, 2
Let s(j) be the first derivative of 0*j - 1/4*j**3 + 27/40*j**5 - 16 + 0*j**2 + 21/32*j**4. Factor s(w).
3*w**2*(w + 1)*(9*w - 2)/8
Let o(y) be the first derivative of -y**6/6 - y**5 + 33*y**4/4 - 31*y**3/3 - 16*y**2 + 36*y + 459. What is u in o(u) = 0?
-9, -1, 1, 2
Suppose 36*f + 10 = -11 + 21. Factor 2/7*o**3 - 3/7*o**4 + 1/7*o**5 + 0 + 0*o + f*o**2.
o**3*(o - 2)*(o - 1)/7
Let t(r) = -r**2 + 9*r + 4. Let k be t(7). Suppose -k = -4*x + 6. Suppose 3*a**2 + 3*a + 0 + x*a**2 - 6 = 0. Calculate a.
-1, 2/3
Suppose 6 = -4*v + 6*v. Determine j, given that 41*j - 41*j + 4*j**4 + 8*j**v + 4*j**2 = 0.
-1, 0
Find n, given that 87 - 462 - 3*n**2 - 267*n - 147 = 0.
-87, -2
Let h be (-12 - -16) + (0 - 1). Factor 5*y**2 + 0*y - 2*y**3 - 17*y**2 - y**h + 12*y**4 + 3*y.
3*y*(y - 1)*(y + 1)*(4*y - 1)
Suppose -227 = -71*r - 85. Factor 0*p + 4/3*p**r - 4/3.
4*(p - 1)*(p + 1)/3
Let v(d) be the first derivative of 5/7*d**2 - 19 + 0*d + 2/21*d**3. Factor v(k).
2*k*(k + 5)/7
Let s(v) be the second derivative of v**4/4 - 15*v**3/2 + 39*v**2 - 48*v. Determine q, given that s(q) = 0.
2, 13
Factor -4*v**4 + 19 + 12*v**2 - v**3 + 11*v - 44 + 27.
-(v - 2)*(v + 1)**2*(4*v + 1)
Factor -1477*k**2 + 733*k**2 - k**3 + 736*k**2 - 4*k - 3*k**3 + 0*k**3.
-4*k*(k + 1)**2
Let a(t) be the third derivative of 0*t**3 - 4/105*t**7 + 1/6*t**4 + 0*t**6 - 40*t**2 + 0 + 2/15*t**5 + t - 1/84*t**8. What is n in a(n) = 0?
-1, 0, 1
Let t(k) be the first derivative of -2*k**5/45 - 5*k**4/18 - 8*k**3/27 - 31. Factor t(i).
-2*i**2*(i + 1)*(i + 4)/9
Let n(y) = y**2 + 9*y - 6. Let u be n(-9). Let z be 6 + ((-14)/u - 7). What is o in -2/3*o**3 + z*o**2 + 0*o - 1/3 + 2/3*o**5 - o**4 = 0?
-1,