3
Find t, given that 18*t**4 + 53*t**3 + 3*t - 86*t**3 + 35 + 12*t**2 - 35 = 0.
-1/6, 0, 1
Let g be (2 - -1)*((-8)/2 + 5). Suppose -6*r + 2 + 6*r**4 - 8*r**4 - r**g + 7*r - 3 + 3*r**2 = 0. What is r?
-1, 1/2, 1
Factor 64*d - 45*d + 14*d - 588 - 3*d**2 + 51*d.
-3*(d - 14)**2
Let u(t) = -t**3 - t. Let q(o) = -3*o**3 + 12*o**2 - 2*o. Let v(k) = 3*q(k) + 6*u(k). Factor v(p).
-3*p*(p - 2)*(5*p - 2)
Factor 28/23*l**2 + 24/23 - 50/23*l - 2/23*l**3.
-2*(l - 12)*(l - 1)**2/23
Suppose c + 2*c**2 - c**2 - 11*c - 15*c + 0*c**2 = 0. What is c?
0, 25
Factor 0 + 1/8*p**2 - 1/8*p.
p*(p - 1)/8
Find q, given that 511*q**4 + 66*q**2 + 19*q - 330*q**2 + 13*q + 432*q**3 - 35*q**4 + 10*q**4 = 0.
-4/3, 0, 2/9
Let z = -1116/35 - -226/7. Let c(l) be the first derivative of z*l**2 + 2/15*l**3 + 7 + 2/5*l. Determine r, given that c(r) = 0.
-1
Let u(i) = i**2 - 5*i + 13. Let s be u(4). Factor 11*c**4 - 25*c**2 - 6*c - 20*c**3 - 7*c**4 - 4*c - s*c**4.
-5*c*(c + 1)**2*(c + 2)
Let p(z) = -z**2 + 4*z. Let o be p(0). Suppose o = -121*h + 122*h. Factor 2/3*b - 2/3*b**2 + h.
-2*b*(b - 1)/3
Let p = -1101 + 1103. Suppose -2*m - 2/5*m**4 + 2/5*m**p + 0 + 2*m**3 = 0. What is m?
-1, 0, 1, 5
Let n be (-9 - 1703/(-195))*5 - 10/(-3). Factor 1/7*s**n - 4/7*s + 3/7.
(s - 3)*(s - 1)/7
Let u(m) be the third derivative of 10*m**2 + 1/45*m**6 - 1/504*m**8 + 0*m**7 - 1/45*m**5 + 0 + 0*m - 1/12*m**4 + 2/9*m**3. Find w such that u(w) = 0.
-2, -1, 1
Find g such that 405*g**3 + 39 - 24 - 406*g**3 + g**2 + 17*g = 0.
-3, -1, 5
Let z(t) = -10*t**2 - 3. Let m be z(3). Let b = m + 95. Factor k - 1/3*k**b + 0.
-k*(k - 3)/3
Let z(b) be the third derivative of b**10/151200 - b**9/10080 + b**8/1680 - b**7/630 + b**5/6 - 7*b**2. Let m(n) be the third derivative of z(n). Factor m(g).
g*(g - 2)**3
Let j(k) be the third derivative of -k**7/1800 + 23*k**6/3600 - k**5/100 + 3*k**4/8 - 7*k**2. Let u(c) be the second derivative of j(c). Factor u(x).
-(x - 3)*(7*x - 2)/5
Let b(q) = -28*q**3 + 1352*q**2 + 1845*q + 616. Let h(s) = -2*s**3 - 2*s**2 + s. Let j(z) = -b(z) + 5*h(z). Solve j(n) = 0 for n.
-2/3, 77
Factor 443*m**2 - 2646 + 1575*m - 830*m**2 + 255*m**2 + 3*m**3.
3*(m - 21)**2*(m - 2)
Let i(c) be the second derivative of c**7/147 + 4*c**6/35 - c**5/35 - 4*c**4/7 + c**3/21 + 12*c**2/7 + 87*c. Solve i(v) = 0.
-12, -1, 1
Let b(t) = 2*t**3 + 13*t**2 + 11*t - 3. Let i(z) = 2*z**3 + 12*z**2 + 10*z - 2. Let c(r) = 4*b(r) - 6*i(r). What is k in c(k) = 0?
-4, -1, 0
Let u(x) be the first derivative of -32/9*x**3 + 0*x - 9 - 4*x**4 - 2/9*x**6 - 8/5*x**5 + 0*x**2. Factor u(h).
-4*h**2*(h + 2)**3/3
Let x(t) be the third derivative of -t**5/150 - 4*t**4/15 - 64*t**3/15 - 38*t**2 - 2*t. Factor x(w).
-2*(w + 8)**2/5
Suppose j - 2*j = -3*t + 15, 4*j = -4*t + 4. Suppose 0 - 8 = -t*b. Factor 2*y**b + 3*y**2 + 0*y**2 - 2*y**2 - 3*y.
3*y*(y - 1)
Let c(w) = -2*w**2 - w. Let p(l) = 18*l**2 + 10*l + 18. Let m(o) = 10*c(o) + p(o). What is q in m(q) = 0?
-3, 3
Let h be -4 + (1 + 0)/(1/102). Find p such that 3*p**2 - 3*p + h + 11*p + p**2 - 94 = 0.
-1
Let o(g) = -39*g**4 - 48*g**3 + 30*g**2 + 3*g. Let v(u) = 19*u**4 + 24*u**3 - 15*u**2 - u. Let s(r) = 3*o(r) + 7*v(r). Factor s(d).
d*(d + 2)*(4*d - 1)**2
Let x(w) be the third derivative of 0*w - 1/15*w**5 - 98/3*w**3 - 7/3*w**4 + 0 - 39*w**2. Factor x(g).
-4*(g + 7)**2
Let n(s) be the third derivative of -s**7/11340 + s**5/540 - s**4/12 + 2*s**2. Let l(f) be the second derivative of n(f). Find u such that l(u) = 0.
-1, 1
Suppose 18*u - 45*u**2 + 31*u**2 + 15*u**2 + 81 = 0. What is u?
-9
Let y(q) be the first derivative of 3*q**4/8 - 3*q**3 - 45*q**2/4 - 12*q + 218. Solve y(r) = 0 for r.
-1, 8
Let v(k) be the third derivative of -k**7/8820 - k**6/840 + k**5/105 + k**4/3 + 3*k**2. Let y(p) be the second derivative of v(p). Factor y(l).
-2*(l - 1)*(l + 4)/7
Let n(g) be the first derivative of -g**8/1344 + g**7/420 - g**6/480 + 7*g**2/2 - 11. Let l(h) be the second derivative of n(h). Factor l(j).
-j**3*(j - 1)**2/4
Let l(w) = -w**4 + 82*w**3 - 106*w**2 + 36*w. Let t(r) = 28*r**3 - 36*r**2 + 12*r. Let n(a) = -4*l(a) + 11*t(a). Factor n(u).
4*u*(u - 3)*(u - 1)**2
Let u = 78 + -71. Let d(y) be the third derivative of -1/24*y**4 + 0 - 1/210*y**u + 0*y**3 + 0*y + 1/60*y**5 + 1/120*y**6 + 2*y**2. Let d(q) = 0. What is q?
-1, 0, 1
Let t = 14609/120 - 365/3. Let c(b) be the third derivative of 0*b - 1/6*b**3 + 1/48*b**6 - t*b**5 + 0 + 3*b**2 - 1/420*b**7 + 7/48*b**4. Factor c(r).
-(r - 2)*(r - 1)**3/2
Let u(p) be the first derivative of 6/5*p**6 + 44/15*p**3 + 16/5*p - 23 - 12/25*p**5 - 41/5*p**4 + 8*p**2. Solve u(y) = 0 for y.
-2, -1/3, 1, 2
Solve 39/2 - 1/2*n**3 + 41/2*n**2 - 79/2*n = 0 for n.
1, 39
Let z(i) = i**3 + 4*i**2 + 4*i + 3. Let m be z(-2). Factor 12 - 8*o + m*o**2 - 2*o**2 - o**2 - 4*o**2.
-4*(o - 1)*(o + 3)
Let j(v) = -v**2 + 6*v + 4. Let o be j(6). Let f be (-30)/(-5)*o/(-63)*-3. Suppose 4/7*c**3 + f*c + 0 + 12/7*c**2 = 0. What is c?
-2, -1, 0
Let l(f) be the first derivative of -5*f**4/4 + 220*f**3/3 + 5*f**2/2 - 220*f - 130. Solve l(w) = 0.
-1, 1, 44
Determine y, given that 37*y - 5*y**5 - 40*y**3 + 8*y - 12*y - 20 + 30*y**4 + 12*y - 10*y**2 = 0.
-1, 1, 4
Let o(x) be the third derivative of 1/3*x**3 + 0 + 1/1344*x**8 + 1/210*x**7 - 1/24*x**4 - x**2 + 1/480*x**6 - 1/24*x**5 + 0*x. Factor o(u).
(u - 1)**2*(u + 2)**3/4
Let c(t) = 2*t**2 + t + 2. Let l be c(0). Factor 15*s**2 - 53*s**2 - 8 + 2*s + 122*s**l + 2*s.
4*(3*s + 1)*(7*s - 2)
Let y be ((-1)/(18/(-12)))/((-4)/(-150)). Suppose -y*f = -14*f - 33. Solve -2/9*g**2 + 0 - 4/9*g + 2/9*g**f = 0 for g.
-1, 0, 2
Find r such that -1 + 2*r**5 - 74*r + 29 - 54*r**4 + 8*r**3 + 18*r**2 + 38*r**4 + 34*r**2 = 0.
-2, 1, 7
Let j = -87/148 + 2019/1924. Factor -2/13 + 0*o + j*o**2 - 4/13*o**3.
-2*(o - 1)**2*(2*o + 1)/13
Let u = 2698/3365 - 6/3365. Find n such that 1521/5*n**2 + 156/5*n + u = 0.
-2/39
Let f be 66/(-363) + 72/33. Determine x, given that 2*x**4 - 38/7*x**3 + 0 + 8/7*x + 16/7*x**f = 0.
-2/7, 0, 1, 2
Let p(s) be the first derivative of -s**7/105 + s**6/20 - s**5/15 + s**2 + 51. Let q(f) be the second derivative of p(f). Factor q(m).
-2*m**2*(m - 2)*(m - 1)
Let r(v) be the first derivative of v**4/5 + 2*v**3/3 - 4*v**2/5 - 6*v/5 - 234. Determine k so that r(k) = 0.
-3, -1/2, 1
Let r(j) be the second derivative of 4/105*j**6 + 0*j**2 + 0*j**3 + 1/147*j**7 + 0*j**4 + 3/70*j**5 + 2 + 8*j. Suppose r(b) = 0. Calculate b.
-3, -1, 0
Let y(u) be the third derivative of -u**6/105 + 17*u**5/70 + 23*u**4/28 + 2*u**3/3 - 48*u**2. Suppose y(x) = 0. Calculate x.
-1, -1/4, 14
Let i be (-6)/(-11) + (3834/231 - 16). Determine y, given that -i + 4/7*y + 4/7*y**2 = 0.
-2, 1
Suppose -21*g + 4 = -17*g. Let y = g - 2/5. Determine v, given that 0 - y*v**5 + 3/5*v**3 + 0*v**4 + 0*v + 0*v**2 = 0.
-1, 0, 1
Let z(u) be the second derivative of u**5/60 + 7*u**4/36 - u**3/18 - 7*u**2/6 + 2*u + 62. Factor z(s).
(s - 1)*(s + 1)*(s + 7)/3
Let k be (-6)/(60/7)*4/7*-2. Solve 8/5*n**2 - 4/5*n**4 - 8/5*n**5 - 8/5*n + 16/5*n**3 - k = 0 for n.
-1, -1/2, 1
Let r be 3/(-1)*(-132)/198. Factor 0 + 0*k + 2/7*k**3 + 6/7*k**r.
2*k**2*(k + 3)/7
Factor -8/9 - 8/9*s - 2/9*s**2.
-2*(s + 2)**2/9
Factor -125*i + 85*i**2 + 0 + 0 - 135*i**2 + 50*i**4 + 5*i**5 + 120*i**3.
5*i*(i - 1)*(i + 1)*(i + 5)**2
Factor -55*s**3 + 124*s**4 + 155 + 115 - 405*s + 225*s**2 - 119*s**4.
5*(s - 3)**3*(s - 2)
Let f(p) = 8*p**3 - 52*p**2 - 66*p + 3. Let o(q) = -7*q**3 + 53*q**2 + 64*q - 2. Let b(g) = -2*f(g) - 3*o(g). Determine k so that b(k) = 0.
-1, 0, 12
Suppose 6*p - 75 = -63. Let m(x) be the second derivative of -2*x**p - 9/10*x**5 - 10/3*x**4 - 5*x + 0 - 13/3*x**3. Factor m(g).
-2*(g + 1)**2*(9*g + 2)
Let b(h) be the first derivative of -1/18*h**6 + 0*h**3 + 0*h**2 - 1/5*h**5 - 1/9*h**4 - h - 6. Let u(m) be the first derivative of b(m). Factor u(q).
-q**2*(q + 2)*(5*q + 2)/3
Suppose -2*v - 2*v - 83 = -5*l, -2*l - 3*v + 24 = 0. Let s = l + -13. Determine y so that 60*y**s + 12*y + 49*y**3 + 21*y**4 + 16*y**3 + 4*y**3 = 0.
-2, -1, -2/7, 0
Let u(g) be the second derivative of 0 - 64/3*g**2 + 1/30*g**5 - 2/3*g**4 + 16/3*g**3 - 2*g. Determine o so that u(o) = 0.
4
Let o be (2/21)/(2/6). Let q(h) = 112*h - 2350. Let x be q(21). Let 0 + 6/7*k**3 + 0*k + 2/7*k**x + o*k**5 + 6/7*k**4 = 0. Calculate k.
-1