)*(n + 1)**2
Suppose 30*p - 279 = -p. Suppose 4*c = g - 2, -13*g + p*g - c + 8 = 0. Factor -3/4*r - 1/4*r**g - 1/2.
-(r + 1)*(r + 2)/4
Let i(g) be the second derivative of -3 - 3/5*g**5 + 3*g - 4/3*g**3 - 3/2*g**4 - 1/15*g**6 + 0*g**2. Factor i(x).
-2*x*(x + 1)**2*(x + 4)
Suppose 0 = -i - 4*x - 8 - 60, 4*x = -57 - 11. Determine b so that 1/8*b**4 + 1/2 + i*b**3 + 0*b - 5/8*b**2 = 0.
-2, -1, 1, 2
Let g(r) = r**3 - 2*r**2 - 11*r - 6. Suppose -3*o = -6*o + 18. Let d(n) = 2*n**3 - 4*n**2 - 20*n - 11. Let c(a) = o*d(a) - 11*g(a). Suppose c(z) = 0. What is z?
0, 1
Let a(z) = -8*z**2 + 68*z - 36. Let g(c) = 39*c**2 - 341*c + 144. Let y(n) = -11*a(n) - 2*g(n). Find i, given that y(i) = 0.
3, 18/5
Let i be 15/20 - 1395/(-60). Let c be ((-30)/45)/((-4)/i). Find w such that -c - 1/4*w**4 + 0*w**3 + 0*w + 2*w**2 = 0.
-2, 2
Let r(b) be the third derivative of -b**7/735 + 17*b**6/140 - 25*b**5/6 + 1775*b**4/28 - 1500*b**3/7 - 18*b**2 + 64*b + 2. Suppose r(l) = 0. What is l?
1, 15, 20
Let a(p) be the second derivative of -2/15*p**6 - 4/5*p**5 + 16*p**4 + 160*p**2 - 67*p - 224/3*p**3 + 0. Factor a(i).
-4*(i - 2)**3*(i + 10)
Suppose -6*g + g = y - 7, 4*y - 2*g + 16 = 0. Let m(i) = 3*i**2 + 5*i - 7. Let r be m(y). Factor -8*d**2 + 13 + 15*d - 7*d**2 + r*d**2 - 3.
-5*(d - 2)*(2*d + 1)
Factor 112*z + 216*z**2 + 4*z**3 + 2218853 - 76*z**2 - 2219669.
4*(z - 2)*(z + 3)*(z + 34)
Let q(v) be the third derivative of v**7/945 + 68*v**6/135 + 3*v**5 + 202*v**4/27 + 269*v**3/27 - 1578*v**2. Suppose q(n) = 0. Calculate n.
-269, -1
Let j be (-18)/(-15)*(-5)/(-10). Let s(x) be the second derivative of 0 + 4/15*x**6 - 8/3*x**4 + 0*x**2 - j*x**5 + 2/21*x**7 - 8/3*x**3 - 4*x. Factor s(a).
4*a*(a - 2)*(a + 1)**2*(a + 2)
Solve -42*z**3 - 54 + 3*z**4 - 49 + 158 - 55 + 39*z**2 = 0 for z.
0, 1, 13
Suppose 197*f - 195*f = 10. Suppose 0 = 16*c - 15*c + y, -16 = -f*c + 3*y. Solve -2/7 - 20/7*a**3 - 12/7*a - 24/7*a**c - 6/7*a**4 = 0 for a.
-1, -1/3
Let t(n) be the third derivative of -n**5/270 + 25*n**4/18 + 516*n**2 - 1. Let t(f) = 0. Calculate f.
0, 150
Suppose h = -h + 4. Let o = -81 + 97. Suppose 6 + 5*t**2 - o*t**2 - 6*t**3 + 7*t + 2*t + 2*t**h = 0. What is t?
-2, -1/2, 1
Suppose -5*j = -194 + 599. Let f = j - -124. Determine m so that -40*m**2 + m**3 + 81*m + 4*m**3 - 80 - 24*m + f*m = 0.
2, 4
Let g(t) be the first derivative of -7/2*t**2 + 8/3*t**3 + 0*t + 107 - 1/4*t**4. Factor g(f).
-f*(f - 7)*(f - 1)
Let t = -6832 - -61496/9. Let o(k) be the second derivative of 23*k + 1/15*k**5 - 1/6*k**4 + 0 - t*k**3 - k**2. Factor o(n).
2*(n - 3)*(n + 1)*(2*n + 1)/3
Let t be -2 - 5/(-1 - 0). Suppose 2*p - 155 = -t*p. Suppose 4*u - p*u**4 + 8*u**2 - 16*u**3 + 54*u**4 + 12*u**5 - 31*u**4 = 0. What is u?
-1, -1/3, 0, 1
Suppose -4*w + 12 = -6*x, -18 = -2*x + 39*w - 45*w. Factor 0*j**4 - 6/5*j**3 + x*j + 0 + 2/5*j**5 + 4/5*j**2.
2*j**2*(j - 1)**2*(j + 2)/5
Let v(g) be the second derivative of 1/30*g**4 - 3*g + 4/15*g**3 + 0*g**2 + 2. Factor v(k).
2*k*(k + 4)/5
Let v(y) = y**4 - y**2 + 2*y. Let x(d) = 152*d**5 - 713*d**4 + 836*d**3 - 145*d**2 - 122*d - 6. Let a(i) = -v(i) + x(i). Determine f, given that a(f) = 0.
-1/4, -1/19, 1, 3
Factor 50*k**3 + 2825*k**2 + 76*k**3 + 104*k**3 - 20*k**3 - 620*k**2 + 5*k**4.
5*k**2*(k + 21)**2
Let n(a) be the first derivative of 4*a**7/735 - a**6/21 + 17*a**5/210 - a**4/21 - 33*a**2 - 2. Let r(y) be the second derivative of n(y). Factor r(z).
2*z*(z - 4)*(2*z - 1)**2/7
Solve -1/2*a**2 + 878*a - 385442 = 0.
878
Factor -378*r - 2911*r**3 + 6*r**4 - 137*r**2 + 2860*r**3 - 298*r**2.
3*r*(r - 14)*(r + 1)*(2*r + 9)
Solve 49320*k**2 - 24300*k**3 + 32/3 - 4336/3*k = 0 for k.
2/135, 2
Let x be (-15)/(-70)*35*(1 + -13). Let q be (5/2)/(x/(-72)). Factor 15/4*n - 3/2 - 9/4*n**q - 3/4*n**3 + 3/4*n**4.
3*(n - 1)**3*(n + 2)/4
Suppose -2*t = -20 + 6. Let s(g) = g**3 - 3*g**2 - 7*g - 1. Let f be s(5). Factor f*p**4 - 8*p**5 + p**4 + 36*p**5 - t*p**4.
4*p**4*(7*p + 2)
Let l(c) be the third derivative of -c**10/378000 + c**9/33600 + c**8/20160 - 47*c**5/60 + 6*c**2 + 21*c. Let n(q) be the third derivative of l(q). Factor n(r).
-r**2*(r - 5)*(2*r + 1)/5
Let j(v) be the third derivative of v**2 + 0*v - 1/540*v**6 + 19/270*v**5 + 3*v**3 + 16 - 11/12*v**4. Factor j(q).
-2*(q - 9)**2*(q - 1)/9
Factor 284/7*s**2 + 16/7*s**3 - 376/7*s + 76/7.
4*(s - 1)*(s + 19)*(4*s - 1)/7
Let q(v) = -18*v**2 - 10700*v + 14257800. Let p(w) = 5*w**2 + 5*w. Let l(b) = 4*p(b) + q(b). Determine x so that l(x) = 0.
2670
Let y(b) = -11*b**4 + 20*b**3 + 180*b**2 + 592*b + 701. Let f(q) = 59*q**4 - 99*q**3 - 900*q**2 - 2960*q - 3504. Let a(m) = 3*f(m) + 16*y(m). Solve a(r) = 0.
-11, -4
Let r(h) = 2*h**2 + 10*h. Let i(x) = -9*x**2 + 210*x + 243. Let n(o) = i(o) + 3*r(o). Solve n(j) = 0.
-1, 81
Let z = -185 - -168. Let j(t) = 3*t + 55. Let u be j(z). Factor 2/9*w**2 + 0*w**u + 1/9*w**5 - 1/3*w**3 + 0*w + 0.
w**2*(w - 1)**2*(w + 2)/9
Let d be (-20 - -35)/((-560)/(-6336)). Suppose -2904/7 - d*z + 18*z**2 - 3/7*z**3 = 0. Calculate z.
-2, 22
Let w(q) = q**2 + 2*q + 5. Let d be w(0). Factor -d*x**4 + x**4 + 0*x**4 + 0*x**4 - 20*x**3 - 24*x**2.
-4*x**2*(x + 2)*(x + 3)
Let z(y) = 23*y**3 - 457*y**2 + 894*y - 8. Let h(v) = 8*v**3 - 152*v**2 + 299*v - 3. Let x(w) = -8*h(w) + 3*z(w). Suppose x(k) = 0. What is k?
0, 2, 29
Let g(a) = 22*a**2 - 43*a + 221. Let m(o) = 36*o**2 - 64*o + 332. Let c(q) = -8*g(q) + 5*m(q). Factor c(z).
4*(z - 3)*(z + 9)
Let p = 47/13103 + -546186063/170339. Let x = 3214 + p. Solve x*c**4 - 106/13*c**2 - 24/13*c + 8/13 + 66/13*c**5 - 42/13*c**3 = 0.
-1, -2/3, 2/11, 1
Let j(p) = 4*p**3 - 4*p**2 + p - 3. Let y be j(2). Suppose 88*l = 89*l - y. Factor 69*f**3 - 6 - 12*f**2 + f - l*f - 72*f**3 - f.
-3*(f + 1)**2*(f + 2)
Suppose -9*f**4 + 473*f**3 + 36*f + 452*f**3 + 18*f**2 - 24 - 946*f**3 = 0. What is f?
-2, 2/3, 1
Let r = 1153298 - 6919787/6. Factor -r*z**2 + 11*z - 363/2.
-(z - 33)**2/6
Let g(k) be the third derivative of 5*k**8/336 + k**7/21 - 13*k**6/12 - 6*k**5 + 135*k**4/8 + 225*k**3 + k**2 + 217*k. Factor g(h).
5*(h - 5)*(h - 2)*(h + 3)**3
Suppose 455*g - 459*g - 44 = 2*y, 18*y - 340 = -4*g. Factor 3/2*j**3 + 45/2*j**2 + 0 - y*j.
3*j*(j - 1)*(j + 16)/2
Let j(b) be the first derivative of 2*b**3/15 - 3*b**2/5 - 1296*b/5 + 5693. Suppose j(i) = 0. What is i?
-24, 27
Suppose -1/7*f**2 - 4700/7*f - 5522500/7 = 0. Calculate f.
-2350
Let v(t) be the first derivative of -t**4/6 + 4*t**3 - 5*t**2 - 68*t/3 + 4869. Suppose v(x) = 0. Calculate x.
-1, 2, 17
Let z(k) = k**2 - k + 3. Let t be z(0). Let y be (-25 - -35) + -2 + -5. Find f, given that 6*f - 4*f + 9 - y*f**2 + t*f + f = 0.
-1, 3
Suppose 0*o + 352 = -8*o. Let m = -40 - o. Determine w so that -m - w**3 - 2*w - 2*w + 0*w**3 - 6*w**2 - 5*w = 0.
-4, -1
Let s(o) = -2*o**3 - 3*o**2 - 1. Let d(p) = 303*p**3 - 650*p**2 + 319*p - 8. Let g(r) = d(r) - 6*s(r). Determine k so that g(k) = 0.
2/315, 1
Let m = 81 + 327. Find w, given that 216*w**2 + 3*w**3 + 41472 + 3961*w + 815*w + m*w = 0.
-24
Let p(s) be the first derivative of 5*s**4 - 284*s**3/3 + 518*s**2 - 196*s + 1528. Determine v so that p(v) = 0.
1/5, 7
Suppose 125*w + 606180 = 1924680. Factor w*s**2 + 2916*s + 169/4*s**5 + 4798*s**3 + 216 + 1547/2*s**4.
(s + 6)**3*(13*s + 2)**2/4
Determine m so that 3/5*m**2 - 396/5 + 48/5*m = 0.
-22, 6
Let u(j) = -j**4 - 12*j**3 + j**2 + j - 1. Let w(l) = -95*l**4 - 8335*l**3 + 6759*l**2 - 1361*l + 5. Let s(o) = -20*u(o) - 4*w(o). Factor s(k).
4*k*(4*k + 339)*(5*k - 2)**2
Let d(g) = g**4 - 346*g**3 - 1068*g**2 - 1070*g - 357. Let s(x) = -2*x**3. Let c(u) = d(u) + 4*s(u). Factor c(b).
(b - 357)*(b + 1)**3
Let l(s) be the third derivative of -s**5 + 0*s**3 - 1/15*s**6 + 2/105*s**7 + 0 - 23*s**2 + 6*s**4 + 0*s. Solve l(m) = 0.
-4, 0, 3
Factor 708/5 - 3/5*o**3 - 177/5*o**2 + 12/5*o.
-3*(o - 2)*(o + 2)*(o + 59)/5
Suppose -5*t**4 + 1380*t**2 - 143*t**3 - 156*t - 187*t**3 + 150*t - 1394*t = 0. What is t?
-70, 0, 2
Let z be 5/(34/272 + (-21)/(-24)). Let k(x) be the third derivative of 0*x**3 + 0*x + 0 + 0*x**4 - 1/780*x**6 + 23*x**2 - 1/195*x**z. Find s such that k(s) = 0.
-2, 0
Let q = 9690 - 203489/21. Let r(a) be the second derivative of 32*a + 1/210*a**5 + q*a**4 - 1/315*a**6 + 0*a**3 + 0*a**2 + 0. Find i, given that r(i) = 0.
-2, 0, 3
Let w(k) = 9*k**5 + 56*k**4 - 63*