pose -5*g = -4*v - 31, -5*g + 12 = -2*v - 11. Suppose -2*y + s + 1 = 0, -s - 22 = -4*y - g*s. Solve y*a**2 - 15 - 4*a + 18 - 2*a**2 = 0 for a.
1, 3
Let w(x) be the third derivative of 1/45*x**5 + 0*x**3 + 0*x + 1/54*x**4 + 2 - 12*x**2 + 1/630*x**7 + 11/1080*x**6. Factor w(u).
u*(u + 1)*(u + 2)*(3*u + 2)/9
Let m = 45097/112705 - 3/22541. Factor -m*j**2 - 12/5*j + 14/5.
-2*(j - 1)*(j + 7)/5
Suppose 0 = 3*t + 2*q - 81, -q = -3*t - 0*q + 72. Suppose 4*v = 7 + t. Solve 2*n**2 - 3*n + 0*n + v + 11*n + 0*n**2 = 0 for n.
-2
What is c in 199*c**2 - 9*c**5 + 3*c**5 - 211*c**2 + 4*c**5 + 14*c**3 = 0?
-3, 0, 1, 2
Let q(o) = -9*o**2 + 30*o - 81. Let s(g) = -11*g**2 + 31*g - 74. Let f(t) = -6*q(t) + 5*s(t). Find m such that f(m) = 0.
-29, 4
Suppose -5*c - 3*j + 10 = 0, 5*c + 8 = -j + 28. Suppose -4*d - 62 = -8*l + 3*l, c*d = -5*l + 35. Solve l*t**3 - 14*t - 5*t**3 + 10*t**2 + 6 - 7*t**3 = 0 for t.
1, 3
Factor 4/5*f + 1/10*f**2 - 64/5.
(f - 8)*(f + 16)/10
Let n(t) = 20*t**2 + t. Let r(a) = -3*a**2. Let k(c) = -n(c) - 6*r(c). Let d(m) = 17*m**2 - 144*m - 155. Let o(i) = d(i) + 6*k(i). Let o(p) = 0. Calculate p.
-1, 31
Let g(u) be the first derivative of -5*u**6/6 - 34*u**5 - 215*u**4 + 9640*u**3/3 - 11200*u**2 + 16000*u + 398. Let g(x) = 0. Calculate x.
-20, 2
Factor -94/3*b - 31 - 1/3*b**2.
-(b + 1)*(b + 93)/3
Let x(d) = -d**3 + 3*d + 2. Let a be x(-2). Let v = -573 - -575. Solve 12*s**3 - 9 - a*s**v + 9 - 8*s**2 + 4*s - 4*s**4 = 0 for s.
0, 1
Factor -2*d**3 + 1295*d**2 + 8301 + 2610*d - 3*d**3 - 8301.
-5*d*(d - 261)*(d + 2)
Suppose -2*z + 3*w - 2 = -z, 2*z + 3*w = 14. Factor -j**2 + 12*j + 7*j**2 - 3*j**2 - 12*j**3 - 5*j**2 - 2*j**z + 4*j**2.
-2*j*(j - 1)*(j + 1)*(j + 6)
Let l(u) = -4*u**4 + 1704*u**3 - 6960*u**2 + 7040*u - 48. Let z(s) = -s**4 + 341*s**3 - 1392*s**2 + 1408*s - 10. Let c(b) = 5*l(b) - 24*z(b). Factor c(k).
4*k*(k - 2)**2*(k + 88)
Let d = -109498 + 109500. Factor 8/5*r**4 - 6/5*r**5 + 0*r + 0 + 2/5*r**3 - 4/5*r**d.
-2*r**2*(r - 1)**2*(3*r + 2)/5
Let k(v) be the first derivative of -v**2 + 8*v + 3. Let u be k(3). Factor u*o**2 - o**4 - o**5 - 2*o - 9*o**3 + 6*o**4 + 5*o**2.
-o*(o - 2)*(o - 1)**3
Let h(i) = -348*i**2 + 48652*i + 98280. Let n(z) = 10*z**2 - 1390*z - 2808. Let v(r) = -3*h(r) - 104*n(r). Factor v(f).
4*(f - 351)*(f + 2)
Let r(w) = -53*w**3 - 22*w**2 + 9*w + 394. Let c(o) = 60*o**3 + 21*o**2 - 9*o - 396. Let q(u) = 8*c(u) + 9*r(u). Determine y so that q(y) = 0.
-3, 6, 7
Let x(q) = -2*q + 20. Let j(n) = 3*n**3 + 2*n**2 - 1. Let k be j(1). Let r be x(k). Suppose -4*l**4 - 6 + 2*l + 0 - 2 + r*l**2 - 4*l**3 + 2*l = 0. Calculate l.
-2, -1, 1
Let r(j) be the second derivative of 0 + 0*j**3 - 11/2*j**2 - 28/15*j**5 + 1/6*j**6 + 27*j - 2*j**4. Let q(n) be the first derivative of r(n). Factor q(g).
4*g*(g - 6)*(5*g + 2)
Let y be (20/6 + (-2 - -1))*(2 + -1). Let i(q) be the first derivative of 17 - y*q**3 + q**4 + q + q**2. Let i(t) = 0. Calculate t.
-1/4, 1
Suppose 3*s - s = 26. Suppose -4*k - 2*w - w = -s, 2*w + 6 = k. Factor -124*d**2 - 174*d**2 - 15*d**k - 140*d**3 - 402*d - 138*d - 152*d**2 - 135.
-5*(d + 3)**3*(3*d + 1)
Let p(o) be the first derivative of o**6/3 + 278*o**5/5 + 2711*o**4 + 27708*o**3 + 117585*o**2 + 228150*o - 558. Let p(h) = 0. What is h?
-65, -3
Let f = -6768 - -6768. Let m(d) be the first derivative of 0*d**2 + 2/5*d**5 - 29 + f*d - d**4 + 2/3*d**3. Factor m(u).
2*u**2*(u - 1)**2
Solve -5*b**2 - 16*b + 137 + 43 - 60 + 26*b = 0.
-4, 6
Let w = -2306 + 11539/5. Let a(p) be the first derivative of 4 - 9/2*p**2 + 3/2*p**4 + 1/2*p**6 + w*p**5 - 3*p - 2*p**3. Suppose a(c) = 0. Calculate c.
-1, 1
Factor 10/17*f - 8/17*f**2 - 2/17*f**3 + 0.
-2*f*(f - 1)*(f + 5)/17
Let g(d) = 2*d**3 + 3*d**2 - 34*d + 26. Let q be g(3). Let 136*l + 4624/5 + q*l**2 = 0. Calculate l.
-68/5
Let l(d) be the second derivative of -d**6/270 - 11*d**5/60 - 31*d**4/36 - 91*d**3/54 - 5*d**2/3 - 440*d. Factor l(m).
-(m + 1)**3*(m + 30)/9
Let p(b) be the third derivative of b**7/15 - b**6/2 - 23*b**5/10 - 5*b**4/3 + 4*b**3 + 1810*b**2. Factor p(f).
2*(f - 6)*(f + 1)**2*(7*f - 2)
Let f(a) be the first derivative of -1/3*a**5 - 2/3*a**2 - 17/12*a**4 - 16/9*a**3 - 52 + 0*a. Factor f(s).
-s*(s + 1)*(s + 2)*(5*s + 2)/3
Suppose -2*z = -x - 12, 4*x - 5*z - 26 = -50. Determine k, given that -34/5*k - 6/5*k**2 - 4 + 2/5*k**x + 2*k**3 = 0.
-5, -1, 2
Let b be 22 - (-6)/(-18)*30. Let y be -9 - -7 - ((-76)/b + 3). Find l, given that 0 + y*l - 4/3*l**2 = 0.
0, 1
Let w = -53/9170 - -9/262. Let b(a) be the second derivative of 4/7*a**2 + 1/7*a**4 + 0 - 2/105*a**6 - 10/21*a**3 + 14*a + w*a**5. Factor b(y).
-4*(y - 1)**3*(y + 2)/7
Let i(l) be the second derivative of -l**5/60 - 133*l**4/36 - 7*l**3 + 132*l**2 + 76*l - 13. Factor i(m).
-(m - 2)*(m + 3)*(m + 132)/3
Suppose 0 - 6 = -3*c. Let h = 469/180 + -106/45. Suppose -h*d**c + 0 - d = 0. Calculate d.
-4, 0
Factor -26*g**2 - 87/7*g**3 + 348/7*g + 712/7 + 1/7*g**4.
(g - 89)*(g - 2)*(g + 2)**2/7
Let n(g) be the third derivative of g**8/56 - 58*g**7/525 + 11*g**6/50 - 8*g**5/75 - 3*g**4/20 + 2*g**3/15 - 1486*g**2. Find x, given that n(x) = 0.
-1/3, 1/5, 1, 2
Let k(h) be the third derivative of h**5/270 - 8*h**4/9 + 188*h**3/27 + h**2 + 2*h + 218. Factor k(q).
2*(q - 94)*(q - 2)/9
Factor 24*d**3 - 11*d**3 + 16*d - 16*d**2 - 12*d**3 - 40*d + 14*d**2.
d*(d - 6)*(d + 4)
Let p(i) = 10*i**3 - 8*i**2 - 20*i - 22. Let f(h) = 4*h**3 - 6*h**2 + h + 1. Let x(u) = 4*f(u) - 2*p(u). Solve x(o) = 0 for o.
-4, -1, 3
Let x(h) = -h**2 + 1898*h - 5565. Let w(q) = -3*q**2 + 6327*q - 18549. Let t(s) = 8*w(s) - 27*x(s). Factor t(b).
3*(b - 207)*(b - 3)
Determine y so that 1812*y**2 + 0 - 6300*y**3 - 22197*y**4 + 516*y - 1029/4*y**5 = 0.
-86, -2/7, 0, 2/7
Suppose 884*i - 5300 = -3532. Solve 0 + 9/4*q + 3/8*q**i = 0.
-6, 0
Let d(s) = 413*s + 281. Let n be d(-4). Let z = 1371 + n. Let -6/7*y**4 - 2/7*y**5 - 2/7*y**2 - 6/7*y**3 + z + 0*y = 0. What is y?
-1, 0
Let r(q) be the second derivative of q**6/105 - 39*q**5/70 - q**4/42 + 13*q**3/7 + 22*q + 14. Factor r(f).
2*f*(f - 39)*(f - 1)*(f + 1)/7
Let q(d) = d**3 + 2. Let u(m) be the second derivative of -7*m**5/20 + 35*m**3/6 + 13*m**2 + m + 29. Let h(t) = -2*q(t) - u(t). Factor h(j).
5*(j - 3)*(j + 1)*(j + 2)
Let h be 1/4 - ((-987)/(-12))/(-7). Let w be (-6)/(-9)*h - 2. Factor -6*f + w*f**2 - f + 3*f + 0*f**3 - 2*f**3.
-2*f*(f - 2)*(f - 1)
Solve -219*r**3 - 405*r**3 - 77*r**4 - 1061*r - 2304*r**2 - 2011*r - 3*r**5 + 5*r**4 = 0 for r.
-8, -4, 0
Let z be (24/1515)/(((-24)/10)/6). Let s = z - -121/505. Solve 0 - s*u**2 + 1/10*u**3 + 1/10*u = 0 for u.
0, 1
Let b(g) be the third derivative of -g**6/60 - 7*g**5/60 + g**4/8 + g**3/2 - 11*g**2 + 4. Let m(n) = -n**2 + 3*n - 1. Let x(c) = -b(c) - 3*m(c). Factor x(a).
2*a*(a - 1)*(a + 6)
Let s = 1887 - 1049. Let f = s + -5862/7. Factor 0 + 2*p**2 + f*p + 18/7*p**3 + 2/7*p**5 + 10/7*p**4.
2*p*(p + 1)**3*(p + 2)/7
Let v = -9/1015 - -5291/24360. Let a(w) be the third derivative of 0 - 13*w**2 + 0*w**3 - 1/12*w**5 - v*w**4 + 0*w. Factor a(x).
-5*x*(x + 1)
Let l = -55 - -55. Suppose -2*t - 1 + 9 = l. Find q such that q**2 - 2*q - 3*q**2 - 36*q**3 - 4*q - 25*q**2 - 15*q**t = 0.
-1, -2/5, 0
Factor 2001/4*m + 153 + 39/4*m**2.
3*(m + 51)*(13*m + 4)/4
Let t be (30/(-25))/((-2)/10). Suppose l - 10 = -t. Solve 3*m**4 + 0*m - 3 - m + l*m - 9*m + 6*m**3 = 0.
-1, 1
Let d(t) = 5*t**2 - 55*t + 100. Let l(m) = 23*m - 98 - 16*m - 15*m**2 + 17*m + 10*m**2 + 31*m. Let i(j) = 4*d(j) + 5*l(j). Factor i(c).
-5*(c - 9)*(c - 2)
Factor -4608 + 2/3*d**3 - 66*d**2 + 1728*d.
2*(d - 48)**2*(d - 3)/3
Let z = 117490 + -117490. Factor 86/19*f**3 - 2/19*f**4 - 320/19*f**2 + 312/19*f + z.
-2*f*(f - 39)*(f - 2)**2/19
Let b be -8 + 330/108 - (-9 + -1 + 5). Let v(d) be the first derivative of 0*d + 0*d**2 + b*d**4 + 13 - 2/9*d**3. Suppose v(y) = 0. Calculate y.
0, 3
Suppose 2*a + 20 = 4*b, 0 = -a - 11*b + 6*b + 25. Let n be (56/(-10))/(66/22) - -2. Let 0*l**4 + n*l**5 - 4/15*l**3 + a*l**2 + 2/15*l + 0 = 0. What is l?
-1, 0, 1
Let u(n) = -13*n - 588. Let k be u(34). Let j = 1034 + k. Solve 4/15*y**2 - 2/15*y**5 + 4/15 + 2/3*y - 8/15*y**j - 8/15*y**3 = 0 for y.
-2, -1, 1
Let t be 278/14 - (-253 + 272). Factor 2/21*o**2 + 2/21*o**3 - 6/7 - t*o.
2*(o - 3)*(o + 1)*(o + 3)/21
Let c(o) be the third der