(m) = -30*m**2 - 35*m + 20. Let p(j) = j**2 + j - 1. Let y(r) = x*p(r) - z(r). Factor y(o).
5*(o + 1)**2
Let c(w) be the third derivative of w**7/1050 - 7*w**6/600 + 7*w**5/200 - w**4/30 - 49*w**3/6 + 28*w**2. Let d(b) be the first derivative of c(b). Factor d(t).
(t - 4)*(t - 1)*(4*t - 1)/5
Suppose -8*r + 3*r - 2*g + 27 = 0, r - 3 = -g. Suppose -r = -4*q + 5. Find c such that 4*c**q - c**4 - 2*c**4 + c**4 = 0.
0, 2
Let n be (-3)/(-6) + (-2354)/363 + 6. Let f(j) be the second derivative of n*j**4 + 0*j**2 + 2/33*j**3 - 5*j + 0. What is a in f(a) = 0?
-2, 0
Let a(n) = -250*n**4 - 1040*n**3 - 1265*n**2 - 295*n - 15. Let h(y) = -y**4 + 2*y**3 + y + 1. Let v(q) = a(q) - 5*h(q). Determine j so that v(j) = 0.
-2, -1/7
Let b(i) be the third derivative of i**5/300 - i**4/120 + 33*i**2 - 2. Factor b(n).
n*(n - 1)/5
Determine c, given that -2176/3*c - 2/3*c**3 - 2048/3 - 130/3*c**2 = 0.
-32, -1
Let q = 93 - 89. Let m be (-1)/q + (-65)/(-20). Find n, given that 1/3*n**2 + 0*n**m + 0*n + 0 - 1/3*n**4 = 0.
-1, 0, 1
Let m(d) be the second derivative of -1/10*d**2 + 0 + 1/10*d**3 + 17*d + 1/100*d**5 - 1/20*d**4. Factor m(s).
(s - 1)**3/5
Let i(y) = y**2 + 5*y - 43. Let f be i(-16). Let x = f - 1195/9. Factor -4/9*j + 2/9 + x*j**2.
2*(j - 1)**2/9
Let v(b) be the third derivative of b**8/448 - b**7/140 - b**6/40 + b**5/40 + 3*b**4/32 - b**2 - 8. Find h such that v(h) = 0.
-1, 0, 1, 3
Let u(c) = -c**2 - 5*c + 2. Let q(f) = -5*f**2 - 19*f + 6. Let d(a) = -2*q(a) + 9*u(a). Determine g, given that d(g) = 0.
1, 6
Let w(z) be the second derivative of -z**4/12 + 5*z**3/6 - z**2 + 2*z. Let n be w(4). Let -n*b**3 + 0*b**4 + 2*b**5 + b**4 - b**4 = 0. What is b?
-1, 0, 1
Let j(b) be the third derivative of 0 - 1/60*b**6 - b**2 + 5/12*b**4 - b**3 - 1/30*b**5 - 6*b. Determine d so that j(d) = 0.
-3, 1
Determine d, given that 4 + 7*d**3 + 8*d**4 + d**2 + d - 9*d - 13*d**4 + d**5 = 0.
-1, 1, 2
Let k(q) be the second derivative of -5*q**7/42 + 3*q**6/2 - 13*q**5/2 + 85*q**4/6 - 35*q**3/2 + 25*q**2/2 + 2*q - 21. Let k(i) = 0. Calculate i.
1, 5
Let d(g) = -9*g + 21. Let i be d(27). Let u = 222 + i. Factor -3/4*j**3 + 0*j + 0*j**2 - 3/8*j**4 + 3/8*j**5 + u.
3*j**3*(j - 2)*(j + 1)/8
Let q be (-4)/30 + (-4)/(-12). Let -q*z + 1/5 + 1/5*z**3 - 1/5*z**2 = 0. Calculate z.
-1, 1
Let o = -4304 + 4306. Factor -1/5*k**o + 1/5*k + 2/5.
-(k - 2)*(k + 1)/5
Let w be (1 - 1)/((-128)/(-8) + -12). Solve w*y**3 - y**2 + 0 + 1/2*y - 1/2*y**5 + y**4 = 0 for y.
-1, 0, 1
Factor 3/4*k**2 - 7/4*k + 1/2.
(k - 2)*(3*k - 1)/4
Let z(j) be the third derivative of j**5/105 + 16*j**4/21 + 40*j**3/7 - 431*j**2. Factor z(d).
4*(d + 2)*(d + 30)/7
Let t(u) be the first derivative of u**3 + 63*u**2/2 + 176. What is p in t(p) = 0?
-21, 0
Let r(l) = -l**3 - 19*l**2 - 10*l - 5. Suppose 12*m - 13 + 73 = 0. Let i(s) = s**3 + 9*s**2 + 6*s + 3. Let h(f) = m*i(f) - 3*r(f). Factor h(p).
-2*p**2*(p - 6)
Factor 80/9*i + 2/9*i**2 + 800/9.
2*(i + 20)**2/9
Suppose -5*h + x - 1 = 0, 5 = -h + 2*x + 3*x. Solve -4*a**4 - 2 + 26*a**3 - 2*a**4 + h - 9*a - 9*a**5 = 0.
-2, -1/3, 1
Suppose 65 = y + 4*y + 3*z, 43 = 3*y + z. Solve 12*q**5 + 8*q - 6*q**5 - y*q**2 - 27*q**3 + q**3 + 4*q**4 = 0.
-2, -1, 0, 1/3, 2
Suppose 19*h - 72 = 194. Suppose -5*y = -3*n - 9, -4*y + 24 - h = -n. Find w, given that 2/9*w**4 + 0*w**n + 4/9*w**3 - 2/9 - 4/9*w = 0.
-1, 1
Let p(m) be the first derivative of 1/4*m**3 + 0*m + 0*m**2 + 9/32*m**4 + 3/40*m**5 - 40. Solve p(o) = 0.
-2, -1, 0
Let b = -1369 + 1369. Let d(z) be the second derivative of b - 11*z - 1/6*z**4 - 8/3*z**3 - 16*z**2. Solve d(h) = 0 for h.
-4
Let u be 2 - (-4 + 2 + 0). Let v be -20*(-1 + u/20). Let -9*j + 2 - 4*j**3 - 4*j + v*j**2 - 7*j + 6 = 0. Calculate j.
1, 2
Let j(y) = 6*y**3 + 30*y**2. Let v(r) = r**3 + 6*r**2. Let p(d) = -2*d**2 + 32*d + 3. Let h be p(15). Let l(t) = h*v(t) - 6*j(t). Factor l(u).
-3*u**2*(u - 6)
Let t be 1904/(-18) - (-28)/7. Let u = t + 102. Factor 0*x - u*x**2 + 0.
-2*x**2/9
Let a = -2/8775 + 17564/61425. Let -2/7*n**3 + 0 + 2/7*n**4 - 2/7*n**2 + a*n = 0. Calculate n.
-1, 0, 1
Let d(r) be the first derivative of 4*r**6/15 - 58*r**5/25 - 5*r**4/2 + 16*r**3/15 - 136. Find m such that d(m) = 0.
-1, 0, 1/4, 8
Suppose -4/3*d**2 + 22/9*d**3 + 0 - 8/9*d**4 + 0*d = 0. Calculate d.
0, 3/4, 2
Factor 19/4*h - 1/4*h**3 - 2*h**2 - 5/2.
-(h - 1)**2*(h + 10)/4
Let n(c) = 4*c**4 - 16*c**3 + 23*c**2 - 8*c + 3. Let t(x) = x**2 + 1. Let w(l) = -n(l) + 3*t(l). What is z in w(z) = 0?
0, 1, 2
Factor 0*i**2 - 70*i - 48 + 72 + 72 - 2*i**2 + 52.
-2*(i - 2)*(i + 37)
Solve -1/4*z**4 + 110*z + 5/2*z**3 + 147/4*z**2 + 76 = 0 for z.
-4, -1, 19
Suppose -3*d - 4*h = -7*d - 12, -2*h = d - 12. Suppose 2*n - n - d = 0. Factor 12/7*a**3 + 24/7*a - 26/7*a**n - 2/7*a**4 - 8/7.
-2*(a - 2)**2*(a - 1)**2/7
Let r(j) be the third derivative of 18*j**2 - 1/60*j**5 + 1/24*j**4 + 0 + 0*j + 0*j**3. Factor r(v).
-v*(v - 1)
Factor 0 - 21*y**2 - 39/2*y - 3/2*y**3.
-3*y*(y + 1)*(y + 13)/2
Let g(a) be the third derivative of a**8/1344 + 23*a**7/420 + 29*a**6/160 - 23*a**5/120 - 11*a**4/12 - 610*a**2. Solve g(j) = 0.
-44, -2, -1, 0, 1
Let u(s) = s**3 + 10*s**2 - 11*s + 5. Let h be u(-11). Factor 1352*q - 6*q**2 - q**h - 1350*q + 3*q**3 + q**2 + q**4.
-q*(q - 1)**3*(q + 2)
Let y(q) be the first derivative of 2*q**3/3 - 5*q**2 + 8*q + 239. Factor y(k).
2*(k - 4)*(k - 1)
Let s(r) be the second derivative of -r**6/60 - r**5/40 + r**4/4 + r**3/3 - 2*r**2 - 231*r. Factor s(b).
-(b - 2)*(b - 1)*(b + 2)**2/2
Let k(y) = 2*y**3 - 45*y**2 + 381*y - 1027. Let v(i) = -12*i**3 + 271*i**2 - 2287*i + 6161. Let a = 55 - 49. Let u(x) = a*v(x) + 34*k(x). What is j in u(j) = 0?
8
Let y(d) be the second derivative of d**4/4 - 4*d**3 + 21*d**2/2 - 5*d. Find p such that y(p) = 0.
1, 7
Find k, given that -2/3*k**3 - 2/3*k**5 + 0 + 4/3*k + 2*k**2 - 2*k**4 = 0.
-2, -1, 0, 1
Let g(p) = -p**3 - 7*p**2 - 7*p - 1. Let y be g(-6). Factor -46*n**2 + 34*n**2 + 27*n**2 - 10*n - 15*n**4 + 5*n**5 + y*n**3.
5*n*(n - 2)*(n - 1)**2*(n + 1)
Let q(l) be the third derivative of l**6/200 - l**5/25 - 21*l**4/40 - 22*l**2 + 19. Factor q(a).
3*a*(a - 7)*(a + 3)/5
Let y be 3 + (-1781)/65 + 25. Factor -y*c**2 + 12/5*c - 12/5.
-3*(c - 2)**2/5
Suppose -3*k + 6*k = 21. Suppose 0 = 4*s - k - 1. Suppose 2*c + 4*c**s + 3*c - 5*c + 4*c**3 = 0. What is c?
-1, 0
Let s = -34 - -79. Let c be 314/10 + (-18)/s. Solve c*d**2 - 13*d**2 - 14*d**2 - d**4 - 3*d**4 = 0 for d.
-1, 0, 1
Let j(o) be the first derivative of o**6/33 + 14*o**5/55 + 3*o**4/11 - 36. Determine r so that j(r) = 0.
-6, -1, 0
Determine c, given that -2 + 81*c + 92*c + 221*c**2 - 53*c - 1121*c**2 - 2 = 0.
1/15
Suppose 6*x - 3*x = 0. Solve 7*o**2 + 4*o**3 - 4*o + x*o**2 - 7*o**2 = 0 for o.
-1, 0, 1
Determine c so that 0 - 2/11*c**2 - 42/11*c = 0.
-21, 0
Let d(u) be the second derivative of -u**4/42 + 458*u**3/21 - 52441*u**2/7 - 839*u. Factor d(l).
-2*(l - 229)**2/7
Let m(d) = -2*d**4 + d**3 + d**2 - 1. Let s(u) = u**5 + 5*u**4 - 12*u**3 + 8*u**2 + 16*u + 4. Let c(b) = -20*m(b) - 5*s(b). Let c(q) = 0. What is q?
-2, -1, 0, 2, 4
Let p(d) = 24*d**4 + 3*d**2 - 12*d + 15. Let j(l) = -l**4 - l**3 + l - 1. Suppose 25*f + 7 = 18*f. Let a(k) = f*p(k) - 15*j(k). Factor a(y).
-3*y*(y - 1)**2*(3*y + 1)
Factor 9*k + 81/2 + 1/2*k**2.
(k + 9)**2/2
Suppose 0 = -6*g + 21 - 3. Suppose -g*w - 403 + 1009 = 3*u, 4*u = -5*w + 803. Factor -65*y**2 + 207 - u + 10*y.
-5*y*(13*y - 2)
Let p(c) = 5*c**2 + 2*c + 4. Let a be p(-2). Suppose -z = 3*z - a. Factor -4 - z*b**2 - 5*b + b**2 - 3*b.
-4*(b + 1)**2
Let v = 13/115 + 521/1495. Suppose v*o + 2/13*o**2 + 0 = 0. Calculate o.
-3, 0
Let c(t) be the first derivative of 0*t**2 + 0*t**3 + 0*t + 14 + 1/20*t**4. Determine w, given that c(w) = 0.
0
Let w(m) = -m**2 - m - 1. Let f = -14 + 17. Let s(c) = 6*c**4 + 9 - 4*c**4 - 6*c**f + 7*c + c**2 + 14*c**2. Let h(g) = 2*s(g) + 18*w(g). What is u in h(u) = 0?
0, 1
Suppose 4*m - 163 = 149. Factor m*k**2 - 165*k**2 + 88*k**2 - 2*k**3 - k**4 + 2*k.
-k*(k - 1)*(k + 1)*(k + 2)
Let x = 12/605 - -17437/5445. What is v in -x*v**2 - 4/9 - v**3 - 8/3*v = 0?
-2, -1, -2/9
Suppose 3*a + 4*q = -11 + 38, 2*a + 5 = 5*q. Let d(z) be the first derivative of 2/5*z**a + 0*z**4 - 2 - 2/3*z**3 + 0*z + 0*z**2. Factor d(f).
2*f**2*(f - 1)*(f + 1)
Suppose -2*h - 2*h - 32 = 