2*t**3.
-2*(t - 2)*(t - 1)*(t + 1)
Let t(u) = -37*u - 12. Let l be t(-5). Suppose l*c = 174*c - 5. Factor 3/4*s + 3/2*s**2 - 3/4*s**4 - 3/4 + 3/4*s**c - 3/2*s**3.
3*(s - 1)**3*(s + 1)**2/4
Let y(n) = 24*n**2 - 10*n + 12. Let c(o) = o**2. Let u(j) = -44*c(j) + 2*y(j). Factor u(i).
4*(i - 3)*(i - 2)
Factor 89882/3*i**2 + 49/6*i**4 - 2954/3*i**3 - 16880*i + 2400.
(i - 60)**2*(7*i - 2)**2/6
Let n be 7 - 4 - 5 - -3. Let d be (n + 5)*(-4)/(-8). Find s such that -3*s + 6*s**4 + 3*s**3 + d*s**2 - 2*s**2 - 7*s**2 = 0.
-1, -1/2, 0, 1
Let v(r) = -r**3 + 4*r**2 + 3*r - 7. Let h = -2 + 5. Let f be v(h). Factor f - 3*z**2 + 17 - 103 + 30*z.
-3*(z - 5)**2
Let b(l) be the first derivative of l**4/30 - 2*l**3/9 + 217. Let b(i) = 0. Calculate i.
0, 5
Let v be 1076/4842 + 20/18. Factor v*y + 0 + 1/3*y**2.
y*(y + 4)/3
Factor 5*g**3 - 97*g - 75 - 2*g**2 + 32*g + 17*g**2.
5*(g - 3)*(g + 1)*(g + 5)
Let u be (-4)/(-18)*(20 + -5)/5. Let q(c) be the first derivative of -2 - u*c**3 - 2*c**2 - 2*c. Find y, given that q(y) = 0.
-1
Let x be (-4)/(-70) - (-725)/2625. Let y be (-24)/(-18)*(-6)/(-4). Suppose 1/3*m**3 - x*m - 1/3*m**4 - 2/3 + m**y = 0. Calculate m.
-1, 1, 2
Let u(s) be the second derivative of -s**8/36960 + s**6/3960 - 11*s**4/6 - 17*s. Let n(a) be the third derivative of u(a). Determine b so that n(b) = 0.
-1, 0, 1
Let h(k) be the second derivative of -k**5/90 - k**4/18 + k**3/3 - 5*k**2/9 + 487*k. Solve h(y) = 0 for y.
-5, 1
Let c be (-250)/(-4) - (-9)/(-6). Determine i so that -28 - 37 - 8*i**2 + c - 18*i = 0.
-2, -1/4
Factor 0 - 3/4*o**2 + 0*o + 1/4*o**3.
o**2*(o - 3)/4
Let l be 230/70 - ((-12)/(-14))/3. Let u(h) be the first derivative of -3*h**4 + 0*h - 4*h**l - 3/5*h**5 + 1 + 0*h**2. Factor u(a).
-3*a**2*(a + 2)**2
Let q(c) be the first derivative of -5*c**6/6 - 3*c**5 - 15*c**4/4 - 5*c**3/3 + 109. Factor q(r).
-5*r**2*(r + 1)**3
Let v = -2305 - -2307. Factor 1/4*b**v - 3/4*b + 1/2.
(b - 2)*(b - 1)/4
Suppose 0 = -u + 2*k + 3, 0*k - 6 = -2*u + k. Let f be 1/u - (-70)/42. Factor -4*q**3 + 3*q**f + 4*q**3 + 3*q**3.
3*q**2*(q + 1)
Let w(k) = -50*k**4 - 64*k**3 + 28*k**2. Let o(s) = -7*s**4 - 9*s**3 + 4*s**2. Let b(m) = -44*o(m) + 6*w(m). Solve b(p) = 0 for p.
-2, 0, 1/2
Let r(u) be the second derivative of u**6/15 - 11*u**5/20 + u**4/3 + 5*u**3/6 - 39*u. Factor r(x).
x*(x - 5)*(x - 1)*(2*x + 1)
Let z(w) be the second derivative of -5*w**7/42 + 2*w**6 - 17*w**5/2 - 5*w**4 + 175*w**3/6 + 127*w + 2. Find h such that z(h) = 0.
-1, 0, 1, 5, 7
Let 8/7 - 10/7*r**4 + 2/7*r**5 - 16/7*r + 2*r**3 + 2/7*r**2 = 0. What is r?
-1, 1, 2
Let p(b) be the first derivative of -4*b**5/5 + 26*b**4 - 436*b**3/3 - 1560*b**2 - 3600*b - 15. Factor p(x).
-4*(x - 15)**2*(x + 2)**2
Let b be (-42)/(-4)*(-14)/21. Let g = b - -15. What is z in 2 - 6*z - 2*z**5 + 30*z + 4*z**2 + 4*z**4 + g*z**4 - 22*z**3 - 18 = 0?
-1, 1, 2
Factor 166*p**3 - 16/5 + 1128/5*p - 1668/5*p**2 - 138/5*p**4.
-2*(p - 2)**3*(69*p - 1)/5
Let d(i) = -3*i + 0*i - 6 + 5*i. Let r be d(3). Factor 1/2*x**2 + 1/4*x + 1/4*x**3 + r.
x*(x + 1)**2/4
Solve 0 - 8/3*d**2 + 0*d + 2/9*d**3 = 0 for d.
0, 12
Let l(v) be the third derivative of 0*v**3 + 1/105*v**7 + 1/30*v**5 - 1/48*v**4 - 1/672*v**8 + 0*v + 0 - 1/40*v**6 - 8*v**2. Factor l(i).
-i*(i - 1)**4/2
Let m(s) be the second derivative of 0*s**2 + 1/63*s**7 + 0*s**3 - 1/30*s**5 + 1/45*s**6 - 1/18*s**4 + 0 - s. Factor m(u).
2*u**2*(u - 1)*(u + 1)**2/3
Let h(w) be the third derivative of -11/180*w**7 + 0 - 1/90*w**5 - 7/288*w**8 + 0*w**3 - 2/45*w**6 - 7*w**2 + 0*w**4 + 0*w. Let h(c) = 0. What is c?
-1, -2/7, 0
Let r = 32 - 16. Suppose 4*g - 12 = -2*b, 4*g = 6*b - 7*b + r. Suppose 0*f - 2/3*f**2 - 2/3*f**g + 0 + 2/3*f**3 + 2/3*f**4 = 0. Calculate f.
-1, 0, 1
Let p be 5/7 - 4/(-14). Suppose 0 = -3*a + 8 + p. Find d such that a*d - 3*d**3 - 4 + 0*d**4 + d**4 + d - d**3 + 3*d**2 = 0.
-1, 1, 2
Let d be ((-3)/2)/(1 + -7). Let j be 36 + (2403/(-36) - -31). What is w in -1/2*w + 1/2*w**3 - j*w**4 + d*w**2 + 0 = 0?
-1, 0, 1, 2
Let w(j) be the first derivative of j**6/63 - 4*j**5/21 - j**4/14 + 40*j**3/9 + 28*j**2/3 - 68. Determine b, given that w(b) = 0.
-2, 0, 7
Let k(z) be the third derivative of 1/5*z**6 + 6/5*z**5 + 0 + 0*z - 7*z**2 + 8*z**3 + 1/70*z**7 + 4*z**4. Find a such that k(a) = 0.
-2
Let p be (16/(-28))/(0 - (-260)/(-210)). Find m, given that 10/13*m**3 + 0 - 2/13*m**4 + p*m - 14/13*m**2 = 0.
0, 1, 3
Let c(z) = 3*z**4 + 15*z**3 + 9*z**2 - 6*z - 3. Let r(t) be the second derivative of -t**5/20 - t**4/12 - t. Let a(g) = -c(g) - 9*r(g). What is q in a(q) = 0?
-1, 1
Find j such that -1/7*j**3 + 0*j**4 + 0 + 1/7*j**5 + 0*j + 0*j**2 = 0.
-1, 0, 1
Suppose -4*w = w, -2*i - w = -8. Factor i*s**2 + 2*s**2 + 4*s - 5*s**2 + s**2.
2*s*(s + 2)
Let m(j) be the first derivative of -2*j**3/27 - 4*j**2/9 - 599. Determine u so that m(u) = 0.
-4, 0
Let u(k) be the second derivative of k**7/280 - k**6/30 + 3*k**5/40 - 8*k**3/3 + 28*k. Let h(a) be the second derivative of u(a). Solve h(q) = 0 for q.
0, 1, 3
Let x(a) be the first derivative of -3*a**5/20 + 7*a**4/4 - 15*a**3/2 + 27*a**2/2 + 4*a - 17. Let w(l) be the first derivative of x(l). Solve w(b) = 0 for b.
1, 3
Let v(u) = 2*u - 44. Let z be v(-16). Let j = 76 + z. Factor -4/7*o**3 + 0*o + 0 - 2*o**4 + j*o**2.
-2*o**3*(7*o + 2)/7
Factor -4*p**3 + 63 - 255 - 415*p + 0*p**3 + 27*p - 200*p**2.
-4*(p + 1)**2*(p + 48)
Let d(j) be the third derivative of -j**5/20 + 23*j**4/8 - 11*j**3 + 2*j**2 - 60*j. Factor d(r).
-3*(r - 22)*(r - 1)
Let h be 49/42 - (-5)/50*-5. Factor -4/3*o - h*o**2 + 2.
-2*(o - 1)*(o + 3)/3
Factor 69 - 144 + 8*p**2 + 75 + 2*p**3.
2*p**2*(p + 4)
Solve -11*o**3 + 19*o**4 - 37*o**4 + 20*o**4 + 5*o**2 = 0 for o.
0, 1/2, 5
Let m be ((-2)/15*6)/((-4)/10). Find r, given that 20*r - m*r + 92*r**3 + 6*r**5 - 3 - 42*r**2 - 44*r**3 - 27*r**4 = 0.
1/2, 1
Let d(y) = -y**3 - 2*y**2 + 23*y - 4. Let l be d(-6). Let s(m) be the first derivative of l + 0*m**4 - 2/15*m**3 + 0*m**2 + 1/25*m**5 + 1/5*m. Factor s(v).
(v - 1)**2*(v + 1)**2/5
Let s(m) be the third derivative of m**8/1344 - m**7/84 + m**6/60 + m**5/24 - 3*m**4/32 + 3*m**2 + 15. Solve s(p) = 0.
-1, 0, 1, 9
Let l(c) be the third derivative of 4/3*c**3 + 0*c - 3/4*c**4 + 0 - 1/60*c**6 + 18*c**2 + 1/5*c**5. Suppose l(o) = 0. Calculate o.
1, 4
Suppose 40*a - 35/2*a**2 - 10 = 0. What is a?
2/7, 2
Factor -21*t**2 + 69 + 3*t**2 - 16 - 17 - 18 + 3*t**3 - 3*t.
3*(t - 6)*(t - 1)*(t + 1)
Let z = -38 - -41. Factor -2*x**2 + z*x + 7*x**3 - 6*x - 8*x**3 + 2*x.
-x*(x + 1)**2
Determine m, given that 0 - 12*m**2 + 3*m**5 - 144/5*m**3 + 48/5*m - 21/5*m**4 = 0.
-2, -1, 0, 2/5, 4
Let q(g) = -3*g**2 + 37*g - 70. Let d be q(10). Factor -1/3*m**4 + 2/3*m + d + 2/3*m**2 + 1/6*m**5 - 1/2*m**3.
m*(m - 2)**2*(m + 1)**2/6
Let z(v) be the third derivative of v**5/100 + v**4/30 - 2*v**3/15 + 235*v**2 - v. Solve z(g) = 0 for g.
-2, 2/3
Let a(g) be the second derivative of -3*g**4 - 112*g**3 - 1568*g**2 - 10*g + 2. Let a(l) = 0. Calculate l.
-28/3
Let f(k) be the first derivative of 3/20*k**2 + 1/5*k + 1/30*k**3 + 12. Factor f(j).
(j + 1)*(j + 2)/10
Let d = 54380/3 - 18126. Factor 2/3*z**3 - 2/3*z + 2/3*z**4 - d*z**2 + 0.
2*z*(z - 1)*(z + 1)**2/3
Let a = -92 - -93. Let q(t) = -t**3 - t. Let u(j) = -5*j**2 + 5*j. Let z(h) = a*u(h) + 5*q(h). Let z(o) = 0. What is o?
-1, 0
Solve 2*p**3 - 3*p**3 + 28 - 52 - 5 - 3 + 6*p**2 = 0 for p.
-2, 4
Let u(g) be the second derivative of -g**4/3 - 8*g**3/3 - 8*g**2 + 509*g. Factor u(d).
-4*(d + 2)**2
Let k = -1085/157 + -46390/6123. Let f = -43/3 - k. Factor f*p**2 + 0 + 2/13*p.
2*p*(p + 1)/13
Let t = -623 + 3117/5. Suppose -46/5*h**2 + 32/5*h**5 - 14/5*h**3 - t + 48/5*h**4 - 18/5*h = 0. What is h?
-1, -1/4, 1
Let x = 575/9 + -64. Let g = 5/9 - x. Factor -g*f**2 - 2/3*f**3 + 2/3*f + 2/3.
-2*(f - 1)*(f + 1)**2/3
Let m(p) be the third derivative of -p**6/160 + 13*p**5/40 - 6*p**4 + 36*p**3 + 7*p**2 - p. Factor m(j).
-3*(j - 12)**2*(j - 2)/4
Let z be (6*(-6)/24)/(6/(-20)). Let m(v) be the second derivative of 0 + 1/2*v**3 + z*v - 9/2*v**2 + 5/12*v**4 + 1/20*v**5. Solve m(q) = 0 for q.
-3, 1
Suppose 5*w - 22 = -5*c - 2, c = w + 2. Factor -8*v - c*v + 3*v + 0 - 4 - 4*v**2.
-4*(v + 1)**2
Let o(f) = -2*f**3 + 12*f**2 - 56*f. Let h be o(6). Let i = h - -339. Suppose 2/5*z**i - 6/5*z**2 + 