p be (41 + -7 + -50)*2*2/(-40). Factor -p*r**2 + 0 + 4/5*r**3 + 0*r.
4*r**2*(r - 2)/5
Suppose 1139 - 1095 = 22*g. Determine k so that -4/5*k**5 + 0 - 12/5*k**4 - 4/5*k**g - 12/5*k**3 + 0*k = 0.
-1, 0
Determine f so that 12/7*f**3 - 38/7*f**2 + 8/7 - 6*f = 0.
-1, 1/6, 4
Let c be (12 - 4) + -5 - (1 - 31). Let -c*g - 4 + 79*g - 37*g - 22*g - 3*g**2 = 0. Calculate g.
-4, -1/3
Let v(b) be the first derivative of -20/3*b**3 + 12 + 4/5*b**5 + 16*b + 0*b**4 + 0*b**2. Determine k, given that v(k) = 0.
-2, -1, 1, 2
Let g(f) = 16*f**3 - 7*f**2 - 4*f. Let c be (2/(-6))/(9/(-81)). Let x(o) = 8*o**3 - 3*o**2 - 2*o. Let p(s) = c*g(s) - 5*x(s). Find b, given that p(b) = 0.
-1/4, 0, 1
Let d(t) be the third derivative of t**5/75 + 7*t**4/15 + 98*t**3/15 + 58*t**2. Find y such that d(y) = 0.
-7
What is r in 0 - 3*r + 1/5*r**3 + 14/5*r**2 = 0?
-15, 0, 1
Let p(c) be the second derivative of 0*c**2 - 35*c - 9/20*c**5 - 1/2*c**3 + 1/10*c**6 + 0 + 3/4*c**4. Factor p(y).
3*y*(y - 1)**3
Suppose 6*x - 5*x + 2 = 0. Let i be x/6*54/(-42). Determine a, given that -6/7*a**2 + 9/7*a - 6/7*a**3 + 9/7*a**4 - 3/7 - i*a**5 = 0.
-1, 1
Let u(x) be the third derivative of 0 + 319/150*x**5 - 32/15*x**4 + 4/5*x**3 + 121/300*x**6 + 0*x + 24*x**2. Factor u(f).
2*(f + 3)*(11*f - 2)**2/5
Let a(y) be the third derivative of -y**5/150 + y**4/6 + 85*y**2. What is n in a(n) = 0?
0, 10
Let y(n) be the first derivative of 1/22*n**4 + 8 + 2/33*n**3 + 0*n**2 + 0*n. Suppose y(h) = 0. What is h?
-1, 0
Let o(w) = -9*w**2 + 11*w**2 + 5*w + 11*w**3 + 15*w**2 + 0*w**2 + 5. Let m(g) = -5*g**3 - 8*g**2 - 2*g - 2. Let z(a) = 5*m(a) + 2*o(a). What is b in z(b) = 0?
-2, 0
Let n = 2154 - 1055459/490. Let z(a) be the third derivative of 0*a**3 + n*a**7 + 0*a**6 + 0*a + 0*a**4 + 5*a**2 + 0 - 1/140*a**5. Factor z(k).
3*k**2*(k - 1)*(k + 1)/7
Factor -3*h**4 + 47*h**3 + 3*h**4 - 29*h**3 + 69*h**2 + 33*h + 3*h**4 + 21*h**3.
3*h*(h + 1)**2*(h + 11)
Let r(f) be the third derivative of 1/72*f**4 + 0*f**3 + 0 - 17*f**2 - 1/1260*f**7 + 1/120*f**5 + 0*f**6 + 0*f. Determine d so that r(d) = 0.
-1, 0, 2
Let z = -1 + 3. Let -17*v**4 + 60*v**3 + 481*v**z - 445*v**2 + 45*v**4 + 4*v**5 = 0. What is v?
-3, -1, 0
Factor -1050 - y**2 + 1037 + 4*y + 10*y.
-(y - 13)*(y - 1)
Let q(z) be the first derivative of z**3 + 135*z**2/2 - 239. Factor q(t).
3*t*(t + 45)
Let h(j) = 8*j**2 - 3. Let k(f) = -f**2 + 2*f - 1. Let z(w) = -4*h(w) + 12*k(w). Let z(i) = 0. Calculate i.
0, 6/11
Let r = 54 + -44. Factor -12*z**3 - 10*z**3 - r*z + 17*z**3 + 15*z**2.
-5*z*(z - 2)*(z - 1)
Let s(t) = -t**4 + t**3. Let m(n) = -n**4 - 5*n**3. Suppose 0 = o - 24 + 5. Let w = o - 21. Let g(f) = w*s(f) - m(f). Factor g(p).
3*p**3*(p + 1)
Suppose -5*n + 4*i - 212 = 0, -2*n + 7*i - 86 = 6*i. Let o be n/55*1/(-2). Let 2/5*z**3 + 2/5 - 2/5*z - o*z**2 = 0. Calculate z.
-1, 1
Let j(d) be the first derivative of -d**6/180 - 13*d**5/180 - 2*d**4/9 - 5*d**3/18 - 5*d**2/2 - 15. Let w(f) be the second derivative of j(f). Factor w(y).
-(y + 1)*(y + 5)*(2*y + 1)/3
Let c = -29 + 6. Let j = 23 + c. Let 0*x**2 + j*x + 0 + 2/11*x**3 + 2/11*x**4 = 0. Calculate x.
-1, 0
Determine m so that 1964*m**4 - 1966*m**4 - 7*m**5 - 2*m**2 + 2*m**2 = 0.
-2/7, 0
Let g be (-63 - -5)*4/(-4). What is w in -w**3 - 27*w**2 - 139*w + g*w - 2*w**3 - 81 = 0?
-3
Let l(z) = -z**2 + 10*z + 15. Let g be l(11). Suppose g*j - 8*j + 16 = 0. Let -j*x**3 - 4*x**2 - 3*x**2 + x**3 + x**2 = 0. Calculate x.
-2, 0
Let r be 5/(-2)*(-18)/(-15). Let o be ((-10)/r)/(2/3). Suppose 2*t**3 - t**3 + o*t**2 - 4*t**2 = 0. What is t?
-1, 0
Suppose 487 = 97*k + 293. Solve -6*g + 15/4*g**4 + 3 + 6*g**3 - 27/4*g**k = 0.
-2, -1, 2/5, 1
Let m = -1277 - -5111/4. Let q(g) be the second derivative of 7/4*g**4 + 0 - 8*g - m*g**5 - g**3 + 0*g**2. Determine v so that q(v) = 0.
0, 2/5, 1
Let d(u) be the first derivative of u**7/280 - u**6/20 + 9*u**5/40 + 4*u**3/3 + 17. Let j(p) be the third derivative of d(p). Let j(s) = 0. What is s?
0, 3
Factor -3*f**3 - 3/2*f**4 + 15/2 + 18*f**2 - 21*f.
-3*(f - 1)**3*(f + 5)/2
Let t be (-10)/2*2*(-6)/10. Determine g, given that 15*g + 2*g**3 + g**3 + 4*g**3 + t - 4*g**3 + 12*g**2 = 0.
-2, -1
Let l = 3833 + -26829/7. Suppose -l*p**2 - 6/7*p - 4/7 = 0. Calculate p.
-2, -1
Let k = 144845/11 + -13153. Factor 0 - 2/11*i**5 + 0*i - 126/11*i**3 - k*i**2 + 34/11*i**4.
-2*i**2*(i - 9)**2*(i + 1)/11
Let z(x) be the third derivative of -x**6/120 + x**5/15 - 86*x**2. Find h such that z(h) = 0.
0, 4
Let z(c) = 8*c**3 + 78*c**2 + 50*c - 16. Let h(f) = 8*f**3 + 78*f**2 + 49*f - 15. Let g(o) = 2*h(o) - 3*z(o). Determine u, given that g(u) = 0.
-9, -1, 1/4
Let c(y) be the first derivative of -5/2*y**2 - 1/6*y**6 + y**5 + y + 10/3*y**3 + 1 - 5/2*y**4. Factor c(f).
-(f - 1)**5
Let p(l) be the third derivative of l**6/210 + 64*l**5/105 - 131*l**4/42 + 44*l**3/7 - 3*l**2 - 16*l. Let p(x) = 0. Calculate x.
-66, 1
Let u(o) = -10*o**2 + 8*o - 3. Let y be u(4). Let q = y - -404/3. Factor 0 + 2/3*v**2 + 0*v + q*v**3.
v**2*(11*v + 2)/3
Let i(k) be the first derivative of -k**4/4 + 41*k**3/9 + 8*k**2/3 - 28*k/3 - 50. Solve i(w) = 0 for w.
-1, 2/3, 14
Find g such that 615*g**4 + 846*g**5 - 580*g**3 - 1760*g**2 - 80 + 550*g**4 + 800*g - 391*g**5 = 0.
-2, 2/13, 2/7, 1
Let k(l) = l**2 - 9*l + 32. Let r be k(5). Let p be r/4*(-3)/(-2). Solve p*z**3 - 3*z**2 + 0*z**4 - 3/2*z**5 + 0*z + 0 = 0.
-2, 0, 1
Let k(c) be the first derivative of -2*c**3/15 + 2*c**2/5 - 2*c/5 + 132. Factor k(z).
-2*(z - 1)**2/5
Suppose x = -21 + 108. Determine q, given that 2*q**2 - x*q + 40*q + 45*q = 0.
0, 1
Solve 6184*y - 2*y**3 - 21997284 - 163465*y - 1260*y**2 - 107319*y + 3475284 = 0.
-210
Let n(f) = -2*f**3 + 3*f**2 + 11*f. Let p(g) = -4*g**3 + 5*g**2 + 23*g. Let q(v) = 7*n(v) - 3*p(v). Determine c, given that q(c) = 0.
-1, 0, 4
Let u be (-7)/(-3) - (-4)/(-3). Solve 51*d**2 - u - 54*d**2 + 13 = 0 for d.
-2, 2
Let b(l) be the third derivative of -l**10/90720 + l**8/6720 - l**7/3780 - l**4/4 - 17*l**2. Let u(j) be the second derivative of b(j). Solve u(w) = 0.
-2, 0, 1
Let n(d) = 16*d**2 + 150*d + 509. Let s(f) = 9*f**2 + 75*f + 255. Let k(y) = -3*n(y) + 5*s(y). Factor k(u).
-3*(u + 4)*(u + 21)
Suppose 4*o = -2*c + 4*c, 5*c - 30 = -5*o. Let i = 35/237 + 44/237. Determine k so that 0 - 1/3*k**o - i*k = 0.
-1, 0
Let b = 22456 + -157191/7. Determine p, given that 1/7*p**4 + b*p**5 + 0 - 4/7*p**2 + 0*p - 4/7*p**3 = 0.
-2, -1, 0, 2
Factor 0*h + 8/9 - 2/9*h**2.
-2*(h - 2)*(h + 2)/9
Let p = -71 - -262. Let w = p - 565/3. Factor -2/3*m**3 + 2/3*m**4 - 8/3*m**2 + w*m + 0.
2*m*(m - 2)*(m - 1)*(m + 2)/3
Let d be -304 - -3 - (1 + 3 + -4). Let x = -301 - d. Let 27/7*t**3 - 15/7*t**4 + 3/7*t**5 + 6/7*t + x - 3*t**2 = 0. What is t?
0, 1, 2
Let z = -47 - -48. Let g be (2/8)/z - 9/(-36). Factor g*r**3 + 0 + 0*r**2 - 1/2*r.
r*(r - 1)*(r + 1)/2
Let v(d) be the third derivative of d**6/660 - d**4/33 - 34*d**2 - d. Find z such that v(z) = 0.
-2, 0, 2
Let g(m) be the second derivative of -2*m**6/15 + 76*m**5/5 - 1444*m**4/3 - 2*m - 11. Factor g(q).
-4*q**2*(q - 38)**2
Suppose 0 = -8*m - 24 + 40. Let v(a) be the first derivative of -3 + 6/7*a**m + 2/21*a**3 + 18/7*a. Let v(x) = 0. What is x?
-3
Let l(q) be the third derivative of -q**6/160 + q**5/10 - 17*q**4/32 + 5*q**3/4 - 14*q**2 - 4*q. Factor l(y).
-3*(y - 5)*(y - 2)*(y - 1)/4
Let x(w) be the second derivative of w**6/180 + w**5/30 + 16*w**3/3 - 23*w. Let j(z) be the second derivative of x(z). Suppose j(c) = 0. Calculate c.
-2, 0
Let u(t) = -4*t. Let c be u(0). Let j be (8/10 - (-18)/(-45)) + c. Suppose 3/5*g + 1/5*g**2 + j = 0. Calculate g.
-2, -1
Let l(c) be the first derivative of -c**6/24 + c**5/3 + 5*c**4/8 - 15*c**3 + 21*c**2/2 - 24. Let z(s) be the second derivative of l(s). Factor z(n).
-5*(n - 3)**2*(n + 2)
Let u(v) be the third derivative of -v**7/735 - 3*v**6/35 - 179*v**5/105 - 51*v**4/7 - 289*v**3/21 + 79*v**2. Factor u(n).
-2*(n + 1)**2*(n + 17)**2/7
Let y(s) = -13*s**3 + 29*s - 4*s**2 + 16 + 10*s**2 - s**2. Let j(o) = 72*o**3 - 28*o**2 - 160*o - 88. Let h(p) = 5*j(p) + 28*y(p). Factor h(b).
-4*(b - 2)*(b + 1)**2
Let a(r) = -2*r**3 - 9*r**2 - 37*r. Let v(f) = -f**3 - 5*f**2 - 18*f. Let m(j) = -4*a(j) + 9*v(j). Find b, given that m(b) = 0.
-7, -2, 0
Let j(o) be the second derivative of -1/40*o**5 + 15*o 