20*w**2 + 30*w + 120. Let x(y) = -3*y**3 - y + 4. Let z(c) = -b(c) + 30*x(c). Let z(p) = 0. What is p?
-2, 0, 6
Let s(x) be the third derivative of x**8/112 + 2*x**7/35 + x**6/8 + x**5/10 + x**2 + 56*x. Suppose s(p) = 0. Calculate p.
-2, -1, 0
Let c(j) be the first derivative of j**5/5 + 9*j**4 + 388*j**3/3 + 576*j**2 + 1024*j - 687. Factor c(b).
(b + 2)**2*(b + 16)**2
Let q(i) = -2*i**3 + i**2 + i + 2. Let u(s) = 11*s**3 + 7*s**2 + 31*s + 22. Let k(b) = -5*q(b) - u(b). Find f, given that k(f) = 0.
-8, -2
Let r(q) be the third derivative of -1/336*q**8 + 0 + 1/60*q**5 - 22*q**2 - 1/210*q**7 + 0*q**3 + 0*q + 0*q**4 + 1/120*q**6. Factor r(y).
-y**2*(y - 1)*(y + 1)**2
Let f(u) be the first derivative of 1/7*u**2 - 2/21*u**3 - 32 + 0*u. Find b, given that f(b) = 0.
0, 1
Determine w, given that 0*w**2 + 13/2*w - 1/2*w**3 - 6 = 0.
-4, 1, 3
Let u(i) be the third derivative of 3*i**2 + 0 - 1/42*i**4 + 0*i + 0*i**3 + 1/210*i**5. Solve u(w) = 0.
0, 2
Suppose 36/5*n**2 - 54/5 - 14/5*n**4 + 4*n**3 - 54/5*n + 2/5*n**5 = 0. Calculate n.
-1, 3
Let a(b) = -b**2 + 6*b - 7. Let j(k) = 3*k**2 - 17*k + 21. Let s(v) = 14*a(v) + 4*j(v). Factor s(h).
-2*(h - 7)*(h - 1)
Let d(o) be the first derivative of -2*o - 1/20*o**5 - 2 + 0*o**3 + 0*o**2 - 1/6*o**4. Let y(t) be the first derivative of d(t). Factor y(h).
-h**2*(h + 2)
Factor 140/3*h - 2/3*h**2 - 2450/3.
-2*(h - 35)**2/3
Suppose -415 = 15*y - 20*y. Factor -11 - 5*i**2 - 68*i + 31 + y*i.
-5*(i - 4)*(i + 1)
Let b(d) be the first derivative of -1/6*d**4 - 1/3*d + 1/15*d**5 + 9 + 0*d**3 + 1/3*d**2. Suppose b(g) = 0. What is g?
-1, 1
Let f(p) = -p**3 + 8*p**2 - 12*p + 2. Let m be f(2). Suppose -1/8 + 1/8*c**3 + 3/8*c - 3/8*c**m = 0. What is c?
1
Let u = -1023 - -1025. Let o(d) be the first derivative of 0*d**2 - 2*d**4 + u + 0*d + 0*d**3 + 12/5*d**5 - 2/3*d**6. Factor o(f).
-4*f**3*(f - 2)*(f - 1)
Let 7/5*n**3 + 8/5*n - 4/5 + 19/5*n**2 = 0. What is n?
-2, -1, 2/7
Factor 135123343*q + 5*q**5 + 125659617*q + 121241*q**3 + 1715*q**4 + 12499240*q**2 + 98919*q**3 + 59050298 - 332554378.
5*(q - 1)*(q + 86)**4
Determine x, given that 3/4*x**4 + 21*x**2 + 0 - 15/2*x**3 - 18*x = 0.
0, 2, 6
Suppose -49 + 14 = -7*d. Let y(b) be the second derivative of 0 + 1/10*b**5 + 1/49*b**7 + d*b - 1/21*b**4 - 8/105*b**6 + 0*b**2 + 0*b**3. Factor y(o).
2*o**2*(o - 1)**2*(3*o - 2)/7
Factor 0*n + 2/15*n**2 + 0 - 2/15*n**3.
-2*n**2*(n - 1)/15
Let f(w) be the third derivative of -1/245*w**7 + 0*w**3 + 0*w**4 - 10*w**2 + 0*w - 1/210*w**5 + 0 + 1/105*w**6. Factor f(d).
-2*d**2*(d - 1)*(3*d - 1)/7
Let i(n) be the first derivative of n**3/2 + 6*n**2 + 21*n/2 - 46. What is z in i(z) = 0?
-7, -1
Let t be (-3)/(-1*(-6)/(-4)). Suppose 4*g = -t*f + 6, -5*f + f = 4*g - 4. Factor -10/11*q + 4/11 - 14/11*q**g.
-2*(q + 1)*(7*q - 2)/11
Let v(x) = -2*x**3 - 14*x**2 - 7*x + 3. Let b be v(-7). Determine m, given that 49*m**3 + b*m**3 + 8*m**4 - 104*m**3 - 3*m**5 - 2*m**2 = 0.
-1/3, 0, 1, 2
Factor -95/3*c - 1/3*c**4 - 19*c**2 - 50/3 - 13/3*c**3.
-(c + 1)*(c + 2)*(c + 5)**2/3
Let d be (16 - 0/2)*4. Factor 111*r**2 + d*r**2 + 27 + 144*r + 17*r**2.
3*(8*r + 3)**2
Factor -v**4 - 1/2*v**2 - 1/4*v**5 - 5/4*v**3 + 0*v + 0.
-v**2*(v + 1)**2*(v + 2)/4
Let o = -48119/8 - -6026. Let r = o - 689/72. Suppose 4/9*v**2 + r*v - 2/3*v**3 + 4/9 = 0. Calculate v.
-1, -1/3, 2
Let h(q) be the third derivative of -q**6/540 + q**4/9 + q**3/3 - 12*q**2. Let a(d) be the first derivative of h(d). Let a(y) = 0. What is y?
-2, 2
Let i(f) be the third derivative of -5/2*f**3 - 5/12*f**4 + 0 - 21*f**2 + 1/12*f**5 + 0*f. Factor i(g).
5*(g - 3)*(g + 1)
Suppose 0 = 4*h - 231 - 13. Let u = 65 - h. Suppose 8*y**3 - 7*y**5 + 22/3*y**2 - 20/3*y**u - 2/3 - y = 0. Calculate y.
-1, -2/7, 1/3, 1
Let y(f) be the second derivative of 3 + 0*f**3 + 3*f + 0*f**2 - 1/30*f**5 - 1/63*f**7 + 0*f**4 + 2/45*f**6. Solve y(r) = 0 for r.
0, 1
Let q(i) be the second derivative of i**4/132 - 94*i**3/33 + 4418*i**2/11 + 61*i. Find n such that q(n) = 0.
94
Let v(h) = 7*h**3 - 7*h**2 - 11*h + 6. Let i(b) = b**3 - b**2 - b + 2. Let y(d) = -3*i(d) + v(d). Solve y(j) = 0 for j.
-1, 0, 2
Let s(n) be the second derivative of n**5/150 + n**4/10 - 20*n + 1. Determine a, given that s(a) = 0.
-9, 0
Let n be (7 - 0)*8/28. Factor -2*k**4 + 30*k**n - 10*k**2 - 3*k**4 - 5*k**2 + 10*k.
-5*k*(k - 2)*(k + 1)**2
Factor 7*p + 29/4 - 1/4*p**2.
-(p - 29)*(p + 1)/4
Suppose 20 + 2590*o**2 - 4*o**4 - 911*o**2 - 878*o**2 + 87*o**3 + 39*o - 943*o**2 = 0. Calculate o.
-1/4, 1, 20
Let n(z) = 4*z**4 - 4*z**3 + 16*z**2 + 14*z + 10. Let r(l) = 2*l**4 + l + 1. Let s(j) = -n(j) + 10*r(j). Factor s(g).
4*g*(g - 1)*(g + 1)*(4*g + 1)
Let n(q) = 28*q**3 + 29*q**2 + q. Let g(j) = 28*j**3 + 30*j**2 + 2*j. Let o(f) = -3*g(f) + 2*n(f). Factor o(h).
-4*h*(h + 1)*(7*h + 1)
Let o(z) be the first derivative of -1/54*z**4 + 1 + 0*z**3 + 1/9*z**2 + 2*z. Let c(t) be the first derivative of o(t). Factor c(r).
-2*(r - 1)*(r + 1)/9
Let p be ((-84)/(-280))/(3/5). Factor -1/4*i**2 + 3/4 + p*i.
-(i - 3)*(i + 1)/4
Let f be (1/7)/((-4824)/(-192) - 25). Factor -f*j - 36/7*j**2 + 0 - 4*j**3.
-4*j*(j + 1)*(7*j + 2)/7
Let j be 4/8 - 14/(-4). Suppose -139*a + 1320*a**2 - 1416*a**3 - 156*a - 2*a + 525*a**5 - 135*a + 48 - 45*a**j = 0. Calculate a.
-2, 2/7, 2/5, 1
Suppose 215 = 63*f + 89. Solve -3/4*a**3 + 9/2*a**f + 6 - 9*a = 0 for a.
2
Let x(w) be the first derivative of w**4/16 + w**3/4 + 5*w - 2. Let h(t) be the first derivative of x(t). Factor h(l).
3*l*(l + 2)/4
Let x = 12/5 - 34/15. Let m = 3077/15 + -205. Solve -m*u**2 + 2/15 - 2/15*u**3 + x*u = 0.
-1, 1
Determine n so that -30/7*n**2 - 6/7*n**3 + 48/7*n + 72/7 = 0.
-6, -1, 2
Suppose -7 = 2*f + 5*j, 5*f - 2*j = 2*j + 32. What is m in m**2 - 4*m**5 - 12*m**3 - 7*m**4 - 5*m**2 - 5*m**f = 0?
-1, 0
Let v be (-84)/105 - (-4 + 24/20). Suppose -2*d**3 + 2*d - 2/3*d**4 + 4/3 - 2/3*d**v = 0. Calculate d.
-2, -1, 1
Let n(b) = -b**3 + 3*b**2 - b. Let m be n(0). Determine u so that 0 - 2/7*u**3 + 2/7*u + m*u**2 = 0.
-1, 0, 1
Suppose 0 = 18*g - 48 - 6. Determine q, given that 3*q**2 - q - 4 - 5*q**3 + 9*q**g + q**4 + 0*q**2 - 3*q = 0.
-2, -1, 1
Let m(x) be the first derivative of -x**6/360 - 7*x**5/90 - 49*x**4/72 + 9*x**2 - 19. Let w(p) be the second derivative of m(p). Factor w(d).
-d*(d + 7)**2/3
Let a(h) be the first derivative of 2*h**6 + 28*h**5/5 - 71*h**4/3 - 44*h**3/3 + 28*h**2 - 32*h/3 - 25. Solve a(k) = 0 for k.
-4, -1, 1/3, 2
Let h be ((-1)/(-2))/((-6)/(-48)). Let v = 7 - h. Factor 13*n**3 - 9*n - 3*n**5 - n**v + 3 - 6*n**2 + 3.
-3*(n - 1)**3*(n + 1)*(n + 2)
Let j(t) = -7*t**4 + 20*t**3 - 23*t**2 + 4*t - 3. Let m(v) = 36 - 24*v + 41*v**4 - 119*v**3 + 137*v**2 + 32 - 51. Let o(l) = 34*j(l) + 6*m(l). Factor o(r).
2*r*(r - 2)**2*(4*r - 1)
Let o(w) = -8*w**2 - 205*w - 5414. Let h(v) = 22*v**2 + 616*v + 16240. Let z(q) = 3*h(q) + 8*o(q). Factor z(k).
2*(k + 52)**2
Let n(x) be the first derivative of x**5 - 5*x**4/2 - 95*x**3/3 - 70*x**2 - 60*x - 659. Factor n(o).
5*(o - 6)*(o + 1)**2*(o + 2)
Suppose 0*c = c - 4, -231 = -5*l - 4*c. Determine m so that -3*m**2 + 101*m**2 + 36*m + 8 - l*m - 49*m = 0.
2/7
Suppose 2*i - 5 = 6*o - 9*o, 4*o + 4 = 0. Let z(c) be the third derivative of 8*c**2 + 0 + 1/4*c**i + 0*c - 1/20*c**5 - 1/40*c**6 + 0*c**3. Factor z(t).
-3*t*(t - 1)*(t + 2)
Let i(c) be the second derivative of -c**6/45 - c**5/2 + 4*c**4 - 76*c**3/9 - 59*c - 3. Determine o so that i(o) = 0.
-19, 0, 2
Let r = 375 - 375. Let f(b) be the first derivative of -1/2*b**2 + r*b - 3/2*b**4 - 9 - 4/5*b**5 - 1/6*b**6 - 4/3*b**3. Suppose f(i) = 0. What is i?
-1, 0
Suppose -c + 5*t + 22 = 0, -c + 2*t = 2*c - 14. Factor -5*k**3 + c*k**3 + 12*k**2 + 4*k**3 + 64 + 48*k.
(k + 4)**3
Factor -5 - 4 - 6*a + 8*a**2 - 28*a**2 + 19*a**2.
-(a + 3)**2
Let l be (-6)/4 - (4 + (-625)/100). Factor 3/8*k**2 + 3/8 - l*k.
3*(k - 1)**2/8
Let o = 4 + -2. Factor 45 + x**2 - o*x - 88 + 44.
(x - 1)**2
Suppose 4*n + 5 = -3, -44 = 4*u - 2*n. Let z = -8 - u. Determine q so that z*q**3 - 5*q + 2*q + 2*q - 3*q**3 = 0.
-1, 0, 1
Let v(y) = y**3 + 6*y**2 + 3*y - 4. Let x be v(-3). Let r be (8/x)/(168/196). Let -r*p**3 + 4/3*p + 0 + 2/3*p**2 = 0. What is p?
-1, 0, 2
Let i(v) = -20*v**3 + 28*v**2 - 24*v + 32. Let c(w) = -13*w**3 + 19*w**2 - 16*w + 20. Let s(g) = 8*c(g) - 5*i(g