t is a?
-3, 1, 2
Let g(i) be the third derivative of i**6/360 - i**5/30 + i**4/9 - 27*i**2 - 2. Find q, given that g(q) = 0.
0, 2, 4
Let i(w) be the first derivative of -2*w**6/15 + 88*w**5/25 - 166*w**4/5 + 1792*w**3/15 - 98*w**2/5 - 2744*w/5 - 35. Suppose i(g) = 0. Calculate g.
-1, 2, 7
Let t be 4/(-20) + (-3)/(-15). Suppose -2*u - 6 + 18 = t. What is r in -26/7*r - 4/7 - u*r**2 = 0?
-1/3, -2/7
Let i = 30 - 26. Let m(b) = -2*b**3 - 8*b**2 + 0 - 4*b**i - 5 - 6*b**3 + 1 - 4*b. Let c(f) = -f**3 - f**2 + 1. Let h(r) = 4*c(r) + m(r). Factor h(o).
-4*o*(o + 1)**3
Let c = -34 - -58. Suppose 0 = -x - 18 + c. Let -x*s**3 - 2*s**3 + 4*s + 2*s**3 + 4*s**3 + 2*s**2 = 0. Calculate s.
-1, 0, 2
Let x be (-6)/1 - 7/((-70)/66). Factor -6/5*z + 0 + x*z**2 + 3/5*z**3.
3*z*(z - 1)*(z + 2)/5
Find h such that 0 - 381/5*h**3 + 12/5*h + 18*h**4 + 81/5*h**2 = 0.
-1/10, 0, 1/3, 4
Let n(h) be the first derivative of 4*h**3/3 - 8*h**2 - 128*h + 306. Factor n(o).
4*(o - 8)*(o + 4)
Solve 2/3*f + 0 + 1/3*f**3 - f**2 = 0 for f.
0, 1, 2
Solve 1/3*b**2 + 0 + 7*b = 0 for b.
-21, 0
Let a(s) be the second derivative of 7*s**6 + 0*s**2 - 2*s**3 + 23*s + 0 - 5*s**4 - 7/2*s**7 + 9/20*s**5. What is q in a(q) = 0?
-2/7, 0, 1
Let n(h) be the third derivative of -4/525*h**7 + 0*h**3 + 1/840*h**8 + 0*h**5 + 0*h**4 + 0 + 0*h + 19*h**2 + 1/75*h**6. Factor n(k).
2*k**3*(k - 2)**2/5
Let g(j) = j**2 - 1. Let w(b) = -4*b**2 - 9*b - 5. Let p(h) = -g(h) + w(h). Let c(x) = 2*x**2 + 3*x + 1. Let r(q) = -8*c(q) - 3*p(q). Factor r(d).
-(d - 4)*(d + 1)
Suppose -213*j**2 + 37*j**3 + 2*j**3 + 213 - 44*j**3 + 2*j**3 + 3*j = 0. What is j?
-71, -1, 1
Let q(x) = -80*x**5 - 325*x**4 + 55*x**3 + 55. Let t(h) = -3*h**5 - 12*h**4 + 2*h**3 + 2. Let g(z) = -2*q(z) + 55*t(z). Factor g(f).
-5*f**4*(f + 2)
Let y(r) = -17*r**3 + 7*r**2 + 6*r + 4. Let n(o) = 8*o**3 - 3*o**2 - 3*o - 2. Let m = 20 + -14. Let h(d) = m*y(d) + 13*n(d). Factor h(f).
(f - 1)*(f + 2)*(2*f + 1)
Let a(o) be the first derivative of -3*o**5/20 - o**4/2 - o**3/2 + 5*o - 3. Let g(r) be the first derivative of a(r). Factor g(n).
-3*n*(n + 1)**2
Suppose -4*f + 10 = 3*r, -5*r + 0*r - 2*f + 12 = 0. Factor a - 91 + 91 - 10*a + 3*a**r.
3*a*(a - 3)
Let a = 1535 - 1532. Let k(l) = l**3 + 6*l**2 - 8*l - 7. Let c be k(-7). Suppose 0*u**4 - 2/3*u**a + 2/3*u**5 + 0*u + 0*u**2 + c = 0. What is u?
-1, 0, 1
Let i(f) be the third derivative of 0*f**3 + 0 - 1/42*f**7 - 5/8*f**4 - 17*f**2 + 1/8*f**6 + 1/12*f**5 + 0*f. Factor i(c).
-5*c*(c - 3)*(c - 1)*(c + 1)
Let d be ((-14)/(-49))/((-4)/(-28)). Solve -3 - 15*j - 7*j**d + 6 + 9*j**2 + 6*j**4 + 25*j**2 - 21*j**3 = 0 for j.
1/2, 1
Factor 3358*l**2 + 137*l**3 - 3183*l**2 + 48*l**3 - 185*l + 5*l**4 - 180 + 0*l**4.
5*(l - 1)*(l + 1)**2*(l + 36)
Suppose -1 - 3 = -u. Suppose 2*k = u*h + 20, -h - 2*h = 12. Factor -13*m**k + 2*m + 0*m + 1 + 14*m**2.
(m + 1)**2
Suppose 568*k - 565*k - 3 = 3. Factor -4/7*b - 6/7*b**k + 0.
-2*b*(3*b + 2)/7
Let o(d) = -98*d**3 - 144*d**2 + 53*d - 17. Let l(g) = 33*g**3 + 48*g**2 - 18*g + 6. Let x(z) = 17*l(z) + 6*o(z). Determine u, given that x(u) = 0.
-2, 0, 2/9
Let q(s) be the second derivative of -5*s**7/42 + 7*s**6/6 - 4*s**5 + 5*s**4 - s + 117. Factor q(k).
-5*k**2*(k - 3)*(k - 2)**2
Let z(v) be the third derivative of v**7/105 + v**6/36 - 2*v**5/45 - v**4/9 - 61*v**2. Suppose z(t) = 0. Calculate t.
-2, -2/3, 0, 1
Let a(o) be the second derivative of -21*o**5/20 + 93*o**4/4 - 13*o**3 + o + 162. Factor a(j).
-3*j*(j - 13)*(7*j - 2)
Let k be 4/14 - 72/(-140). Let p be (-48)/36*-3 - 18/5. Factor -k*f**2 + 0 + p*f**4 - 2/5*f**3 + 0*f.
2*f**2*(f - 2)*(f + 1)/5
Let f(i) = i**3 + 5*i**2 - 8*i - 4. Let p be f(-6). Suppose 2*s + 12 = p*s. Factor 0 - 1/2*w**s - 1/2*w.
-w*(w + 1)/2
Let b(h) be the third derivative of -h**7/280 - h**6/80 + 7*h**5/80 + h**4/4 - 3*h**3/2 - 195*h**2. What is m in b(m) = 0?
-3, -2, 1, 2
Suppose 2*b - 37 - 31 = 0. Let j = -34 + b. Suppose 0*s**2 - s**3 - 5/2*s**4 + 0*s + j - 3/2*s**5 = 0. What is s?
-1, -2/3, 0
Let 47/4 - 23/2*r - 1/4*r**2 = 0. What is r?
-47, 1
Let q(z) = 4*z**2 + z. Let w(d) = 7*d**2 - 165*d + 68. Let m(b) = 3*q(b) - w(b). Suppose m(x) = 0. What is x?
-34, 2/5
What is r in -10280*r + 4998*r + 5*r**2 + 4767*r = 0?
0, 103
Suppose 7*s = 3*s. Suppose 5*b - 21 = -s*b - d, -4*d + 20 = 4*b. Determine f, given that 0*f**2 + f**2 - 6 - 9*f - b*f**2 + 0*f**2 = 0.
-2, -1
Let m(q) be the second derivative of -q**7/252 + q**6/36 + 13*q**5/120 + 7*q**4/72 + 4*q - 7. Factor m(r).
-r**2*(r - 7)*(r + 1)**2/6
Let a(f) = -3*f**3 + 5*f**3 + 13*f - 15*f**2 + 2 - 5 + 0. Let i(l) = -3*l**3 + 30*l**2 - 27*l + 7. Let y(z) = -7*a(z) - 3*i(z). Determine d so that y(d) = 0.
0, 1, 2
Let y be ((-2)/(-10))/((-36)/(-30)). Factor -2/3*r + 1/2 + y*r**2.
(r - 3)*(r - 1)/6
Let y(v) be the third derivative of -v**8/6720 - v**7/840 + v**6/80 + 13*v**5/60 - 2*v**2. Let d(s) be the third derivative of y(s). Factor d(q).
-3*(q - 1)*(q + 3)
Let g(r) = -124*r + 2854. Let y be g(23). Determine j, given that 1/7*j**y + 2/7 + 3/7*j = 0.
-2, -1
Let n(g) be the third derivative of -5/3*g**3 + 0*g + 0*g**4 + 1/1980*g**6 - 5*g**2 + 1/220*g**5 + 0. Let t(j) be the first derivative of n(j). Factor t(r).
2*r*(r + 3)/11
Let d(m) be the second derivative of 0*m**2 - 1/4*m**4 + 3/80*m**6 - 13*m + 0*m**3 + 0 + 1/112*m**7 - 9/80*m**5. Solve d(k) = 0 for k.
-4, -1, 0, 2
Let w(m) be the second derivative of m**7/70 + 3*m**6/50 - 39*m**5/100 - 7*m**4/20 + 18*m**3/5 - 6*m**2 + m + 56. Let w(q) = 0. Calculate q.
-5, -2, 1, 2
Let h(m) be the first derivative of 2*m**3/33 + 7*m**2/11 - 16*m/11 + 18. Factor h(d).
2*(d - 1)*(d + 8)/11
Let b(d) be the third derivative of 2*d**7/105 - d**6/10 - 4*d**5/15 + 2*d**4 + 169*d**2 - 2. What is q in b(q) = 0?
-2, 0, 2, 3
Let w(a) = -7*a**2 - 5*a + 6. Let j(l) = -3*l - 185*l**2 + 1 + 184*l**2 + 2*l. Let v(q) = 6*j(q) - w(q). Find s, given that v(s) = 0.
0, 1
Let p(f) = f**3 - 17*f**2 - 18*f + 3. Let y be p(18). Factor l**2 - 2*l**2 - 3*l**3 - 5*l**2 - y*l.
-3*l*(l + 1)**2
Let u(b) be the third derivative of b**8/20160 - b**7/1680 + b**5/2 - 2*b**2. Let x(j) be the third derivative of u(j). Solve x(c) = 0 for c.
0, 3
Let s(c) = c**3 + 19*c**2 + 32*c - 32. Let w be s(-17). Determine l, given that 0*l + 20/3 - 5/3*l**w = 0.
-2, 2
Let q(d) be the first derivative of -5*d**3/3 - 15*d**2 + 335. Find j, given that q(j) = 0.
-6, 0
Let t(l) = l**3 + 176*l**2 + 2684*l + 4700. Let h(j) = 177*j**2 + 2682*j + 4698. Let v(r) = -2*h(r) + 3*t(r). Let v(a) = 0. What is a?
-28, -2
Let t be 4/8*-4 - (-126)/48. Let x(z) be the second derivative of 3/16*z**5 + 1/8*z**4 - t*z**3 + 0 - 3/4*z**2 + 2*z. What is f in x(f) = 0?
-1, -2/5, 1
Let j(n) = 2*n - 6. Let m be j(-10). Let w be (39/m)/(1/(-2)). Factor 2*u**w + 2*u - u**3 - u**2 - 2*u.
u**2*(u - 1)
Solve 12/7*b**2 - 3/7*b**3 + 0 - 9/7*b = 0 for b.
0, 1, 3
Let a(c) be the third derivative of c**8/2800 + 9*c**7/1400 - c**6/600 - 9*c**5/200 + c**3 + 3*c**2 - 1. Let g(i) be the first derivative of a(i). Factor g(t).
3*t*(t - 1)*(t + 1)*(t + 9)/5
Let g(w) = 4*w**2 + 20*w + 58. Let r(k) = -k**2 - 8*k - 19. Let y(c) = -2*g(c) - 7*r(c). Let y(q) = 0. What is q?
-1, 17
Let a = 18788 - 150303/8. Find p, given that 1/8*p**2 + 0 + a*p = 0.
-1, 0
Let z(y) be the third derivative of -y**5/20 - 5*y**4/4 - 25*y**3/2 + 89*y**2. Factor z(b).
-3*(b + 5)**2
Let 130*c**2 - 950*c**2 - 227 - 26*c**4 + 4*c**5 - 34*c**4 - 214 + 332*c**3 + 864*c + 121 = 0. Calculate c.
1, 4, 5
Suppose 5*i = 9*p - 6*p - 46, -40 = -4*p - 4*i. Factor 35*k - p - 23*k + 8*k - 5*k**2 + k**2 - 4*k**3.
-4*(k - 1)**2*(k + 3)
Let q = 2445/4 + -610. Factor q*a**2 + 1/2*a + 0.
a*(5*a + 2)/4
Suppose 3*t - 104 = -t. Factor -4*j**5 - 2*j**3 + t*j**4 - 13*j**4 - 10*j**4 + 3*j**5.
-j**3*(j - 2)*(j - 1)
Suppose 16*x + 94 = 94. Let y be (-2 - -2) + (-4)/(-6). Determine i so that -y*i**3 + 2/3*i + x - 2/3*i**4 + 2/3*i**2 = 0.
-1, 0, 1
Let y(k) be the first derivative of -2*k**5/45 - k**4/54 + 16*k**3/27 + 4*k**2/9 + 2*k - 11. Let c(h) be the first derivative of y(h). Factor c(q).
-2*(q - 2)*(q + 2)*(4*q + 1)/9
Let h be 25/125*(18 - 3). What is a in 4/3 - 2*a - 7/6*a**4 - 23/3*a**2 - 11/2*a**h = 0?
-2, -1, 2/7
Factor 0 + 0*u + 3*u**2 + 3/2*u**4 + 9/2*u**3.
3*u**2*(u + 1)*(u + 2)/2
Suppose 3*t + 3*f + 3 = 0,