1. Suppose -n*y = -6*y. Determine t so that -2/7 + 2/7*t**2 + y*t = 0.
-1, 1
Let s be 138/20 - 4/10. Let n = s - 25/6. Solve -n*a + 1/3 + 16/3*a**3 + 8/3*a**2 = 0.
-1, 1/4
Factor -370/3*k**2 - 120 + 5/3*k**3 + 725/3*k.
5*(k - 72)*(k - 1)**2/3
Factor -90 - 572*u**3 + 21*u**2 + 27*u**2 - 39*u + 569*u**3.
-3*(u - 15)*(u - 2)*(u + 1)
Suppose -25*n + 60 = -21*n. Factor -9*i - 27*i**2 - n*i**3 - 27*i - 6 + 15*i - 3*i**4.
-3*(i + 1)**3*(i + 2)
Suppose 0 = -8*n + 6*n + 4. Determine z so that -3*z**2 + 14*z + 0*z**2 - 81 + 4*z + 2*z**n = 0.
9
Let u(b) = 20*b**4 - 162*b**3 - 90*b**2 + 92*b. Let g(s) = 7*s**4 - 54*s**3 - 30*s**2 + 31*s. Let y(n) = -8*g(n) + 3*u(n). Suppose y(t) = 0. Calculate t.
-1, 0, 1/2, 14
Let f(q) be the third derivative of -7*q**2 + 0*q + 0 + 0*q**3 - 1/3*q**4 - 8/15*q**5 - 7/60*q**6. Factor f(g).
-2*g*(g + 2)*(7*g + 2)
What is y in 1/2*y - 7/4*y**2 + 0 = 0?
0, 2/7
Let g be 12*-1*(-6)/9. Let j(m) = m**2 - m + 1. Let w(s) = -12*s**2 + 16*s - 12. Let q(a) = g*j(a) + w(a). Let q(i) = 0. What is i?
1
Let a be ((-1 - -1) + -30)*(-256)/2688. Suppose 4*u - 9 - 7 = 0. Factor -66/7*q**2 - 2/7 - 32/7*q**u - a*q - 80/7*q**3.
-2*(q + 1)**2*(4*q + 1)**2/7
Let a be -1 - 1/(-4)*5. Suppose -3*t + 3*c - 6*c + 3 = 0, 0 = 3*t + 2*c - 4. Solve 0*w + 0 - 1/4*w**4 - a*w**t - 1/2*w**3 = 0.
-1, 0
Let q(a) be the third derivative of -a**8/84 - 2*a**7/21 - 2*a**6/15 + 16*a**5/15 + 16*a**4/3 + 32*a**3/3 - 289*a**2 - a. Suppose q(n) = 0. Calculate n.
-2, -1, 2
Let m(o) = o**3 + o**2 - o - 1. Let q(h) = 40*h**3 - h**2 + 1. Let l be q(1). Let j(z) = -7*z**3 - 7*z**2 + 7*z + 7. Let g(y) = l*m(y) + 5*j(y). Solve g(d) = 0.
-1, 1
Suppose -990*f + 1002*f = 24. Factor -12*t - 4/3*t**3 + 0 - 8*t**f.
-4*t*(t + 3)**2/3
Let w be 40/(-580) + (-463)/(-406). Let l(y) be the first derivative of 8 - w*y**2 + 3/28*y**4 - 1/7*y**3 - 9/7*y. Solve l(n) = 0.
-1, 3
Let d(a) be the third derivative of -a**7/420 - a**6/80 + a**5/24 + a**4/16 - a**3/3 + 60*a**2. Factor d(b).
-(b - 1)**2*(b + 1)*(b + 4)/2
Let x = 859/2940 - 5/196. Factor x*t**3 - 2/15*t - 2/15*t**5 + 0*t**2 + 0 + 0*t**4.
-2*t*(t - 1)**2*(t + 1)**2/15
Let r = -11 - -13. Suppose -m + 5 = r. Factor -m + 3 - 2*c + c**2 + c.
c*(c - 1)
Let b(m) be the third derivative of 2*m**7/735 - 3*m**6/70 + 8*m**5/105 - 85*m**2 - 1. Find h such that b(h) = 0.
0, 1, 8
Let x(g) = -13*g**2 + 13*g - 34. Let a(b) = 11*b**2 - 14*b + 34. Let o(f) = 6*a(f) + 5*x(f). Let o(l) = 0. What is l?
2, 17
Let 0 + 63/2*h + 75/4*h**2 - 1/4*h**4 + 2*h**3 = 0. Calculate h.
-3, 0, 14
Factor -3*f**3 - 1/2*f**4 + 2*f**2 + 0 + 1/2*f**5 + 4*f.
f*(f - 2)**2*(f + 1)*(f + 2)/2
Suppose t + 4*w - 4 = -0*t, 3*w - 8 = -2*t. Suppose -413*b + 419*b + 7*b**3 - 33*b**2 - 21*b**t + 41*b**3 = 0. Calculate b.
0, 2/7, 1
Let h(d) be the first derivative of d**7/280 + d**6/20 + 9*d**5/40 + d**4/2 + d**3/3 - d - 13. Let y(a) be the third derivative of h(a). Factor y(g).
3*(g + 1)**2*(g + 4)
Suppose -16*w + 0 = -32. Let l(u) be the second derivative of -4/3*u**w + 0 - 5*u - 1/30*u**5 - 5/18*u**4 - 8/9*u**3. Factor l(q).
-2*(q + 1)*(q + 2)**2/3
Let f(m) = -56*m + 4. Let y be f(-1). Let x be (80/y)/((-10)/(-9)). Let -2/5*b**5 - 4/5*b**3 + 4/5*b**2 + x*b - 6/5*b**4 + 2/5 = 0. Calculate b.
-1, 1
Let w(l) be the first derivative of l**3/6 + l**2/4 - 10*l + 118. Factor w(d).
(d - 4)*(d + 5)/2
Suppose -2*x - 8 = -6*x. Let t = -13 + 41/3. Determine c, given that t*c + 0 - 8/3*c**x = 0.
0, 1/4
Let s(f) be the second derivative of -f**6/70 - 3*f**5/28 - f**4/4 - 3*f**3/14 + 6*f + 1. Factor s(t).
-3*t*(t + 1)**2*(t + 3)/7
Let w(x) = -x**3 + 4*x**2 - 3*x + 3. Let d be w(3). Suppose h = -d*k + 15, 56 = 5*h - k - 3*k. Factor -1 + 10 + h*u - 4 + 7 + 3*u**2.
3*(u + 2)**2
Solve 0 + 30/11*g**3 + 250/11*g - 150/11*g**2 - 2/11*g**4 = 0 for g.
0, 5
Let s(n) be the first derivative of -n**3/9 + 17*n**2/6 + 384. Find j such that s(j) = 0.
0, 17
Let j = 11 - 5. Let c(b) = 5*b**2 + 3*b**2 + b**2 - 9*b**4 + 3*b**5 - 6*b**2 + 9*b**3. Let w(q) = -q**5 + q**4 - q**3. Let x(v) = j*w(v) + c(v). Factor x(g).
-3*g**2*(g - 1)*(g + 1)**2
Let q(w) be the first derivative of 0*w - 3/7*w**2 - 4/7*w**3 + 14 - 3/14*w**4. Determine v, given that q(v) = 0.
-1, 0
Solve -21/2*a**4 + 3*a**2 - 15*a**3 + 33/2*a + 15/2 - 3/2*a**5 = 0.
-5, -1, 1
Let t(r) = -r**3 - 16*r**2 - 50*r + 18. Let h be t(-12). Let v be ((-6)/h*0)/(-4). Factor -4/5*z**2 + 2/5*z**3 + v + 2/5*z.
2*z*(z - 1)**2/5
Let y = 163 + -156. Let a(z) be the second derivative of 0*z**3 + 0 + 7*z + 0*z**4 - 3/10*z**5 + 0*z**2 - 1/10*z**6 + 3/14*z**y. Let a(i) = 0. What is i?
-2/3, 0, 1
Suppose 6 + 3 = 3*p. Let w(h) = h**3 + 3*h + 4. Let s(d) = -2*d**3 - d**2 - 6*d - 7. Let u(v) = p*s(v) + 5*w(v). Factor u(t).
-(t + 1)**3
Factor 1/7*f**4 + 864/7 + 180/7*f**2 + 22/7*f**3 + 648/7*f.
(f + 4)*(f + 6)**3/7
Let l(c) = -3*c - 3. Let o(d) = 3*d + 47. Let i be o(-16). Let p be l(i). Suppose p*y + 0 + 2*y**2 - 2/3*y**3 = 0. Calculate y.
0, 3
Let x(n) = -18*n - 13*n - 11*n + 6 + 41*n. Let g be x(3). Let -2/7 + 0*s + 4/7*s**g + 6/7*s**2 = 0. What is s?
-1, 1/2
Suppose 16/5*t**3 + 64/5*t**4 + 4*t - 36/5*t**5 - 72/5*t**2 + 8/5 = 0. Calculate t.
-1, -2/9, 1
Factor 9/2*n**3 + 6*n + 39/2*n**2 + 0.
3*n*(n + 4)*(3*n + 1)/2
Let g(k) be the third derivative of -k**8/6720 + k**6/240 + k**5/60 - 2*k**4/3 + 9*k**2. Let m(w) be the second derivative of g(w). Factor m(f).
-(f - 2)*(f + 1)**2
Suppose 0*z + 2*z - 25 = -3*o, 2*o - 35 = -5*z. Factor 30*f**3 - 3*f**5 - 28*f**3 - 12*f**4 + 4*f**4 + 5*f**z + 20*f**2 - 8*f - 16.
2*(f - 2)**3*(f + 1)**2
Let l(u) be the first derivative of -u**3/7 - 69*u**2/14 + 72*u/7 + 15. Factor l(i).
-3*(i - 1)*(i + 24)/7
Determine z so that z + 2*z - 90*z**4 + 10*z**3 + 95*z**4 - 40*z**2 - 3*z = 0.
-4, 0, 2
Let h(y) be the second derivative of y**5/90 + 151*y**4/54 + 5624*y**3/27 - 5776*y**2/9 + 127*y - 2. Solve h(j) = 0 for j.
-76, 1
Let p(u) be the second derivative of 2*u**5/5 + 7*u**4 + 48*u**3 + 160*u**2 - 55*u. Factor p(c).
4*(c + 4)**2*(2*c + 5)
Let v(y) be the second derivative of y**6/10 + 33*y**5/5 + 219*y**4/2 - 506*y**3 + 1587*y**2/2 + 53*y - 2. Determine b so that v(b) = 0.
-23, 1
Suppose 37 - 373 = 2*r. Let f = 1178/7 + r. Factor f*s**2 + 2/7*s + 0.
2*s*(s + 1)/7
Let j = -1858 - -1858. Let o(c) be the second derivative of j - 8*c - 1/72*c**4 - 1/12*c**3 - 1/6*c**2. Determine x, given that o(x) = 0.
-2, -1
Let q(z) be the third derivative of 19*z - 2*z**2 + 1/20*z**5 + 3/80*z**6 - 1/224*z**8 + 0 + 0*z**3 + 0*z**7 + 0*z**4. Let q(h) = 0. Calculate h.
-1, 0, 2
Let x(c) be the second derivative of 7*c - 1/3*c**3 - 9/10*c**5 + 0 + 7/15*c**6 + 5/6*c**4 + 0*c**2 - 2/21*c**7. Factor x(a).
-2*a*(a - 1)**3*(2*a - 1)
Let v(o) be the third derivative of 3/8*o**3 + 0 + 0*o + 1/80*o**5 + 1/160*o**6 - 9*o**2 - 5/32*o**4. Determine a, given that v(a) = 0.
-3, 1
Factor -1083 - 3/4*y**2 - 57*y.
-3*(y + 38)**2/4
Suppose 0 = 4*a + 133 - 81. Let t = 13 + a. Suppose t*s - 8/7*s**3 + 0 - 4/7*s**2 - 4/7*s**4 = 0. Calculate s.
-1, 0
Let 4*f**2 + 6*f**2 + 0*f**5 - 3*f**4 - 4*f**5 + 6*f**3 - 4*f**2 - 3*f + f**5 - 3 = 0. Calculate f.
-1, 1
Let y(b) = b**3 - 12*b**2 + 13*b + 3. Let d be y(11). Find f such that -f**5 - 22*f**3 + 4 + 0*f**5 - 13*f + 7*f**4 + d*f**2 - 3*f + 3*f**3 = 0.
1, 2
Let h be (3/10)/(363/2420). Solve 0*j - 2/9*j**3 + 2/9*j**4 + 0*j**h + 0 = 0 for j.
0, 1
Let j(q) be the first derivative of -q**7/210 - q**6/90 + q**5/15 - 8*q**3 + 16. Let z(h) be the third derivative of j(h). Factor z(i).
-4*i*(i - 1)*(i + 2)
Let b(t) be the third derivative of t**9/181440 + t**8/20160 + t**7/5040 + t**6/2160 - t**5/60 + 11*t**2. Let m(v) be the third derivative of b(v). Factor m(h).
(h + 1)**3/3
Factor h**2 + 179 + 185 - 549 + 101*h + 185.
h*(h + 101)
Let v(g) = -10*g**3 + 19*g**2 - 17*g - 25. Let w(h) = -6*h**3 + 10*h**2 - 8*h - 12. Let d(s) = 4*v(s) - 7*w(s). Let d(l) = 0. What is l?
-4, -1, 2
Let p(r) = -r**2 - 4 + 7 + 0*r**2 + 5*r. Let d be p(5). Solve -12 + 19*f + 17*f - 18*f**2 - 3*f**3 + 6*f**d - 12 = 0 for f.
2
Let y = -36643/15 + 2443. Factor y*a**2 + 8/15 - 8/15*a.
2*(a - 2)**2/15
Suppose -80 = -5*z + 5*k, -2*k = 4*z + 3*k - 55. Let o be 2*4/16 - z/(-50). Factor -8/5 + 4/5*a**2 + o*a.
4*(a - 1)*(a + 2)/5
Let z(b) be the third derivative of b**4/12 - 7*b**3/2 + 21