1
Suppose 0 - 2 = -b. Solve -186 - 2*p**3 + p**4 - p**2 + 186 + b*p = 0.
-1, 0, 1, 2
Let b(s) be the first derivative of -15/2*s**2 + 1/2*s**6 - 12/5*s**5 + 6*s + 2*s**3 + 3*s**4 + 19. Find j, given that b(j) = 0.
-1, 1, 2
Let t(n) be the third derivative of 3*n**8/32 + 23*n**7/140 - 57*n**6/80 - 111*n**5/40 - 4*n**4 - 3*n**3 + 636*n**2. Find m such that t(m) = 0.
-1, -2/3, -3/7, 2
Let u(y) = 17*y**2 - 649*y - 305. Let w(d) = 26*d**2 - 973*d - 455. Let a(m) = -8*u(m) + 5*w(m). Factor a(t).
-3*(t - 55)*(2*t + 1)
Let k(q) = 26*q**4 + 12*q**3 - 44*q**2 - 26*q + 4. Let c(i) = 5*i**4 + 2*i**3 - 9*i**2 - 5*i + 1. Let g(h) = -28*c(h) + 6*k(h). Factor g(t).
4*(t - 1)*(t + 1)*(2*t + 1)**2
Let n(v) = -9*v**4 + 35*v**3 - 59*v**2 + 45*v - 13. Let l(p) = -p**4 - p**3 + p**2 + p - 1. Let x(a) = l(a) - n(a). Factor x(o).
4*(o - 1)**3*(2*o - 3)
Let s(j) be the second derivative of -j**5/80 + j**4/8 + 5*j**3/8 + j**2 - 148*j. Factor s(m).
-(m - 8)*(m + 1)**2/4
Factor 5*m**2 + 160*m**3 + 7*m**4 + 3*m**2 - m**4 - 148*m**3 + m**5.
m**2*(m + 2)**3
Let o(i) be the second derivative of i**5/90 + i**4/12 - 4*i**3/9 - 7*i**2 + 14*i. Let r(y) be the first derivative of o(y). Let r(h) = 0. What is h?
-4, 1
Let p(k) be the third derivative of k**8/2016 + k**7/315 + k**6/240 - 46*k**2 + k. Suppose p(f) = 0. What is f?
-3, -1, 0
Let r(x) be the second derivative of 1/10*x**6 + 0*x**2 - x**3 + 0 + 5/4*x**4 - 22*x - 3/5*x**5. Factor r(a).
3*a*(a - 2)*(a - 1)**2
Let p(a) be the first derivative of 8/3*a**3 - 32/5*a**5 + 0*a**2 + 0*a - 2*a**6 + 27 - 3*a**4. Solve p(v) = 0 for v.
-2, -1, 0, 1/3
Let g(y) be the third derivative of 5*y**8/336 - 20*y**7/21 + 13*y**6 + 440*y**5/3 + 1210*y**4/3 - 5*y**2 - 15. Factor g(a).
5*a*(a - 22)**2*(a + 2)**2
Factor -39/5*w**3 - 27*w**2 - 141/5*w + 3/5*w**4 - 48/5.
3*(w - 16)*(w + 1)**3/5
Let t be (1419/(-154))/43*(1 - 3). Let y(g) be the first derivative of -2/7*g**3 - t*g**2 - 1/14*g**4 - 2/7*g - 3. Factor y(u).
-2*(u + 1)**3/7
Factor 192/5*f - 4/5*f**2 - 2304/5.
-4*(f - 24)**2/5
Let b(c) be the third derivative of 0 + 8/35*c**5 - 31/210*c**6 + 2/21*c**3 - 17/84*c**4 - 3/392*c**8 + 8*c**2 + 0*c + 38/735*c**7. Factor b(q).
-2*(q - 1)**4*(9*q - 2)/7
Let r(d) = 2*d**3 + 4*d**2 + 28*d - 28. Let i(j) = 3*j**3 + 5*j**2 + 29*j - 27. Suppose -5*q + 11 + 9 = 0. Let m(l) = q*i(l) - 5*r(l). Factor m(v).
2*(v - 2)**2*(v + 4)
Let b = 1 + 1. Suppose 2*d = 4*q - 5*q - 1, -20 = -4*q + 4*d. Determine h so that 6*h**q + 12*h + 13*h**b + 5 + 2*h**4 - 1 - h**4 = 0.
-2, -1
Let b(w) be the first derivative of 22/7*w**3 + 15/28*w**4 + 69/14*w**2 + 18/7*w + 4. Solve b(n) = 0 for n.
-3, -1, -2/5
Let b(i) be the first derivative of 2*i**4/5 - 58*i**3/15 + 7*i**2/5 - 307. Determine f, given that b(f) = 0.
0, 1/4, 7
Let y(h) be the second derivative of 5*h**4/12 - 10*h**3 + h + 12. Determine m, given that y(m) = 0.
0, 12
Let n(h) be the third derivative of h**7/112 + 17*h**6/320 + 21*h**5/160 + 11*h**4/64 + h**3/8 + 14*h**2. Suppose n(a) = 0. What is a?
-1, -2/5
Let i(x) be the first derivative of x**8/1848 - x**7/1155 - x**6/220 + x**5/66 - x**4/66 + 11*x**2 - 5. Let a(p) be the second derivative of i(p). Factor a(c).
2*c*(c - 1)**3*(c + 2)/11
Factor 1/2*m**2 - 155/2*m + 0.
m*(m - 155)/2
Let c(b) = -b**3 + 273*b**2 + 1107*b - 2. Let x be c(-4). Factor 2/11*o**x + 128/11 + 32/11*o.
2*(o + 8)**2/11
Suppose p - 3 = 3*d, 2*d = -p + 32 - 34. Factor 2/5*h + p - 2/5*h**2.
-2*h*(h - 1)/5
Let m(h) be the third derivative of 1/45*h**5 + 0 + 2/27*h**3 + 0*h - 1/18*h**4 - 1/270*h**6 + 11*h**2. Determine w so that m(w) = 0.
1
Let b = -56428 + 3555101/63. Let j = b + -17/9. Solve 0*c - 2/7*c**2 + j = 0 for c.
-1, 1
Let y be (-4)/6 - (-38)/(-6). Let z(x) = -x**3 - 8*x**2 - 6*x + 7. Let k be z(y). Factor 2/3*f**5 + 0*f**4 + k*f**2 + 0 + 0*f - 2/3*f**3.
2*f**3*(f - 1)*(f + 1)/3
Suppose -2*k + 4 + 0 = 0. Suppose -4*o + 4*u = -24, 4*u = 2*o - 11 - 7. Factor -4/3*d**k + 2/3*d**o + 4/3 - 2/3*d.
2*(d - 2)*(d - 1)*(d + 1)/3
Let s = -958 - -6714/7. Let -10/7*l - s*l**2 - 4/7 - 2/7*l**3 = 0. Calculate l.
-2, -1
Let v = 21655/3 - 108221/15. Find y such that 39/5*y**2 + 3/5*y**4 - 36/5*y + 12/5 - v*y**3 = 0.
1, 2
Factor 2/13*d**2 + 0 + 102/13*d.
2*d*(d + 51)/13
Let x = -82 - -84. Let v(u) be the third derivative of 0*u - 1/630*u**7 - 1/180*u**5 + 0*u**4 + 1/180*u**6 + 9*u**x + 0*u**3 + 0. Factor v(p).
-p**2*(p - 1)**2/3
Let a(u) = 5*u - 21. Let l be a(-17). Let p = l + 108. Find h, given that 4/7*h + 2/7*h**p + 0 = 0.
-2, 0
Suppose 62 - 244 = -91*l. Suppose -3 - 1/3*g**l - 2*g = 0. Calculate g.
-3
Let g(r) = -5*r**3 - 2*r**2 + r - 18. Let f(q) = -14*q**3 - 5*q**2 + 3*q - 52. Let b(k) = 6*f(k) - 17*g(k). Let b(u) = 0. What is u?
-3, -2, 1
Factor 256*w**2 - w - 2 - 2*w - 4 - 253*w**2.
3*(w - 2)*(w + 1)
Let g(d) be the third derivative of -d**7/105 - 11*d**6/120 + d**5/3 - 7*d**4/24 + 12*d**2 + 10. Factor g(z).
-z*(z - 1)*(z + 7)*(2*z - 1)
Find w, given that 5/4*w**3 + 400*w - 1000 + 95/2*w**2 = 0.
-20, 2
Let w(m) be the second derivative of -m**7/3780 - m**6/810 + m**5/180 + 7*m**3/3 - 2*m. Let a(x) be the second derivative of w(x). Factor a(g).
-2*g*(g - 1)*(g + 3)/9
Suppose 5*o - 5*c = 170, -4*o = -0*c - 5*c - 139. Let a = o - 15. Factor 4*l**2 - 8*l + 4*l**3 - a + 16.
4*l*(l - 1)*(l + 2)
Factor 0 - 2*l**3 + 32/3*l + 1/3*l**5 + 32/3*l**2 - 5/3*l**4.
l*(l - 4)**2*(l + 1)*(l + 2)/3
Let x(n) be the first derivative of -1/3*n**4 + 0*n + 15 - 8/15*n**5 - 1/6*n**6 + 0*n**3 + 0*n**2. Let x(u) = 0. Calculate u.
-2, -2/3, 0
Let c(p) be the second derivative of -p**4/84 + 5*p**3/3 - 68*p**2/7 + 4*p + 77. Factor c(j).
-(j - 68)*(j - 2)/7
Let d(j) be the first derivative of j**6/12 - 16*j**5/15 + 19*j**4/4 - 6*j**3 - 63*j**2/4 + 54*j - 257. Let d(h) = 0. Calculate h.
-4/3, 3
Let u(r) be the third derivative of r**7/140 + r**6/16 + r**5/5 + r**4/4 - 3*r**2 - 33*r. Determine k so that u(k) = 0.
-2, -1, 0
Let x be (9/(-6))/((-9)/24). Suppose x*g - 3 + 5 = -3*b, 0 = 3*b + g - 4. Factor 7*u**2 - 3*u**b - 3*u**2 - 2*u + u**2.
2*u*(u - 1)
Let b = 5174 - 5169. Factor 1/2*l - 1/2*l**b + 0 - l**2 + l**4 + 0*l**3.
-l*(l - 1)**3*(l + 1)/2
Let y(n) be the third derivative of n**9/4536 - n**8/630 + n**7/252 - n**6/270 - 13*n**3/6 - 16*n**2. Let j(s) be the first derivative of y(s). Factor j(k).
2*k**2*(k - 2)*(k - 1)**2/3
Find v, given that 15 + 3*v - 6/5*v**2 = 0.
-5/2, 5
Suppose -54*o + 50*o = -3*v - 17, -2*o + 3*v = -7. Let -4/9*q**4 + 0 + 0*q**2 + 2/9*q**3 + 2/9*q**o + 0*q = 0. What is q?
0, 1
Let i(y) be the second derivative of -1/285*y**6 - 8*y + 0*y**3 + 0*y**2 - 1/114*y**4 + 0 + 1/95*y**5. Let i(r) = 0. What is r?
0, 1
Let h = -2182/3 - -728. Let z be ((-4)/3)/(-6*1). Factor 4/9 + h*x + z*x**2.
2*(x + 1)*(x + 2)/9
Let m(h) be the second derivative of 0 - 36*h - 12*h**2 + 4/3*h**3 + 1/6*h**4. Determine o, given that m(o) = 0.
-6, 2
Factor 157/7*w - 3/7*w**2 - 52/7.
-(w - 52)*(3*w - 1)/7
Suppose -32 = 4*h + 4. Let w(q) = -q**3 + 2*q**2 + 7*q - 4. Let b(f) = 3*f**3 - 9*f**2 - 27*f + 15. Let g(i) = h*w(i) - 2*b(i). Find x, given that g(x) = 0.
-2, 1
Let n = -11 - -18. Let h(v) = -2*v**2 + 4*v. Let k(j) be the second derivative of -j**4/3 + 4*j**3/3 + 10*j. Let r(x) = n*h(x) - 3*k(x). Solve r(z) = 0 for z.
0, 2
Let y(v) be the first derivative of 0*v - 2/15*v**3 - 3/20*v**4 + 1/5*v**5 + 0*v**2 + 39. Factor y(q).
q**2*(q - 1)*(5*q + 2)/5
Let m(p) = 2*p**3 - 16*p**2 + 17*p + 3. Let o(k) = -18*k**3 + 144*k**2 - 152*k - 26. Let l(u) = -52*m(u) - 6*o(u). Factor l(a).
4*a*(a - 7)*(a - 1)
Let q(d) be the second derivative of d**7/1980 + 23*d**6/3960 + d**5/110 + 5*d**4/3 + 18*d. Let m(w) be the third derivative of q(w). Factor m(h).
2*(h + 3)*(7*h + 2)/11
Let l(v) be the first derivative of v**5/2 - 35*v**4/8 - 377. Find a such that l(a) = 0.
0, 7
Let p = -677 - -679. Factor -4/7*l + 0 + 10/7*l**p.
2*l*(5*l - 2)/7
Suppose -3*a = 4*x + 5, -5*x + 1377*a - 1375*a = -34. Factor 10/13*o**3 + 2/13*o**2 + 8/13*o**x + 0 + 0*o.
2*o**2*(o + 1)*(4*o + 1)/13
Suppose 5*j = -2*t + 6 - 61, 0 = 5*t - 4*j + 154. Let n be t/5*(2 - (-7)/(-3)). Factor -2/3*f + 2/3*f**n - 4/3.
2*(f - 2)*(f + 1)/3
Let q(l) be the second derivative of -l**6/720 + l**5/120 - l**3/9 - 5*l**2/2 - 2*l. Let w(a) be the first derivative of q(a). Factor w(f).
-(f 