*2*(v + 1)**2
Let c(r) be the third derivative of -r**6/40 + 19*r**5/10 - 361*r**4/8 - 46*r**2 - 2. Let c(g) = 0. What is g?
0, 19
Let q be (1 + ((-28)/20)/1)*90. Let o be 3/(-4) - 27/q. Solve 1/4*l**2 + o*l + 0 = 0 for l.
0
What is l in -l**4 - 7*l**3 - 25*l**3 - 24*l**5 - 16*l**2 - 19*l**4 + 20*l**5 = 0?
-2, -1, 0
Let k(p) be the second derivative of p**4/6 + 11*p**3/5 + 46*p**2/5 + p + 453. Factor k(g).
2*(g + 2)*(5*g + 23)/5
Let i(l) = 17*l + 51. Let b be i(-3). Let h(g) be the second derivative of 6*g - 6*g**2 - 5/4*g**4 + b - 4*g**3 - 3/20*g**5. Solve h(j) = 0.
-2, -1
Let k(o) be the second derivative of -o**5/510 + o**4/68 + 13*o**2/2 - 10*o. Let x(z) be the first derivative of k(z). Solve x(p) = 0 for p.
0, 3
Let t be (12/(-10))/(22/(-55)). What is a in 2 + 35*a**3 + t + 45*a**2 + 22*a**2 + 45*a + 8*a**2 = 0?
-1, -1/7
Let l(q) be the first derivative of -q**6/180 - q**5/45 + 3*q**2/2 - 5. Let s(t) be the second derivative of l(t). What is g in s(g) = 0?
-2, 0
Let z = 25/41 + -2/205. Determine v, given that 27/5 + z*v**2 + 18/5*v = 0.
-3
Let y(u) = -u**3 - 7*u**2 - 7*u - 4. Let n be y(-6). Factor -4963*m**n + 700*m**2 - 16875*m**3 + 20 - 60 - 900*m - 2487*m**2.
-5*(15*m + 2)**3
Factor -79*q**2 + 30*q - 16*q**3 - 6*q**2 + 51*q**3.
5*q*(q - 2)*(7*q - 3)
Factor 124/9*t - 1/9*t**2 - 3844/9.
-(t - 62)**2/9
Let d(b) be the second derivative of -1/180*b**6 + 4*b + 1/60*b**5 + 5/6*b**3 + 0*b**4 + 0*b**2 + 0. Let w(z) be the second derivative of d(z). Factor w(k).
-2*k*(k - 1)
Let o = 810 + -810. Let q(m) be the third derivative of 1/48*m**3 + 1/480*m**6 - 1/1680*m**7 + 0*m**5 + o*m - 3*m**2 + 0 - 1/96*m**4. What is x in q(x) = 0?
-1, 1
Let s(o) = -25*o + 2. Let z be s(-1). Suppose j + 6 = z. Suppose -j*w + 0*w**3 - 2*w**2 + w**3 + 22*w = 0. What is w?
0, 1
Suppose 4*h = -16*h - 6*h. Let j(s) be the second derivative of -5*s - 8/5*s**2 + 16/15*s**3 + 1/3*s**4 + h. Let j(a) = 0. What is a?
-2, 2/5
Suppose 122*i - 120*i = 3*b, 0 = -i - 5*b. Suppose 0 = 5*y - 10 - 10. Find o such that -1/2*o**3 + i*o**2 + 3/4*o**5 - 1/4*o**y + 0*o + 0 = 0.
-2/3, 0, 1
Let d be -3 + (0 - 3524/(-1172)). Let u = d - -1158/2051. Factor -2/7*y + 4/7*y**3 - u*y**2 + 2/7*y**4 + 2/7 - 2/7*y**5.
-2*(y - 1)**3*(y + 1)**2/7
Let s be (-920 - -2)/(1/3 + -5). Let y = s - 195. Suppose -8/7 + y*j**2 + 4/7*j = 0. What is j?
-1, 2/3
Suppose l + 4*p + 44 = -3*l, 4*p + 16 = 0. Let c be l*(2/(-7) - 0). Factor a - a**2 - 4 + 7*a - 2*a**c.
-(a - 2)*(3*a - 2)
Let r(m) be the first derivative of -7/4*m**3 + 1/8*m**6 + 26 - 7/16*m**4 + 1/4*m**5 - m - 2*m**2. Suppose r(f) = 0. What is f?
-1, -2/3, 2
Let n be ((1/(-15))/(3/(-18)))/((-111)/(-740)). Factor 2/3*o**5 - 8/3*o**2 + 4*o**3 + 2/3*o + 0 - n*o**4.
2*o*(o - 1)**4/3
Let l(v) = -7*v**2 - 31*v - 58. Let i(q) = 48*q**2 + 216*q + 405. Let d(p) = 4*i(p) + 27*l(p). Find c, given that d(c) = 0.
-6, -3
Let p(n) be the second derivative of 7*n**4/36 - 16*n**3/3 - 14*n**2/3 - 2*n + 103. Factor p(w).
(w - 14)*(7*w + 2)/3
Let z(m) = m**4 + 25*m**3 - 46*m**2 + 38*m + 12. Let p(f) = -f**4 - 27*f**3 + 46*f**2 - 39*f - 14. Let q(k) = 6*p(k) + 7*z(k). Factor q(o).
o*(o - 2)*(o - 1)*(o + 16)
Let f(q) be the first derivative of q**7/56 + q**6/10 + 3*q**5/16 + q**4/8 + 11*q + 41. Let l(c) be the first derivative of f(c). Find n, given that l(n) = 0.
-2, -1, 0
Let w be 22/33 + (-104)/(-6). Suppose -8 = 16*g - w*g. Solve 0*o**4 - 9*o**4 + 2*o**3 - 3*o + 3*o**g + 11*o + 16*o**2 = 0 for o.
-1, -2/3, 0, 2
Let b = -52 + 33. Let n = -19 - b. Let -3/2*w**3 + n + 3/2*w + 0*w**2 = 0. What is w?
-1, 0, 1
Let j be (-3)/(-7) - 3164/7840. Let s(d) be the third derivative of -1/24*d**4 + 0 + 0*d**3 + j*d**5 - 3*d**2 + 0*d - 1/240*d**6. Let s(i) = 0. What is i?
0, 1, 2
Let f(k) be the third derivative of k**6/40 - 3*k**5/20 - 9*k**4/8 - 5*k**3/2 - 644*k**2. Suppose f(q) = 0. Calculate q.
-1, 5
Suppose 4*m + 5*i - i = 56, 0 = -m - 3*i + 22. Suppose 0 = -3*y - 2*y + m. Factor 6*q**4 - 3*q**5 + 7*q - 6*q**2 - 6*q + y*q.
-3*q*(q - 1)**3*(q + 1)
Suppose -3*o + 7*o - 712 = 5*r, -o = -5*r - 718. Let x be 58/40 + r/120. Let -x*a**3 + a**2 + 0 - a = 0. Calculate a.
0, 2
Find v, given that -144/7 - 24/7*v - 2/7*v**3 + 20/7*v**2 = 0.
-2, 6
Let p = -1892 + 13250/7. Let y be (-16)/(-21) + (-2)/(-3). Let p*m**2 + 4/7*m - y*m**3 + 0 = 0. What is m?
-2/5, 0, 1
Let t(j) be the first derivative of -j**5/70 + j**4/7 - 11*j**3/21 + 6*j**2/7 - 23*j - 21. Let n(o) be the first derivative of t(o). Factor n(x).
-2*(x - 3)*(x - 2)*(x - 1)/7
Let q(a) = -8*a**3 + 24*a**2 - 40*a - 3. Let h(s) = 95*s**3 - 290*s**2 + 480*s + 35. Let p(u) = 3*h(u) + 35*q(u). Factor p(t).
5*t*(t - 4)*(t - 2)
Let h = -3002/9 - -334. Let v(f) be the first derivative of -2 + 0*f - f**2 - h*f**3. What is c in v(c) = 0?
-3/2, 0
Let f(c) be the second derivative of c**6/80 + 51*c**5/80 + 249*c**4/32 + 77*c**3/2 + 75*c**2 + c + 98. Find v, given that f(v) = 0.
-25, -4, -1
Factor -32/5*a**2 + 4*a**3 + 0 + 0*a - 2/5*a**4.
-2*a**2*(a - 8)*(a - 2)/5
Let z(d) = 23*d**3 - d**2 + d - 1. Let c be z(1). Let x(r) = -r**2 + 22*r + 2. Let m be x(c). What is q in 0 + 0*q - 3/2*q**m = 0?
0
Let d = -533 + 1603/3. Let i(v) be the first derivative of 2/3*v**3 - 5 + 5/3*v**2 - 2/15*v**5 - 1/6*v**4 + d*v. Find j, given that i(j) = 0.
-1, 2
Let a(o) be the second derivative of -1/140*o**5 + 29*o + 1/28*o**4 + 0*o**2 + 0 + 1/294*o**7 + 0*o**3 - 1/70*o**6. Find x such that a(x) = 0.
-1, 0, 1, 3
Let g(v) = -5*v**5 + 5*v**2 + 5. Let q(m) = -m**4 - m**2 - 1. Let h(c) = g(c) + 5*q(c). Factor h(a).
-5*a**4*(a + 1)
Let a(y) = y**3 + 13*y**2 + 43*y - 8. Let k be a(-7). Let g be 4 - (3 - (-35)/k). Solve -25/3 + g*j - 1/3*j**2 = 0.
5
Let x(f) = 14*f**2 + 110*f + 1346. Let j(z) = -12*z**2 - 109*z - 1347. Let i(h) = 6*j(h) + 5*x(h). Factor i(y).
-2*(y + 26)**2
Let k(w) = -13*w**2 - 4 + 0 - 7 + 31*w. Let t(l) = 0 - l**2 - 3*l**2 - l + 5*l**2 + 1. Let c(r) = -2*k(r) - 10*t(r). Factor c(m).
4*(m - 3)*(4*m - 1)
Let l = -11 + 8. Let k = -1 - l. Factor -3*c + 20*c + 7*c - 48 - 3*c**k.
-3*(c - 4)**2
Let z(i) be the first derivative of i**6/30 + i**5/30 - i**4/12 - 4*i**2 + 10. Let y(b) be the second derivative of z(b). Let y(k) = 0. What is k?
-1, 0, 1/2
Factor 3*g + 453*g**2 - 227*g**2 - 227*g**2.
-g*(g - 3)
Let q = -22 - 1. Let w = q - -25. Suppose 1/2*a**2 + w*a + 2 = 0. What is a?
-2
Let -25/2*t**2 - 10*t + 5/2 = 0. Calculate t.
-1, 1/5
Let b(n) = -n + 6. Let x be b(3). Factor v**5 + 45*v**2 + 27*v**2 - x*v**3 - 4*v**5 - 18*v**4 - 48*v.
-3*v*(v - 1)**2*(v + 4)**2
Let l(p) = 2*p**2 + 38*p + 76. Let z(s) = -4*s**2 - 76*s - 156. Let q(v) = -5*l(v) - 2*z(v). Factor q(w).
-2*(w + 2)*(w + 17)
Suppose 21/4 + 15/4*y**2 + 39/4*y - 3/4*y**3 = 0. What is y?
-1, 7
Let w(t) be the third derivative of t**7/1400 - t**6/300 - t**5/200 + t**4/20 + 17*t**3/6 - 16*t**2. Let n(z) be the first derivative of w(z). Factor n(k).
3*(k - 2)*(k - 1)*(k + 1)/5
Let j = -377 - -3397/9. Let h = j - -1/18. Factor h*x + 1/2*x**2 - 1/2 - 1/2*x**3.
-(x - 1)**2*(x + 1)/2
Let o(z) be the first derivative of -z**3 - 6*z**2 - 42. Let o(s) = 0. What is s?
-4, 0
Let c(x) be the second derivative of 0 - 5*x - 1/2*x**3 + 0*x**2 - 1/4*x**4. Factor c(i).
-3*i*(i + 1)
Let t be (-3)/(-7) + (-55)/(-35). Let c(z) be the third derivative of 0 + 1/2*z**4 - 1/10*z**5 + 9/70*z**7 - 3/10*z**6 - 3*z**t + 1/2*z**3 + 0*z. Factor c(o).
3*(o - 1)**2*(3*o + 1)**2
Factor -159*j - 28 + 28*j**3 - 4*j**4 - 96*j**2 + 247*j + 12*j**3.
-4*(j - 7)*(j - 1)**3
Let b(g) = -3*g**5 - 11*g**4 - 10*g**3 - 5*g**2 - 3. Let r(z) = -z**5 - z**4 + z**2 + 1. Let f(j) = -2*b(j) - 6*r(j). Factor f(l).
4*l**2*(l + 1)**2*(3*l + 1)
Let j(z) = z**3 + 8*z**2 + 4*z - 11. Let x be j(-7). Find k such that -x*k**5 + k**4 - 2*k**4 + 11*k**5 = 0.
0, 1
Let j = -221738/5 - -44348. Solve -j*h**3 + 6/5*h + 4/5 + 0*h**2 = 0 for h.
-1, 2
Let j be (-6)/10 - 1*511/(-735). Let i(t) be the second derivative of 1/42*t**4 + 5*t + 0 + j*t**3 + 1/7*t**2. Find n such that i(n) = 0.
-1
Let i(v) = 13*v**2 + 34*v - 2. Let a(s) = -20*s**2 - 35*s + 3. Let f(p) = -2*a(p) - 3*i(p). Factor f(o).
o*(o - 32)
Solve -36*b**2 - 192/7 + 33/7*b**4 + 9/7*b**5 + 96*b - 120/7*b**3 = 0.
-4, 1/3, 2
Let u be 522/(-27) + 5 + 15. What is i in -1/3*i**3 - 4/3*i**2 - 5/3*i - u = 0?
-2, -1
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