 g, given that 66*g - 15 + 111*g**2 - 40 - 234*g**2 + 120*g**2 - 8 = 0.
1, 21
Let m(g) be the first derivative of -43/3*g**3 + 0*g + 10 - 1/24*g**5 + 0*g**2 + 1/6*g**4 + 1/360*g**6. Let r(x) be the third derivative of m(x). Factor r(n).
(n - 4)*(n - 1)
Let q be 14/(-8)*(-630)/2205. Factor 1/2*j**3 - 4*j**2 + 4 - q*j.
(j - 8)*(j - 1)*(j + 1)/2
Let l = -57610 + 57613. Let -9/7*j + 3/7*j**2 + 9/7*j**l - 6/7 + 3/7*j**4 = 0. What is j?
-2, -1, 1
Let m(u) = -18*u + 9. Let g(f) = -53*f + 28. Let b(t) = -3*g(t) + 8*m(t). Let a be b(8). Factor -28*q + 106*q**2 - 74 - 24 - a*q**2.
-2*(q + 7)**2
Let i be 90/1*8/144*9. Suppose -i*g - 14*g**2 - 12*g**2 - g**2 - 3*g**3 + 75 = 0. What is g?
-5, 1
Find r such that -17/3*r - 1/3*r**3 + 0 - 6*r**2 = 0.
-17, -1, 0
What is v in 197/3*v**2 - 29/3*v**3 - 114 - 115/3*v + 1/3*v**4 = 0?
-1, 2, 9, 19
Suppose 1/4*k**3 + 105/4*k + 225 - 13/2*k**2 = 0. Calculate k.
-4, 15
Let c(a) be the first derivative of 28/3*a**3 + 43 + 32*a + a**4 + 28*a**2. Let c(d) = 0. What is d?
-4, -2, -1
Let o = -2 + 4. Let i(p) = -p**3 + 22*p**2 - 20*p - 15. Let j be i(21). Factor -y**o + 5*y**2 + 0*y**2 + 2*y - j*y.
4*y*(y - 1)
Let -128*d**3 + 1768*d**2 - 279*d**2 + 33*d**3 - 822*d**2 - 14*d = 0. Calculate d.
0, 2/95, 7
Let m(w) = w + 10. Let c(p) = -p**3 + 6*p**2 + 16*p - 8. Let i be c(8). Let u be m(i). Factor 7*d + d**3 - 20*d + 4*d + 10*d + u*d**2.
d*(d + 1)**2
Suppose -30*i**2 - 70*i - 1032 + 2*i + 322*i + 14*i**2 + 17*i**2 = 0. Calculate i.
-258, 4
Let p(f) be the first derivative of 4/3*f**3 - 64*f - 36 - 12*f**2. Factor p(o).
4*(o - 8)*(o + 2)
Let j be 4540/770 - 10*(-3)/(-165). Find g such that -4/7*g**4 - j + 12/7*g**2 + 52/7*g - 20/7*g**3 = 0.
-5, -2, 1
Let d = -19212/935 - -1156/55. Factor -d*n - 12/17*n**4 - 24/17*n**2 - 26/17*n**3 + 0 - 2/17*n**5.
-2*n*(n + 1)**2*(n + 2)**2/17
Let t(u) be the first derivative of -u**6/18 - 17*u**5/15 - 43*u**4/6 - 172*u**3/9 - 20*u**2 - 1353. Solve t(n) = 0 for n.
-10, -3, -2, 0
Solve 14/11*q**2 + 156/11*q + 142/11 = 0 for q.
-71/7, -1
Let q(w) be the third derivative of 0 + 2/105*w**7 - 1/6*w**4 + 0*w**3 - 1/15*w**5 + 0*w + 1/30*w**6 + 20*w**2. Let q(v) = 0. What is v?
-1, 0, 1
Let y(g) be the first derivative of -3*g**4/28 + 46*g**3 + 1941*g**2/14 + 972*g/7 - 1618. Suppose y(a) = 0. Calculate a.
-1, 324
Let k(v) be the second derivative of -29/75*v**6 + 11*v + 0 + 13/30*v**4 + 2/5*v**3 + 0*v**2 - 1/7*v**7 - 7/50*v**5. Let k(z) = 0. What is z?
-1, -3/5, 0, 2/3
Let f(q) = 4*q**2 + 89*q - 12. Let u be f(-22). Let i be 2/(-5) - (u/10 - -3). Solve 14/5*a**2 - 4/5*a + i - 6/5*a**3 = 0.
0, 1/3, 2
Let r(w) be the third derivative of -w**7/1470 - 61*w**6/840 - 1117*w**5/420 - 1881*w**4/56 - 1215*w**3/7 - 27*w**2 + 2*w. Find l, given that r(l) = 0.
-27, -5, -2
Let h(r) be the first derivative of -r**4 - 28*r**3/3 - 22*r**2 - 20*r + 410. Factor h(v).
-4*(v + 1)**2*(v + 5)
Suppose 864 = 1105*h - 1346. Solve -484/3 - 1/3*g**h - 44/3*g = 0 for g.
-22
Let k(u) be the second derivative of -u**5/240 + u**4/32 + u**3/6 + 19*u**2/2 - u + 5. Let q(r) be the first derivative of k(r). Factor q(i).
-(i - 4)*(i + 1)/4
Let u(l) = -l**3 - 145*l**2 - 2603*l + 23. Let x be u(-21). Factor 35/2*m**3 + 147/2*m**4 + 0 - 8*m**x - 2*m.
m*(3*m - 1)*(7*m + 2)**2/2
Suppose -c = -20*i + 23*i + 70, 38 = -2*i - 5*c. Let n be (-17)/(-9) - (-8)/(i/5). Suppose -2/9 + 2/9*q**2 + 2/9*q - n*q**3 = 0. What is q?
-1, 1
Factor 50*d**3 - 11 + 20*d**5 - 65*d**4 + 157061*d - 157131*d + 40*d**2 + 36.
5*(d - 1)**3*(d + 1)*(4*d - 5)
What is c in -2700*c - 204*c**2 - 291*c**3 - 2500 - 288*c**3 + 575*c**3 = 0?
-25, -1
Let d(k) = 14*k**4 - 99*k**3 - 347*k**2 + 330*k + 1647. Let v(n) = -2*n**4 - n**3 - n**2 + 2*n + 1. Let z(f) = d(f) + 9*v(f). Let z(u) = 0. Calculate u.
-23, -3, 2
Let d(r) = -r**2 + 5*r - 3. Let o be d(3). Let j = 1567 - 1565. What is t in -6*t**j - 25*t**4 - 22*t**o - 18*t**3 - 14*t**2 - 7*t**5 + 2*t**5 = 0?
-2, -1, 0
Let w(b) be the third derivative of 2*b**7/15 - 13*b**6/10 + 4*b**5/3 + 407*b**2. Factor w(m).
4*m**2*(m - 5)*(7*m - 4)
Let m(q) be the first derivative of q**3/24 - 23*q**2/4 - 485*q/8 - 149. Find a, given that m(a) = 0.
-5, 97
Let t(u) be the first derivative of -2*u**3/33 + 536*u**2/11 - 143648*u/11 + 3227. Find a such that t(a) = 0.
268
Let g(v) be the third derivative of -v**6/300 - v**5/30 + 28*v**4/15 - 196*v**3/15 - 83*v**2 + 5*v. Solve g(y) = 0.
-14, 2, 7
Factor -77/2*n + 115/3 + 1/6*n**2.
(n - 230)*(n - 1)/6
Let f(u) be the first derivative of u**3/8 + 33*u**2/4 + 180*u - 527. Determine p, given that f(p) = 0.
-24, -20
What is l in -302/11*l + 2/11*l**3 - 36/11*l**2 + 336/11 = 0?
-7, 1, 24
Let j(z) = 4*z**3 - 33*z**2 - 10*z - 2. Let r(q) = q**2 + q + 1. Let v be (16*(-1)/(-2))/(4 - 6). Let n(h) = v*r(h) - 2*j(h). Determine m so that n(m) = 0.
-1/4, 0, 8
Let l(v) be the third derivative of 49*v**5/75 + 587*v**4/60 - 2*v**3/5 + 5236*v**2. Find p, given that l(p) = 0.
-6, 1/98
Suppose -u + 2*a + 18 - 26 = 0, -4*u = 3*a - 12. Let w(o) be the third derivative of 0*o + 2/3*o**3 + 1/30*o**5 + 1/4*o**4 + u - 8*o**2. Factor w(s).
2*(s + 1)*(s + 2)
Let b(g) = -g**2 - 28*g - 189. Let m be b(-12). Let y(p) be the third derivative of 1/120*p**5 + 0 + 0*p**m + 0*p + 1/24*p**4 + 15*p**2. Factor y(h).
h*(h + 2)/2
Let y(g) be the first derivative of g**8/5880 - g**7/490 + g**6/252 + 16*g**3/3 - 41. Let i(b) be the third derivative of y(b). Find z, given that i(z) = 0.
0, 1, 5
Let u(m) be the first derivative of -2443/8*m**4 + 89 + 144*m - 25/6*m**6 + 301/4*m**5 - 5975/12*m**3 - 66*m**2. Let u(n) = 0. What is n?
-3/5, 1/4, 8
Let b be (1/(5 + -3))/((-4)/(-80)). Factor 3 - 2 - b*i - 7*i**2 + i**3 + 1 + 14.
(i - 8)*(i - 1)*(i + 2)
Let x be (-1)/(-9)*-4 - (-1584)/22032*595. Factor -6615*j + 903*j**2 + 2/3*j**4 - x*j**3 + 3087.
(j - 21)**3*(2*j - 1)/3
Suppose 4*c - 28 = -3*c. Suppose -7*a + 12 = -c*a. Factor 25*p + 32*p**2 - 89*p - 16 - 104*p**2 + 27*p**a.
(p - 2)*(3*p + 2)**3
Suppose -133 = -5*t + 107. Suppose -3*p = -d - t, p - 18 + 2 = -3*d. What is v in -4 - p*v**2 - 28*v**3 - 4 + 32*v**3 + 20*v = 0?
1, 2
Let k = -266899/33 - -8088. Let o(t) be the second derivative of -17*t - 6/11*t**2 - k*t**3 - 1/66*t**4 + 0. Determine j, given that o(j) = 0.
-3, -2
Let -994/3*a - 206/3*a**3 + 2/3*a**4 + 802/3*a**2 + 132 = 0. What is a?
1, 2, 99
Suppose -21*v - 140 = -89*v + 64. Let i(r) be the second derivative of 0*r**v + 1/12*r**4 - 1/30*r**6 + 0*r**2 + 0*r**5 + 10*r + 0. Factor i(c).
-c**2*(c - 1)*(c + 1)
Let l be (-2)/(118/20 + -6). Determine t so that -68*t**2 - 68*t**3 + 19483*t**4 + 16 - 19471*t**4 - 8*t**2 + l*t**5 = 0.
-1, 2/5, 2
Let l(o) be the second derivative of 0 + 9*o + 10125/8*o**2 + 5/48*o**4 + 75/4*o**3. Factor l(p).
5*(p + 45)**2/4
Let x(m) be the second derivative of m**5/360 + m**4/18 - 8*m**2 - 20*m + 2. Let l(h) be the first derivative of x(h). Find g, given that l(g) = 0.
-8, 0
Factor 0*t + 7/6*t**4 - 32/3*t**2 + 18*t**3 + 0.
t**2*(t + 16)*(7*t - 4)/6
Let a = 121762/3 + -608804/15. What is o in -a*o**2 + 58/5*o - 56/5 = 0?
1, 28
Let u be (2748/15)/((-18)/(-72)). Let k = u - 731. Solve 0 + 6/5*r - k*r**2 + 3/5*r**3 = 0 for r.
0, 1, 2
Let h(s) = s**2 - 116*s + 88. Let z(k) = -4*k**2 + 340*k - 264. Let d(n) = -8*h(n) - 3*z(n). Solve d(r) = 0.
1, 22
Suppose -432 - 19881*i**2 - 103823/4*i**3 - 5076*i = 0. What is i?
-12/47
Let v = 9006 - 9006. Let l(p) be the second derivative of -10/3*p**3 + 0*p**4 + 0 + 1/4*p**5 + v*p**2 - 6*p. Suppose l(z) = 0. What is z?
-2, 0, 2
Determine w so that 140/3*w**4 - 268/3*w**3 - 4/3*w**5 + 0 + 0*w + 44*w**2 = 0.
0, 1, 33
Let l be -16 - -8*(-6 + 3)/(-12). Let c be (-1 - 29/l)*28/24. Solve 17/4*g - c*g**2 - 3/2 = 0 for g.
2/5, 3
Let d(y) = 7*y**2 - 2*y. Let r(s) = 3*s + s**2 + 8*s**2 + 9*s - 14*s. Let a(w) = 5*d(w) - 4*r(w). Solve a(b) = 0 for b.
-2, 0
Let i(d) be the second derivative of -5*d**7/1512 - 7*d**6/36 - 49*d**5/10 - 21*d**4/4 + 29*d + 1. Let l(w) be the third derivative of i(w). Factor l(s).
-(5*s + 42)**2/3
Solve -152490*x + 1569/4*x**4 + 50700 + 613083/4*x**2 - 207489/4*x**3 - 3/4*x**5 = 0 for x.
1, 260
Suppose 2*j + j = -15. Let u(z) = 3*z + 18. Let v be u(j). Factor -3*t + 4*t**4 + 11*t + 4*t**2 - 5*t**4 - 67*t**v + 65*t**3.
-t*(t - 2)*(t + 2)**2
What is c in -2/5*c**3 +