 3*d**2. Factor h(i).
-4*(i - 1)*(i + 1)*(i + 6)
Suppose 0 = -4*h - 2 + 50, -91*y + 80 = -86*y + 5*h. Let -64/3*w - 106/9*w**3 - 8/3*w**y - 2/9*w**5 - 64/9 - 212/9*w**2 = 0. What is w?
-4, -2, -1
Let w(i) = 373*i - 6711. Let f be w(18). Let v(m) be the first derivative of 6/7*m - 1/7*m**f + 13 + 3/14*m**2. Suppose v(a) = 0. What is a?
-1, 2
Let q be 315/420*(-14)/105*-14. Suppose -1/5 + 9/10*y**3 + 9/10*y - q*y**2 - 1/5*y**4 = 0. Calculate y.
1/2, 1, 2
Let x(a) be the third derivative of -a**6/30 + 1613*a**5/15 - 2*a**2 - 3027. Factor x(n).
-4*n**2*(n - 1613)
Let t(x) = -x**2 + 3*x. Let n(y) be the first derivative of 2*y**3 - 8*y**2 - 50. Let u(a) = -2*n(a) - 14*t(a). Factor u(h).
2*h*(h - 5)
Factor 0*d + 312/19*d**2 + 2/19*d**3 + 0.
2*d**2*(d + 156)/19
Let x(k) be the first derivative of -5*k**2 - 20*k + 16. Let f be x(-2). Determine y, given that -9*y**2 + f - 5*y + 6*y**3 + 10 - y**2 - y**3 = 0.
-1, 1, 2
Let p(s) be the second derivative of s**7/630 + s**6/20 + s**4/12 + s**2 - 61*s. Let u(z) be the third derivative of p(z). Suppose u(b) = 0. What is b?
-9, 0
Factor -249*s - 28*s**5 - 924*s**4 + 1740*s**3 + 224*s**5 - 171*s**2 + 602*s - 1465*s**2 - 144 + 415*s.
4*(s - 1)**3*(7*s - 6)**2
Let m = -1024 - -1029. Let j = -1594/3 - -532. Solve -j*o**3 + 4/3*o**2 - 4/3*o**4 + 0*o + 2/3*o**m + 0 = 0.
-1, 0, 1, 2
Let w(l) be the second derivative of -21*l**5/32 - 9*l**4/4 - 39*l**3/16 - 3*l**2/8 + 901*l. Factor w(h).
-3*(h + 1)**2*(35*h + 2)/8
Let z(g) be the third derivative of g**5/30 + 5*g**4 - 288*g**3 - 14*g**2 + 240. Factor z(p).
2*(p - 12)*(p + 72)
Let v(z) = 23*z**2 + 174*z + 218. Let x be v(-6). Find r such that 2/5*r**x + 0 + 0*r - 2/5*r**4 + 3/5*r**3 = 0.
-1/2, 0, 2
Let d(t) = 4. Let b(i) = 5*i**3 + 75*i**2 - 170*i + 40. Let g(p) = -b(p) + 10*d(p). Suppose g(w) = 0. Calculate w.
-17, 0, 2
Suppose -4 = -11*g + 29. Determine m, given that 20*m + 15 + 28*m - 21*m - 1 + 12*m**2 - m**g = 0.
-1, 14
Let k be (-118)/8 + 7/(-28). Let x = 9 + k. Let a(l) = l**3 + l**2 - l. Let i(m) = 4*m**4 + 16*m**3 - 6*m. Let d(y) = x*a(y) + i(y). Factor d(r).
2*r**2*(r + 3)*(2*r - 1)
Let z(j) be the second derivative of 0*j**2 + 2*j**5 - 5/6*j**6 + 0 + 95/12*j**4 - 196*j + 5*j**3. Factor z(p).
-5*p*(p - 3)*(p + 1)*(5*p + 2)
Let g = -34 + 36. Suppose -g*a + 23 = 4*i + i, -3*i = a - 13. Suppose 265*j**2 + 253*j**3 + 320*j**5 - 105*j + 0*j - 45 + 32*j**i - 720*j**4 = 0. What is j?
-3/8, 1
Suppose r = -4*y + 9, 6 = 2*r + r + 5*y. Let t be (1 - -4)*12/(-45)*r. Suppose -2*a**2 + t*a + 7*a**2 - 5*a - 4*a**2 = 0. What is a?
0, 1
Let n(h) be the third derivative of -h**7/3780 - h**6/405 + h**5/135 + 4*h**4/27 + 43*h**3/6 + h**2 + 11. Let t(g) be the first derivative of n(g). Factor t(x).
-2*(x - 2)*(x + 2)*(x + 4)/9
Let o = 165175/23046 - 2/3841. Let z = o - -16/3. Factor -20*x - z*x**2 + 10.
-5*(x + 2)*(5*x - 2)/2
Factor -4 + 282*p**3 + 14*p**4 - 9*p**4 + 4 - 162*p**3.
5*p**3*(p + 24)
Find y such that 4*y**2 - 273 - 50*y - 158*y - 1119 = 0.
-6, 58
Let m = 40072 - 120214/3. Determine t, given that 1/12*t**4 - 4/3 + 5/4*t**2 - m*t + 2/3*t**3 = 0.
-4, -1, 1
Let m(k) be the first derivative of 25*k**4/2 - 20*k**3/3 - 51*k**2/4 - 9*k/2 - 69. Suppose m(t) = 0. Calculate t.
-3/10, 1
Let a = 981/5 - 3923/20. Let c(w) be the second derivative of a*w**5 - 1/6*w**3 + 1/60*w**6 + 35*w + 3/4*w**2 + 0 - 1/6*w**4. Factor c(i).
(i - 1)**2*(i + 1)*(i + 3)/2
Suppose a + 3*z + 6 + 10 = 0, 2*a - 3*z + 14 = 0. Let u be -20*5/a*1. Factor 2*m**3 + 18 - 18 + 16*m - 2*m**2 - u*m**2.
2*m*(m - 4)*(m - 2)
Let a = -52 - -53. Let -34*r**4 - 6*r + a + 104*r**2 + 145*r**5 + 48*r**3 - 1 - 155*r**5 + 38*r = 0. What is r?
-4, -1, -2/5, 0, 2
Let d(h) be the first derivative of 56 + 2/5*h**3 - 18/5*h - 3/20*h**4 + 3/2*h**2. Factor d(m).
-3*(m - 3)*(m - 1)*(m + 2)/5
Suppose h + 29 = 33. Suppose -h*w + 338 + 274 = 2*c, 2*w = -4*c + 312. Factor 269*m + w*m + 4*m**3 + 63*m**2 + 1029 + 20*m - m**3.
3*(m + 7)**3
Determine t so that 9*t**2 + 0*t + 0*t**3 - 1/2*t**4 - 81/2 = 0.
-3, 3
Let k(z) be the first derivative of 1/12*z**4 + 1/36*z**6 - 50 - 1/9*z**3 - 1/6*z + 1/10*z**5 - 1/4*z**2. Factor k(w).
(w - 1)*(w + 1)**4/6
Let r(c) be the third derivative of -c**6/60 - 11*c**5/30 + 25*c**4/12 - 13*c**3/3 + 2*c**2 - c - 4. Factor r(p).
-2*(p - 1)**2*(p + 13)
Suppose -4*f + 15 - 3 = 0. Suppose 0 = -f*h + 2 + 7. Let -15*b**3 - 6*b - 3*b**2 + 13*b**h + 11*b**2 = 0. Calculate b.
0, 1, 3
Let w(i) be the first derivative of -i**4/6 - 170*i**3/9 - 616*i**2 - 1176*i - 832. Suppose w(h) = 0. Calculate h.
-42, -1
Factor 680 - 132*p**3 + 296*p**3 - 1630*p + 880 - 159*p**3 + 65*p**2.
5*(p - 12)*(p - 1)*(p + 26)
Suppose 0 + 86/7*p**3 - 2/7*p**5 + 12*p**2 + 0*p + 0*p**4 = 0. What is p?
-6, -1, 0, 7
Let p(l) be the second derivative of l**6/90 - l**5/2 - 17*l**4/3 + 47*l**3/6 + l**2 - 258*l. Let h(q) be the second derivative of p(q). Factor h(x).
4*(x - 17)*(x + 2)
Let k(a) be the first derivative of -3*a**5/20 - 2*a**4 - 8*a**3 + 124*a - 73. Let s(z) be the first derivative of k(z). What is h in s(h) = 0?
-4, 0
Let s = 660567/3614897 - 193/49071. Let m = s + 2/663. Factor m*u + 2/11*u**2 + 0.
2*u*(u + 1)/11
Let r(n) = 7*n**2 + 49*n + 114. Let s(f) = 95*f**2 + 685*f + 1595. Let h = -300 + 304. Let d(c) = h*s(c) - 55*r(c). Factor d(j).
-5*(j - 11)*(j + 2)
Factor 141*m - 107*m + 6*m**3 + 154*m + 123*m**2 + 20*m + 108 + 68*m.
3*(m + 2)*(m + 18)*(2*m + 1)
Let s be -9 - (-1*8)/4. Let q(k) = -k - 5. Let y be q(s). Factor 3*l - y*l**2 + 0*l**2 - l + 6*l.
-2*l*(l - 4)
Let q(b) = b**2 - 6*b + 13. Let g = -42 + 46. Let k be q(g). Factor 25 + 106*c**2 + 58*c**3 + 373*c**5 - 372*c**k + 85*c + 13*c**4 + 0.
(c + 1)**3*(c + 5)**2
Suppose q**4 + 8*q**5 - 19270 - 88*q**3 - 3*q**4 - 122*q**2 - 11*q + 19286 - 17*q = 0. Calculate q.
-2, -1, 1/4, 4
Let k(u) = 0*u + 37*u + 14*u**2 - 48 - 3*u**2. Let o(d) = -3*d**2 - d. Let g(q) = k(q) + 5*o(q). Determine f, given that g(f) = 0.
2, 6
Let m be (3/(-10))/(1568/(-40) + 39). Find c, given that 15*c - m*c**2 - 75/2 = 0.
5
Suppose d + 28*g - 25*g + 3 = 0, 4*d + g - 10 = 0. Let w(t) be the second derivative of 3/11*t**2 - 1/66*t**4 + 17*t + 0 - 2/33*t**d. Let w(x) = 0. What is x?
-3, 1
Factor -6/5*d**2 + 596/5 - 178*d.
-2*(d + 149)*(3*d - 2)/5
Let b(g) be the second derivative of -2*g**6/75 - 6*g**5/25 + 5*g**4/3 - 12*g**3/5 + 73*g. Solve b(c) = 0.
-9, 0, 1, 2
Let g(d) be the second derivative of -5*d**7/42 + 6*d**5 + 80*d**4/3 + 40*d**3 - 2994*d. Find j, given that g(j) = 0.
-2, 0, 6
Let m(u) = -u**2 - 11*u + 21. Let v be m(-26). Let h = v - -1477/4. Suppose -5/4*g + h*g**3 + 1/2 + 3/4*g**2 - 1/4*g**4 = 0. What is g?
-2, 1
Let f(g) be the third derivative of -g**7/210 + g**6/70 + 5*g**5/84 + g**4/28 + g**2 + 925*g. Solve f(w) = 0 for w.
-1, -2/7, 0, 3
Let n(x) be the first derivative of x**4/12 - 7*x**3/2 + 56*x - 131. Let g(a) be the first derivative of n(a). Factor g(o).
o*(o - 21)
Let o(w) be the first derivative of -5*w**3/3 - 355*w**2/2 - 1020*w + 4344. Determine j so that o(j) = 0.
-68, -3
Let l = 17317 + -10370. Factor -4*v**2 - 64*v - 108*v**2 - v**5 - l*v**4 - 33*v**3 + 6961*v**4.
-v*(v - 8)**2*(v + 1)**2
Suppose 11*d - f - 6 = 7*d, 5*d - 14 = -2*f. Factor 89*a**2 + 10*a - 3*a**3 - d*a**3 - 94*a**2.
-5*a*(a - 1)*(a + 2)
Let n(f) = -8*f**2 - 64*f - 120. Let v(m) = -4*m**2 - 32*m - 60. Let y(j) = -j - 18. Let d be y(-29). Let z(p) = d*v(p) - 6*n(p). Factor z(s).
4*(s + 3)*(s + 5)
Let m(g) be the third derivative of 2*g**4 + 3*g**3 - 6*g + 0 + 13*g**2 - 3/80*g**6 - 13/40*g**5. Factor m(r).
-3*(r - 2)*(r + 6)*(3*r + 1)/2
Let u be -1*((-26)/117 - 71/(-360)). Let r(l) be the second derivative of -15*l - 2*l**2 + 1/4*l**4 + 0 - 1/3*l**3 - 1/60*l**6 + u*l**5. Solve r(v) = 0.
-2, -1, 2
Let d = -133855 + 133857. What is v in -15/7*v - 18/7*v**d + 36/7 - 3/7*v**3 = 0?
-4, -3, 1
Solve -238*q - q**2 - 32*q**2 - 1 + 22*q**3 + 14*q**4 - 26*q**4 + 13*q**4 - 183 = 0 for q.
-23, -2, -1, 4
Let g(t) = -430*t**2 + 185*t + 325. Let m(a) = -33*a**2 + 14*a + 25. Let c(j) = 3*g(j) - 40*m(j). Factor c(x).
5*(x - 1)*(6*x + 5)
Let h(n) be the first derivative of -n**5/10 - 417*n**4/16 - 11125*n**3/6 - 53457*n**2/8 - 10609*n/2 + 1726. Solve h(j) = 0.
-103, -2, -1/2
Solve 2/5*v**2 + 84872/5 + 824/5*v = 0.
-206
Factor 72 - 5