5 = 2. Solve 1/3*f**3 + 3*f + t + 2*f**2 = 0.
-3, 0
Let w = 146 - 143. Factor 28*a**2 - a**3 - 38*a**2 + w*a**3.
2*a**2*(a - 5)
Let i(j) be the first derivative of -j**6/27 - 4*j**5/45 + 11*j**4/3 + 32*j**3 + 111*j**2 + 180*j - 1114. Factor i(g).
-2*(g - 10)*(g + 3)**4/9
Let k(x) = -5*x**3 + 29*x**2 + 78*x - 120. Let a(d) = 20*d**3 - 110*d**2 - 310*d + 480. Let n(g) = 4*a(g) + 15*k(g). Find i such that n(i) = 0.
-4, 2, 3
Factor -32/3*z**2 - 8*z - 2/3*z**4 - 14/3*z**3 + 0.
-2*z*(z + 2)**2*(z + 3)/3
Let n be 42/110 - (15487/(-187) + 83). Determine x so that n*x**2 + 28/5*x + 0 = 0.
-28, 0
Let c(s) = -9*s**2 + 25*s + 4. Let v(b) = 8*b**2 - 20*b - 4. Let l(g) = 4*c(g) + 5*v(g). Factor l(h).
4*(h - 1)*(h + 1)
Let r(k) be the third derivative of -k**5/150 + 31*k**4/60 - 10*k**3 - 2*k**2 + 947. Factor r(u).
-2*(u - 25)*(u - 6)/5
Let g(a) be the third derivative of -a**5/60 - 169*a**4/24 - 167*a**3/3 + 2396*a**2. Factor g(s).
-(s + 2)*(s + 167)
Determine q, given that 6237/4*q - 5929/2 - 39*q**2 + 1/4*q**3 = 0.
2, 77
Let a(z) be the second derivative of z**5/50 + 2*z**4/15 - z**3/3 - 3*z - 69. Factor a(o).
2*o*(o - 1)*(o + 5)/5
Suppose k - 5*x - 72 = 0, -2*k - k + 3*x = -216. Suppose 5*n + 55 = 2*f, 2*n = -3*f - n + k. Factor 42*h**2 - 11*h**2 - 11*h**2 - 10*h**2 - f*h**3.
-5*h**2*(5*h - 2)
Let x be (8/12)/(4/6). Let s be x + -5 - 147/(-21). Solve 187/3*v**2 - 200/3*v**s - 59/3*v + 2 + 16*v**4 = 0.
1/4, 2/3, 3
Let w(q) = -4175*q - 59. Let j be w(-2). Let -8*o**2 - 5*o**4 + o**2 - j*o**5 + 8290*o**5 + 13*o**3 = 0. What is o?
-7, 0, 1
Factor -234 - 1405/6*i - 1/6*i**2.
-(i + 1)*(i + 1404)/6
Find i, given that 1357 + 4*i**3 + 14*i**2 + 18367 + 1436 - 34*i**2 - 124*i**2 + 276*i = 0.
-10, 23
Let g(n) be the second derivative of -1/28*n**4 - 11/14*n**3 + 17 + 0*n**2 + n. Factor g(i).
-3*i*(i + 11)/7
Let p(l) be the second derivative of 1/24*l**6 + 15*l + 9/2*l**2 + 0 - 15/2*l**3 - 7/12*l**5 + 25/8*l**4. Let t(c) be the first derivative of p(c). Factor t(q).
5*(q - 3)**2*(q - 1)
Suppose 0 = -g - 2 + 10. Let a = -1888 - -1888. Factor -2*b - 15*b**2 + g*b + a*b.
-3*b*(5*b - 2)
Determine z so that -15/4*z - 99/8*z**3 - 3/8*z**5 - 39/8*z**4 + 0 - 93/8*z**2 = 0.
-10, -1, 0
Suppose 0 = 5*z + 65, -62*z + 77 = b - 70*z - 29. Determine w so that 1/6*w - 1/6*w**b + 1/3 = 0.
-1, 2
Let h(w) be the third derivative of -1/8*w**3 + 4*w - 1/48*w**5 - 1/480*w**6 + 0 + 3*w**2 - 7/96*w**4. Suppose h(v) = 0. What is v?
-3, -1
Let w be (40/(-28))/(6/(-7)) + -10 + 9. Factor w*x + 1/6*x**2 + 0.
x*(x + 4)/6
Suppose -49*w = -54*w + 20. Suppose -5*g = 4*b - 35, 5*g + 57 + 28 = w*b. Factor u**2 - 35*u**4 - 6*u**2 + 8*u**3 + 17*u**3 + b*u**5.
5*u**2*(u - 1)**2*(3*u - 1)
Let q(s) = -33*s**2 - 561*s - 600. Let z(c) = 18*c**2 + 281*c + 303. Let n(x) = -5*q(x) - 9*z(x). Factor n(m).
3*(m + 1)*(m + 91)
Let h(a) be the first derivative of -3*a**4/44 + 29*a**3/33 - 21*a**2/11 + 16*a/11 + 160. Determine l, given that h(l) = 0.
2/3, 1, 8
Solve 82/3*y**3 + 0*y + 34*y**2 - 1/6*y**5 + 29/6*y**4 + 0 = 0 for y.
-3, -2, 0, 34
Suppose 145*y - 6 = -6. Let p(f) be the first derivative of y*f**2 - 1/3*f**3 + 0*f + 17 - 1/4*f**4. Determine g, given that p(g) = 0.
-1, 0
Let l(w) be the first derivative of w**7/1120 - w**6/24 - w**5/160 + 5*w**4/8 + 2*w**3 - w**2/2 - 111. Let o(a) be the third derivative of l(a). Factor o(t).
3*(t - 20)*(t - 1)*(t + 1)/4
Let m(r) = 53*r**3 - 23*r**2 - 208*r - 6. Let h(t) = -45*t**3 + 25*t**2 + 210*t + 5. Let s(f) = -6*h(f) - 5*m(f). Determine l, given that s(l) = 0.
-4, 0, 11
Let x be 4 + -5 - (-6)/((-6)/3). Let c be (3/x)/(((-2025)/(-192))/(-25)). Suppose -8/3*f - c + 2/3*f**3 + 4/9*f**2 = 0. What is f?
-2, -2/3, 2
Determine j, given that -25*j**4 + 4*j + 95*j**2 - 12*j - 30 + 10*j**5 - 4*j - 45*j**3 + 8*j - j = 0.
-2, -1/2, 1, 3
Let s = 4436/8173 + 2/743. Let n = -694047/110 - -63097/10. Factor 0 + n*a**3 + 0*a + s*a**2.
2*a**2*(a + 3)/11
Let s(b) be the first derivative of b**7/420 - b**6/240 - b**5/30 + b**4/12 - 31*b**2/2 - b - 144. Let y(p) be the second derivative of s(p). Factor y(j).
j*(j - 2)*(j - 1)*(j + 2)/2
Let r(m) be the third derivative of m**8/48 - m**7/14 - m**6/18 + 17*m**3/6 - 303*m**2. Let z(h) be the first derivative of r(h). Factor z(u).
5*u**2*(u - 2)*(7*u + 2)
Let y = -1184755/4 + 296193. Solve -15/2 + y*i - 1/4*i**2 = 0 for i.
2, 15
Let s = 1622 + -3475. Let z = s - -1856. Factor -1/7*n + 1/7*n**z + 2/7*n**2 - 2/7.
(n - 1)*(n + 1)*(n + 2)/7
Let i(c) = -21*c**2 + 99*c - 243. Let u = -523 - -496. Let h(s) = -3*s**2 + 14*s - 35. Let l(f) = u*h(f) + 4*i(f). What is x in l(x) = 0?
3
Let q(g) be the third derivative of g**4/6 + 17*g**3/6 - 4*g**2. Let f be q(-3). Solve 4*w**f - 10*w**2 + 3*w**3 + 2*w**2 + 10*w**2 - 5*w**5 = 0 for w.
-1, 0, 2
Let s(k) be the third derivative of k**8/112 - 53*k**7/35 + 189*k**6/2 - 4655*k**5/2 + 42875*k**4/8 + 896*k**2. What is z in s(z) = 0?
0, 1, 35
Let f(a) be the third derivative of a**6/60 + 2*a**5/15 - 11*a**4/12 - 10*a**3 + 12*a**2 + 88*a. Suppose f(l) = 0. What is l?
-5, -2, 3
Factor -788*l**2 + 5472 + 1617*l + 792*l**2 - 1913*l.
4*(l - 38)*(l - 36)
Let p(z) be the first derivative of 243/5*z + 0*z**3 - 10 - 81/5*z**2 - 3/25*z**5 + 9/10*z**4. Factor p(b).
-3*(b - 3)**3*(b + 3)/5
Determine i so that -4/5*i**4 + 24*i**2 + 224/5 + 304/5*i + 4/5*i**3 = 0.
-2, 7
Let v(y) be the third derivative of y**8/1176 - 17*y**7/2205 + y**6/126 - 2*y**2 + 57. What is w in v(w) = 0?
0, 2/3, 5
Suppose 146*q = 25*q + 363. Let h(m) be the second derivative of -5/12*m**4 + 0*m**2 + 0 + 1/6*m**6 - 1/4*m**5 + 5/6*m**q - 6*m. Factor h(b).
5*b*(b - 1)**2*(b + 1)
Suppose -93/4*d**2 - 35*d - 11/2*d**3 - 1/4*d**4 - 17 = 0. What is d?
-17, -2, -1
Let a be (-9 - (-330)/30) + 2/3. Factor -32/9*s**2 - 2/9*s**4 - 14/9*s**3 + 0 - a*s.
-2*s*(s + 2)**2*(s + 3)/9
Let l(i) be the second derivative of 0 + 0*i**2 + 7/3*i**4 + 8*i**3 - 87*i + 1/5*i**5. Let l(s) = 0. What is s?
-4, -3, 0
Let n(k) be the second derivative of -4/15*k**3 + 1/105*k**7 + 2/15*k**4 + 3/50*k**5 + 0 - 4/75*k**6 + 0*k**2 + 45*k. Find b, given that n(b) = 0.
-1, 0, 1, 2
Determine l so that 2/5*l**3 + 2/5*l**2 - 4/5*l + 0 = 0.
-2, 0, 1
Suppose -3*i = k + 2*i - 2, -4*k + 8 = -3*i. Factor 10*d**2 - 5 - 10*d**2 - 15*d - 67 + 3*d**k.
3*(d - 8)*(d + 3)
Factor 342/5 - 21/5*c**2 - 129/5*c.
-3*(c - 2)*(7*c + 57)/5
Let k(v) = -2*v**2 - 20*v - 20. Let h be k(-8). Let b be (17 - 21) + 1 + 39/h. What is i in 0 + 0*i - 1/4*i**4 - b*i**3 + 0*i**2 = 0?
-1, 0
Let h = 1147861/4591428 - 1/1147857. Let 3*y + 13/4 - h*y**2 = 0. What is y?
-1, 13
Let f be 14/(-56) + ((-15)/(-12) - -1). Let -78 - 3*u**f - 172 - 182 + 72*u = 0. Calculate u.
12
Determine g, given that -7*g**3 - 2*g**3 - 35*g**4 - 128*g + 4*g**2 - 21961*g**5 + 21962*g**5 + 58*g**3 + 47*g**3 = 0.
-1, 0, 2, 32
Let o(c) be the third derivative of -2*c**7/315 - 31*c**6/90 - 2*c**5/3 + 3635*c**2. Find v, given that o(v) = 0.
-30, -1, 0
Let w(d) be the second derivative of -7*d**6/10 - 17*d**5/2 - 163*d**4/12 - 7*d**3/3 + 2*d + 141. Factor w(k).
-k*(k + 1)*(k + 7)*(21*k + 2)
Let j be (((-72)/440)/((-144)/480))/((-9)/(-66)*1). Factor -100/7*y + 0 + 10/7*y**2 + 16/7*y**3 + 2/7*y**j.
2*y*(y - 2)*(y + 5)**2/7
Let t be (-1260)/(-78) + 11 + -23 + 4/(-1). Let o(r) be the first derivative of 10 + 2/39*r**3 + 0*r**2 - t*r. Determine p, given that o(p) = 0.
-1, 1
Let d = -117 - -242. Suppose 12 = d*i - 119*i. Solve 0 - 3/2*b**i + 3/2*b = 0 for b.
0, 1
Let -1/4*f**3 - 1/4*f**2 + 13/2*f - 6 = 0. Calculate f.
-6, 1, 4
Let c(y) be the first derivative of -y**4/2 - 14*y**3 + 54*y**2 + 368*y + 8482. Factor c(g).
-2*(g - 4)*(g + 2)*(g + 23)
Suppose -4*a + 4 = -4*c, -3*c - 17*a = -15*a - 17. Let h(s) be the first derivative of 8 + 0*s - 6/5*s**2 + 2/3*s**c - 1/10*s**4. Let h(p) = 0. What is p?
0, 2, 3
Let d(b) be the second derivative of -b**5/4 + 10*b**4/3 - 55*b**3/6 - 50*b**2 - 1138*b. Solve d(n) = 0.
-1, 4, 5
Let m(c) be the second derivative of c**6/60 - 13*c**5/80 - 127*c**4/48 - 5*c**3/2 + 3253*c. Suppose m(g) = 0. Calculate g.
-5, -1/2, 0, 12
Let m = 314215 + -314203. Factor 6*l**2 + m - 162/5*l.
6*(l - 5)*(5*l - 2)/5
Let a(y) be the third derivative of -y**6/180 + 2*y**5/45 + 3*y**4/4 - 10*y**3 - 1487*y**2. Determine j so that a(j) = 0.
-5, 3, 6
Factor