- 2)**2
Let n(c) = -15*c**2 + 50*c - 45. Let i(y) be the first derivative of 8*y**3/3 - 13*y**2 + 23*y + 62. Let q(f) = -5*i(f) - 3*n(f). Suppose q(u) = 0. What is u?
2
Let l be (2/(-2))/(15/6)*-5. Solve 3*g**2 + 7*g**2 - 3*g**l + 5*g**2 + 36 - 15*g**2 - 33*g = 0 for g.
-12, 1
Let l(g) = 8*g**3 - 20*g**2 + 43*g + 145. Let a(f) = -11*f**3 + 30*f**2 - 65*f - 203. Let v(q) = 5*a(q) + 7*l(q). Factor v(r).
r*(r - 2)*(r + 12)
Suppose 30*n - 5*n**2 + 32858 - 16430 - 16428 = 0. Calculate n.
0, 6
Let o(u) be the second derivative of -1/60*u**5 - 5/36*u**4 - 2/9*u**3 - 25*u + 0*u**2 + 0. Find x, given that o(x) = 0.
-4, -1, 0
Let o(m) be the second derivative of 0*m**2 + 1/357*m**7 + 0 - 9/170*m**5 + 51*m - 2/51*m**4 + 0*m**6 + 4/17*m**3. Find q such that o(q) = 0.
-2, 0, 1, 3
Let j(u) be the third derivative of -u**5/210 - 2*u**4 + 169*u**3/21 + 3847*u**2. Determine a so that j(a) = 0.
-169, 1
Factor -5*f**2 + 3*f**2 - f + 12*f - 8*f + 6 - f**2.
-3*(f - 2)*(f + 1)
Let r(q) be the first derivative of q**6/200 + 2*q**5/75 + 7*q**4/120 + q**3/15 + 18*q**2 - 96. Let x(j) be the second derivative of r(j). Solve x(t) = 0.
-1, -2/3
Let z be 14400/241920*(-144)/(-10). Suppose z - 1/7*n**2 - 5/7*n = 0. Calculate n.
-6, 1
Let m(j) = -j**3 - j**2 + 56*j + 146. Let v be m(8). Factor 9*x**3 - v*x**2 + 12*x + 0 - 3/2*x**4.
-3*x*(x - 2)**3/2
Find r, given that 204/5*r - 288/5 - 21/5*r**2 = 0.
12/7, 8
Let r(h) be the first derivative of 4/25*h**5 - 18/5*h**2 + 0*h + 4/5*h**3 + h**4 + 90. Suppose r(c) = 0. What is c?
-3, 0, 1
Suppose 3*o + 3*c = -24, 0 = -4*o + c + 7 - 39. Let h(u) = 2*u**2 + 124*u - 134. Let a(n) = n**2 + 83*n - 89. Let w(x) = o*a(x) + 5*h(x). Factor w(y).
2*(y - 21)*(y - 1)
Find n such that 0*n**3 - 1710 - 375*n - 160*n**2 - 720*n + 3*n**3 + 2*n**3 = 0.
-3, 38
Factor -45 - 3*s - 665*s**2 + 3496*s**3 + 303*s - 3006*s**3.
5*(2*s - 1)*(7*s - 3)**2
Let r be (50 - -24)*(4 - 2). Factor -156 - 1184 - 2*w**2 + 268 - 1666 + r*w.
-2*(w - 37)**2
Solve -7/3*w**4 - 62/3*w + 22/3*w**3 + 13*w**2 + 8/3 = 0.
-2, 1/7, 1, 4
Solve 4*t**3 - 309*t**4 + 639*t**4 - 42*t**3 + 18*t**2 - 2*t**5 - 308*t**4 = 0.
0, 1, 9
Determine i so that -1201*i + 2048*i - 204*i**2 - 1207*i - 16*i**3 + 4*i**4 = 0.
-3, 0, 10
Let d(p) be the third derivative of -p**6/540 - 959*p**5/135 + 3839*p**4/108 - 640*p**3/9 - 4512*p**2. Find v such that d(v) = 0.
-1920, 1
Find k such that -1/3*k**5 + 41/3*k**3 - 448/3 + 236/3*k**2 - 4/3*k**4 + 176/3*k = 0.
-4, 1, 7
Let u(y) = -32*y**3 + 44*y**2 + 169*y + 59. Let b(c) = -11*c**3 + 15*c**2 + 56*c + 18. Let l(s) = -17*b(s) + 6*u(s). Solve l(r) = 0.
-2, -1, 24/5
Solve -10985/2*x**5 + 54080*x**4 + 213440*x**2 + 20480 - 175240*x**3 - 110080*x = 0 for x.
8/13, 4
Determine p so that -50/3*p**2 - 5/3*p**3 - 125/3*p + 0 = 0.
-5, 0
Factor 122*z - 4*z**3 - 369*z - 128*z**2 + 132*z + 128 + 119*z.
-4*(z - 1)*(z + 1)*(z + 32)
Factor 16*r**3 + 109560*r - 2185*r**2 + 5078*r**2 - 27556 - 241*r**2.
4*(r + 83)**2*(4*r - 1)
Let n(j) = 4*j**2 + 4*j - 227. Let l(q) = -3*q**2 - 7*q + 151. Let g(a) = -7*l(a) - 5*n(a). What is t in g(t) = 0?
-26, -3
Let x(m) = m**4 - 27*m**3 + 66*m**2 - 49*m + 15. Let v(s) = 3*s**4 - 79*s**3 + 195*s**2 - 149*s + 46. Let z(b) = -3*v(b) + 8*x(b). Factor z(i).
-(i - 18)*(i - 1)**3
Let w = 697 + -479. Let n = w + -215. What is m in -1/3*m**5 - 10/3*m**2 - m + 0 - 2*m**4 - 4*m**n = 0?
-3, -1, 0
Suppose 72*u - 2424 = -2280. Let d(s) be the first derivative of s**u + 14 + 2/5*s**5 + 0*s - 1/2*s**4 - 2/3*s**3. Suppose d(h) = 0. What is h?
-1, 0, 1
Let x be ((-5)/(-15))/((16/(-180))/(-4)). Let a be (-323)/(-10) - (-2 + 42/15). Solve x*d + 49/4*d**3 + 2 + a*d**2 = 0 for d.
-2, -2/7
Factor -15 - 1/6*z**2 - 23/6*z.
-(z + 5)*(z + 18)/6
Let o = -25289 - -278187/11. Factor -2/11*w**2 + 10/11 - o*w.
-2*(w - 1)*(w + 5)/11
Let m(r) be the third derivative of -r**6/30 + 3*r**5/5 - 72*r**2. Factor m(k).
-4*k**2*(k - 9)
Let z = 327197/306705 + -3/20447. Find u, given that z*u**4 + 88/15*u**3 + 36/5*u**2 + 10/3*u + 8/15 = 0.
-4, -1/2
Let q(k) be the third derivative of 3*k**5/4 - 655*k**4/6 + 290*k**3/3 - 1621*k**2. Determine j so that q(j) = 0.
2/9, 58
Let f(m) be the first derivative of -7*m**5/60 + 4*m**4/9 + 101*m**3/18 - 5*m**2 + 99*m - 136. Let n(x) be the first derivative of f(x). Factor n(z).
-(z - 5)*(z + 3)*(7*z - 2)/3
Let v(q) = -196*q**3 + 7454*q**2 + 1824*q - 2100. Let m(n) = 39*n**3 - 1493*n**2 - 365*n + 420. Let k(u) = -14*m(u) - 3*v(u). Suppose k(o) = 0. Calculate o.
-2/3, 3/7, 35
Suppose 3*o - 3*h + 70 = 241, -177 = -3*o + 5*h. Let i be 1/(-7)*0 + o/33. Solve -6/11*w**2 - 12/11 + i*w = 0 for w.
1, 2
Let -171*v**3 + 1996*v - 408 + 48075*v**4 + 201*v**3 + 324*v**3 - 48103*v**4 + 242*v**3 - 2156*v**2 = 0. Calculate v.
2/7, 1, 3, 17
Suppose -64 = -108*v + 92*v. Let h(t) be the second derivative of 14*t + 0*t**2 + 0 + 0*t**3 + 1/8*t**v. Factor h(r).
3*r**2/2
Let j(w) be the third derivative of w**7/525 - w**6/60 - 2*w**5/25 + 4*w**4/3 - 64*w**3/15 + 2721*w**2. Solve j(y) = 0.
-4, 1, 4
Factor -218/9*s**2 + 0 + 2/9*s**4 - 16/3*s**3 - 56/3*s.
2*s*(s - 28)*(s + 1)*(s + 3)/9
Let q(r) be the third derivative of 0 - 968/3*r**3 + 77*r**4 + 29/20*r**5 + 1/120*r**6 + 2*r + 16*r**2. Factor q(z).
(z - 1)*(z + 44)**2
Let t be 1/2*(0 - -1 - 1). Factor -1/6 + t*g + 1/6*g**2.
(g - 1)*(g + 1)/6
Let j(p) be the first derivative of -3*p**6/10 - 3*p**5/2 - p**4 + 4*p**3 + 74*p + 164. Let k(t) be the first derivative of j(t). Solve k(x) = 0.
-2, 0, 2/3
Let l(b) be the first derivative of -2*b**6/3 + 72*b**5/5 - 45*b**4 - 16*b**3/3 + 120*b**2 + 1998. Find o, given that l(o) = 0.
-1, 0, 2, 15
Let z be (-100)/33750*27*(3 + -8). Determine t so that 0 - z*t**3 - 12/5*t**2 - 2*t = 0.
-5, -1, 0
Let h = 4139 + -4064. Let i(a) be the first derivative of -11*a**3 - 3/4*a**4 - 105/2*a**2 - h*a + 3. Suppose i(s) = 0. What is s?
-5, -1
Let n(o) = -o**2 + 371*o - 39556. Let c(z) = -z**2 + 374*z - 39561. Let m(t) = -9*c(t) + 8*n(t). Factor m(a).
(a - 199)**2
Let v(i) be the first derivative of 3*i**5/5 + 51*i**4/4 - 20*i**3 - 54*i**2 + 1385. Solve v(t) = 0 for t.
-18, -1, 0, 2
Let m(t) be the first derivative of 1/45*t**5 + 98 - 11/36*t**4 - 13/9*t**2 + 1/54*t**6 - 29/27*t**3 - 8/9*t. Factor m(d).
(d - 4)*(d + 1)**3*(d + 2)/9
Let h(z) be the first derivative of z**5/5 + 3*z**4 + 16*z**3 + 40*z**2 + 158*z + 21. Let a(s) be the first derivative of h(s). Factor a(r).
4*(r + 2)**2*(r + 5)
Let l(v) = -v**3 + 3*v**2. Let w be l(3). Let f be (-11 - -2) + -66*182/(-1078). Let 18/7*g - 39/7*g**2 + w - f*g**3 = 0. Calculate g.
-3, 0, 2/5
Let b be (-18*6/120)/(1536/(-800)). Let a(i) be the third derivative of 1/6*i**6 + 0*i + b*i**4 + 5/24*i**3 - 9*i**2 + 0 + 1/2*i**5. Factor a(t).
5*(t + 1)*(4*t + 1)**2/4
Let c(v) = -v**2 + 17*v + 26. Let d be c(20). Let k = 36 + d. Let 10*p - 9*p - p**5 - 2*p**2 + k*p**5 + 2*p**4 - 2*p = 0. Calculate p.
-1, 0, 1
Suppose 12*n**2 - 1/10*n**3 - 234/5*n + 232/5 = 0. Calculate n.
2, 116
Suppose -5*u + 5*b = -0*b - 10, 0 = 3*u + 3*b - 18. Solve 2*x - 20*x**4 + 10*x**2 - 10*x**3 + 24*x**3 + 26*x**u = 0.
-1, -1/3, 0
Let h = -637656 - -1912969/3. Factor 4/3*k**3 - h*k**4 - 16/3*k + 0*k**2 + 16/3.
-(k - 2)**3*(k + 2)/3
Factor -2048*k - 8366*k**2 + 3*k**3 + 6812*k**2 - 21*k**3 - 680.
-2*(k + 85)*(3*k + 2)**2
Let b be 720/12 + ((-65)/(-5) - 2). Suppose -24 = -4*y + 4*a, 0*y - y + 3*a = -6. Find x such that b - y*x - 71 + 5*x**2 - 2*x**2 = 0.
0, 2
Let a(x) be the second derivative of 0*x**2 - 3/50*x**5 + 0 + 42*x + 0*x**4 + 1/5*x**3. Factor a(l).
-6*l*(l - 1)*(l + 1)/5
Suppose 6*r + 7*r - 26 = 0. Find l, given that -3*l**2 - 19 - 1 - 6 + 30*l + l**r - 2 = 0.
1, 14
Let i(m) be the third derivative of m**7/840 + 11*m**6/240 + 2*m**5/3 + 4*m**4 - 1320*m**2. Factor i(f).
f*(f + 6)*(f + 8)**2/4
Let z(r) = -r**4 - 48*r**3 + 646*r**2 + 48*r - 621. Let u(c) = c**3 + 2*c**2 - c. Let d(a) = 12*u(a) - z(a). What is j in d(j) = 0?
-69, -1, 1, 9
Factor -573/2*m + 0 - 1/2*m**2.
-m*(m + 573)/2
Find s such that 9513/8*s**2 + 1755/8 - 49/8*s**3 + 8181/8*s = 0.
-3/7, 195
Suppose 40*a - 10*a + 60 = 0. Let l be a/3*(-30)/(-20)*-2. Determine k so that 3/8*k**3 + 0*k + 0 + 9/8*k**l = 0.
-3, 0
Let z(r) = -12*r**2 + 4*r + 16. Let i be z(-6). Let y be 2/3*5/(i/(-24)). Let -y + 10/11*f**2 - 8/11*f = 0